Department of Mechanical Engineering Massachusetts Institute of Technology 2.20 Marine Hydrodynamics, Fall 2015 Laboratory Assignment Assigned: Wednesday, November 20, 2015 Lab time: Monday, 11/23/2015 and Tuesday, 11/24/2015 Report Due: Thursday, December 10, 2015 The laboratory assignment requires that you do the following: 1. Read through the details of the lab. 2. Perform the Pre-Lab exercise. 3. Perform the experiment at the time you have signed up. 4. Write a lab report, which is due Tuesday, December 10, 2015. Although the experiments are performed in a group effort, the lab report should be individual. The lab report is expected to be type-written, complete yet concise. 1 SURFACE WAVE KINEMATICS AND WAVE INDUCED MOTIONS The laboratory will be performed on Monday (11/23/2015) and Tuesday (11/24/2015) at the Towing Tank, Room 48-015, x3-4348 during the time slots for which you have signed up. Reports are to be done individually and are due before the lecture on Thursday, December 10, 2015. Introduction This lab is designed to familiarize you with some of the test capabilities of the Towing Tank, and help you understand important concepts related to two important phenomena in marine hydrodynamics: dispersive surface water waves and wave induced motions. In this lab, you are asked to make quantitative measurements of surface wave phase and group speed as a function of wave frequency, and to observe the dispersion phenomenon of surface waves. You will have to make quantitative analysis of the response of a inverted pendulum in waves. You will also observe the phenomenon of vortex-induced vibrations (VIV) of a cylinder phenomenon and its suppression. Pre-Lab Preparations Write a “pre-lab” report of the following pre-lab preparations before the lab. In your final lab report you should include a copy of your “pre-lab” (in addition to the one turned in on the day of the lab) along with a short paragraph that discusses the lab preparation. (Time spent here will certainly save you many times the effort during and after the lab!) 1. Read through the entire lab assignment carefully so that you have a clear idea of what has to be accomplished. Be familiar with the expected results and calculations so that you can repeat suspicious measurements or reject spurious data (during the lab). 2. Understand the physical meaning of basic wave properties such as wave length, wave number, period, frequency, phase velocity, group velocity, dispersion relation, etc. You need to choose three different water depths corresponding to shallow, intermediate, and deep water. Make plots of the: wave length as a function of frequency (dispersion relation); phase velocity as a function of frequency; and group velocity as a function of frequency for these three different water depths. Discuss how does the water depth affect the wavelength, phase velocity, group velocity for given frequency? 2 3. Find the response of a simple harmonic oscillator with harmonic forcing F = F0 cos ωt, i.e. find the solution x = X0 cos(ωt + φ) of: M ẍ + B ẋ + Kx = F0 cos ωt (1) (i) Find the expression of X0 . (ii) Discuss how will the response amplitude X0 be affected by M, B, K and F0 ? (iii) If F = 0, how could damping B be determined from measurements of the motion? 4. Apply the approach in part(3) to the problem of an inverted pendulum: a long buoyant cylinder moored to the bottom by a wire, as shown in Figure 1. For this case, (i)Calculate corresponding M , K, and F0 ( in terms of the pendulum geometry). (ii) Discuss the possible sources of damping for this pendulum. (iii) What non-dimensional quantities govern these problems? 5. Think through and plan the lab with the other group members. Prepare an action plan for the lab and tables or graphs to roughly plot the data you anticipate. Be prepared to discuss with the lab staff your action plan when you enter the lab. 3 LABORATORY ASSIGNMENT Objectives: The specific objectives of this laboratory assignment are to: • Measure the frequency, wavelength, phase velocity, and group velocity of various waves generated by the wavemaker. • Observe the phenomenon of long wave overtaking short wave due to dispersion effect. • Measure the natural frequency of an inverted pendulum in calm water. • Measure the forced response of the inverted pendulum in waves. • Observe the VIV phenomenon and suppression of VIV using hand-towed cylinders. Equipment: The towing tank is a long rectangular basin of water, 35m x 2.5m x 1.5m. At one end of the tank there is a wave-maker and at the other end there is absorbing “beach”. The wave-maker is a hydraulically driven vertical paddle with controllable amplitude and frequency. The “beach” is a region of absorbing material intended to prevent the reflecting of waves from this end of the tank. Measurements: The TA will provide instructions for the operation of the wavemaker. Please follow his instructions. Detailed descriptions how to perform the measurements will be given during the exercise. 1. Part I: Surface Wave Kinematics (a) Measure the water depth in the tank. (b) Calibrate wave probes. (c) Generate a regular wave using wavemaker and measure the wave period, length, phase velocity and group velocity. Repeat this for 5 different frequencies. (d) Generate a wave consisting of a short wave followed by a long wave and observe the difference between the wave passing a location near the wavemaker and that for a location far away from the wavemaker. 2. Part II: Wave-Induced Motion We will study the motion of an inverted pendulum in waves. Waves have amplitude A, wave-length λ and angular frequency ω. 4 The inverted pendulum consists of a buoyant horizontal circular cylinder connected with a wire (at each end) to the bottom of the tank. The ratio of the length and the diameter of the cylinder is very large so that the cylinder is assumed to be a slender body. The sketch of the setup is shown on Figure 1. not to scale λ, A SWL R m h L wall wall bottom Figure 1: Inverted pendulum setup. (a) Measure the length of the pendulum. Measure the mass, radius and length of the cylinder. (b) Give the pendulum an initial displacement in calm water and then release. Measure the natural frequency and the response (angular deflection θ) of the pendulum. (c) Measure the forced response (angular deflection θ) of the system in 3 waves with different frequencies. Be sure to note the wave height at each frequency for normalization in the post-lab exercise. (d) For each frequency, observe the wave pattern as the wave passes by the pendulum. Do you notice any changes due to the presence and motion of the pendulum? 3. Part III: Vortex-Induced Vibration (a) Tow a hand-held bare cylinder through the water at several different speeds to feel and observe the VIV motion of the cylinder. How does the frequency of the motion of the cylinder vary with the forward speed you move it? 5 Post-Lab Exercise (To be done individually) Note that the final results you present in your lab report must be in non-dimensional form. Tables and graphical plots should be used. The lab report should include a copy of your pre-lab preparation, the specific procedure of your group’s experiment, data analysis, and a discussion of your results. The following results must be analyzed and discussed in your lab report. In addition, you are encouraged to discuss other hydrodynamic aspects you have observed in the experiments. Any novel idea and insightful discussion will be given extra credit in the lab grade. 1. Plot the wave length, phase velocity, and group velocity as functions of frequency. Compare your results with theory and discuss. 2. For the pendulum experiment in calm water, obtain the natural frequency of the pendulum and the added mass of the cylinder based on the measurements. Compare both results to the theoretical predictions and try to explain the difference. Plot the measured response θ as a function of time and calculate the damping of the system. Discuss the possible sources of damping. 3. For the induced wave motion experiment, plot the non-dimensional response amplitude operators (RAOs) Lθ/A as a function of non-dimensional frequency. Discuss the results. Is there a resonant peak? 4. Compare the obtained responses (RAOs) by measurement of the inverted pendulum with theoretical predictions for long waves. In order to get theoretical solution, you can use Froude-Krylov approximation to calculate the wave force. For the damping, you can use the result of measurement. The lab report should be written in a professional way. It should be type-written and should have been edited for grammatical and spelling errors. Although it needs to be complete, conciseness is also emphasized. Unnecessary length will be regarded as a negative factor in the lab grading. 6