regular waves are investigated for input frequencies and strokes corresponding to wavelengths .... of the range of interest, except the largest wave steepnesses.
IIHR TOWING-TANK WAVEMAKER Joe Longo, Shin-Hyung Rhee, Dave Kuhl, Bryson Metcalf, Rebecca Rose, and Fred Stern Iowa Institute of Hydraulic Research The University of Iowa Iowa City, IA 52242
ABSTRACT A description is provided of the acquisition and calibration of a plunger wavemaker for the Iowa Institute of Hydraulic Research 100x3.048x3.048 m towing tank. The calibration procedure determines the wavemaker response function, i.e., nature of generated waves over range of single (regular waves) or multiple (irregular waves) input plunger frequencies, strokes, and phase angles. Capacitance wires are used to measure wave time histories, which are analyzed (using average wave crests and troughs, Fast Fourier Transforms, and Fourier series) for evaluation of wave amplitudes and frequencies. Only regular waves are investigated for input frequencies and strokes corresponding to wavelengths 0.5-6.0 m and steepnesses 0.025-0.3. The uncertainty assessment methodology follows the AIAA Standard S-071-1995. The results indicate that the primary frequency wave frequency response is equal to the input wavemaker frequency within the uncertainty in the data and analysis, i.e., 1-3% for low-high frequency, whereas the primary frequency wave amplitude significantly exceeds the wavemaker stroke for most wavelengths and steepnesses. The wavemaker meets the design requirements and limits. The response function is less than the theoretical prediction used in its design. The uncertainty in the wave-elevation measurement is small compared to the magnitude and trends of the primary frequency amplitude response such that the magnitudes and trends exhibited are much larger than the noise. The sub-frequency amplitudes are small, except for small wavelength and steepness. The super-frequency amplitudes are also small, but do show the trend of increasing with wave steepness and correlate with second-order Stokes wave theory. The uncertainty in the wave-elevation measurement is large compared to the magnitude and trends of the sub and super-frequency amplitude responses such that only the largest values and trends are larger than the noise. The effects of sidewalls are significant for wavelengths less than the tank width (520% for λ=3-1.5 m). Similarly the effects of attenuation/amplification with propagation distance are significant (10%), but more testing is needed. The uncertainty in the wave-elevation measurement is medium/large compared to the magnitude and trends of
the sidewalls and attenuation/amplification with propagation distance such that the magnitude and trends exhibited are somewhat larger than the noise. The plunger motion frequency is equal to the input frequency within the uncertainty in the data and analysis, whereas the amplitude differs from the input stroke by ±5%. The uncertainty in the plunger motion measurement is small compared to its magnitude and trends such that the magnitude and trends exhibited are larger than the noise. 1 Introduction The Iowa Institute of Hydraulic Research (IIHR) has been active in procurement of towing-tank data for validation of Reynolds-averaged Navier-Stokes (RANS) simulations and explication of flow physics for modelscale surface ship resistance and propulsion. Previous work has been for calm-water conditions using the Series 60 cargo/container hull form (Toda et al., 1992; Longo et al., 1993; Longo and Stern, 1996). The results have been used extensively for validation of steady RANS methods, including selection as test cases for the CFD Workshop Tokyo (1994) and adoption by the International Towing Tank Conference (ITTC) as recommended benchmarks for Computational Fluid Dynamics (CFD) validation for resistance and propulsion (ITTC, 1996). Present interest is for more modern hull forms and procurement of data for validation of unsteady RANS methods. For this purpose, tests will be conducted for a naval combatant geometry [i.e., David Taylor Model Basin (DTMB) model 5512] in regular head waves. DTMB model 5512 is a 3.048-m geosym of DTMB model 5415, which is also adopted by the ITTC as a recommended benchmark and is currently the subject of an international collaborative project between IIHR, Istituto Nazionale per Studi ed Esperienze di Architettura Navale (INSEAN), and DTMB on complementary experimental fluid dynamics (EFD)/CFD and uncertainty assessment. The tests in regular head waves require the acquisition, installation, and calibration of a wavemaker for the IIHR towing tank, which is the subject of this paper. A companion paper at this conference, provides results from steady-flow resistance, sinkage and trim, wave profile, and nominal wake tests and uncertainty assessment for DTMB model 5512 (Longo and Stern, 1998).
A plunger wavemaker (2:1 wedge-shape, scotch yoke and pulleys, motor, and control panel) was designed, installed, and calibrated by Professor L. Landweber for the IIHR towing tank (Landweber, 1967). Subsequently, it was used for several projects; however, by 1990, it had not been used for many years and in view of the extensive restoration required it was removed from the tank. Therefore, in planning the present project, it was decided to consider both the previous design and contemporary commercial alternatives. Specifications were developed based on the wave conditions for the planned tests for 5512 in regular head waves (Table 1) and future tests for irregular waves, which were used to evaluate the previous design and for solicitation of commercial alternatives. The planned tests include wavelengths of 0.5L, L, and 1.5 L (where L is the length between perpendiculars of 5512) and steepnesses from 0.031-0.157. The smaller and larger wave steepness values correspond to the linear and nonlinear regimes for typical seakeeping tests. The larger wavelength and steepness values correspond to high sea states (i.e., 5-7). Evaluation of the previous design revealed several limitations, including restricted wavelengths, amplitudes, and form (i.e., irregular waves could not be generated). Improvements required substantial reengineering. Proposals were submitted by MTS Systems Corporation and Fuchs, Regas, & Yao, Inc. (FRY), which both met the specifications. The MTS design featured a piston-type wave board, steel frame, electric servo drive, control system, and personal computer (PC) with capability for large range of regular and irregular waves. The FRY design is based on the wind-wave facility at the Ocean Engineering Laboratory (OEL), University of California Santa Barbara, which was designed by Professor M. Tulin (Waseda, 1995). The FRY design featured a plunger, steel frame, hydraulic drive system, control system, and PC. Both designs have capability for a large range of regular and irregular waves. Primarily for cost considerations, the FRY design was selected. The design, assembly, and installation were done in four parts (Regas, 1996): plunger face shape; structural components; actuator; and controls. The manufacturing of the structural components and installation were organized and completed, respectively, by IIHR. The design, assembly, and installation were completed in early 1997; however, the calibration was delayed due to other uses of the towing tank. Also, an end-wall beach was designed and installed by IIHR to minimize wave reflection and time interval between tests. The following sections provide descriptions of the IIHR plunger wavemaker, calibration test design, waveelevation measurement system and procedures, uncertainty assessment, plunger wavemaker theory, results, and concluding remarks. Appendices A and B
provide operating procedures and details of the design of the end-wall beach, respectively. 2 IIHR Plunger Wavemaker The IIHR plunger wavemaker is shown in Figure 1. The wavemaker was installed at the north end wall of the IIHR 100x3.048x3.048 m towing tank. The end-wall beach was installed at the south end. In previous tests without the wavemaker, the towing tank water level was 39.37 cm below the carriage rails. Sidewall beaches were installed for wave dampening, which enabled 10 minute time intervals between tests. However, for tests with the wavemaker, the towing tank water level must be reduced to 60.96 cm below the carriage rails to provide space for the wave crests to travel unobstructed. Currently, there are no sidewall beaches to aid in wave dampening, which limits the time interval between tests to 40 minutes. The plunger face shape is derived theoretically for improved response function (e.g., in comparison to wedge shape) with capability for large range of regular and irregular waves. The plunger face is constructed from four fiber-glass covered foam panels. The structural components include the plunger body, ram support frame, and false end wall. The plunger body is a tubular-aluminum space frame construction weighing 1200 lbs. In the home position, the buoyant force on the plunger is 4900 lb, and the recommended draft is 65 cm. The plunger spans the width of the tank with 1.5 cm sidewall clearance. A steel ram support frame spans the width of the tank and is anchored to the upper concrete deck of the towing tank walls. At its center, a hydraulic ram is secured in the vertical plane and connected to the plunger. The plunger moves in the vertical plane on linear motion roller bearings that are attached to the ram support frame. A false end wall fabricated from 0.635 cm stainless-steel plate is spaced 30.48 cm from the back of the plunger, spans the tank, and extends 183 cm downward from the free surface. The actuator is the hydraulic unit and ram. The hydraulic unit consists of a 60-gallon oil reservoir, 30-hp motor linked to a variable-volume piston pump, two-stage filter system, safety-relief valve, and bladder accumulator for pressure regulation in the working lines. The hydraulic unit operates at 3000 psi and has a relief valve set at 3400 psi. A two-stage coolant system and heater are integrated with the hydraulic unit to regulate the temperature of the hydraulic fluid. A small and large heat exchanger is supplied water from behind the false end wall via a one-hp pump to remove heat from the system and an electric heater is used on the oil reservoir to add heat to the system when required. Mechanical thermostats control a valve to the large heat exchanger and heater for increased flow or added heat, respectively.
The operating temperature of the hydraulic unit is 110 °F, which is set by adjusting the thermostats and flow rates to the heat exchangers. Two working lines, one each for the upstroke and downstroke of the ram, are installed between the hydraulic unit and a solenoid-controlled servo valve atop the ram. The servo valve receives waveform data from the computer/controller and a position transducer located near the servo valve returns plunger position data to the computer/controller. The servo valve is capable of position resolutions up to 0.0254 mm. The hydraulic ram links the plunger body and ram support frame and provides 30.5 cm of peak-to-peak vertical movement of the plunger body. The controls consist of a programmable motion controller, PC, and software. The programmable motion controller is a MTS XDC700. The XDC700 controls the servo valve for the hydraulic ram to make the plunger motion follow the input waveform. The controller is programmed as a closed loop, position feedback system that updates the position of the plunger at a rate of 200 Hz. The feedback loop is tuned for the up and downstroke of the ram so that the system is neither under or overdamped. Tuning the loop is an iterative procedure whereby three variables are set in the controller, and the response to a step input is graphed and analyzed. Figure 2 shows conditions for the upstroke of the plunger when the system is overdamped, underdamped, and optimally tuned. When the controller is powered on, it is initialized by downloading software from the PC into the controllers memory which is required to complete three tasks: (1) initialization of over sixty variables, i.e., variables that govern the maximum and minimum travel of the ram, resolution of the servo valve, maximum velocity and acceleration of the plunger, home position of the plunger, etc.; (2) drive the plunger to its recommended draft; and (3) put the system in a ready-state where it waits for digital waveform input from the PC. Input waveforms are constructed in software with Labview Virtual Instruments (VI) and saved as files. The inputs include plunger-stroke amplitude, frequency, and phase. Multiple sets of inputs can be superimposed to create irregular waves. Control of the waveform, i.e., choosing a specific waveform, downloading the input to the controller, and stopping execution of the input is controlled at the PC. 3 Calibration Test Design The calibration procedure determines the wavemaker response function, i.e., nature of generated waves over range of single (regular waves) or multiple (irregular waves) input plunger frequencies, strokes, and phase angles. Capacitance wires are used to measure wave time histories, which are analyzed [using average wave crests and troughs, Fast Fourier Transforms (FFT), and Fourier series (FS)] for evaluation of wave amplitudes and
frequencies. Data is procured simultaneously using two wires positioned at the same distance from the wavemaker and with wire 1 on the tank centerline and wire 2 offset transversely half the distance to the east sidewall. Only regular waves are investigated for input frequencies and strokes corresponding to wavelengths 0.5-6.0 m and steepnesses 0.025-0.3, as shown in Table 2. In Table 2, the wavelength λ and number k (=2π/λ) are obtained using the progressive wave dispersion relationship (given later in discussion of plunger wavemaker theory) and the wave steepness is estimated by sk. The cases completed thus far are shown in bold in Table 2, which cover most of the range of interest, except the largest wave steepnesses. The uncertainty assessment methodology follows the AIAA Standard S-071-1995. The primary frequency response is evaluated and compared with the design requirements and limits, the plunger wavemaker theory (used in designing the wavemaker) and predicted design performance, and the OEL wavemaker response function. The sub- and superfrequency responses are evaluated and compared with second-order Stokes wave theory. The effects of sidewalls (i.e., cross-tank asymmetry) and attenuation/amplification with propagation distance are also studied. Cross-tank asymmetry is determined by comparing the data from wires 1 and 2. Attenuation/amplification is determined by comparing the data from wires 1 and 2 for the same wave conditions, but at various distances from the wavemaker (Table 2). Some limited tests are done to confirm the plunger motion, i.e., frequency and stroke using a potentiometer (Table 2). The calibration test design is based in part on the description of the OEL wavemaker (Waseda, 1995) and FRY wavemaker calibration instructions and example (Regas, 1997). 4 Measurement Systems and Procedures The same measurement system is used for wave elevations and plunger motion: two sensors (either wires 1 and 2 or wire 1 and a potentiometer); two signal conditioners; and carriage PC with 12-bit, 16-channel AD card and post-processing software. The instrumentation was mounted to the north trailer, which facilitated use of the carriage PC and positioning of the probes for evaluation of the effects of sidewalls and attenuation/amplification with propagation distance. A Cartesian coordinate system is adopted with the origin at the intersection of the undisturbed free surface, towing-tank centerplane, and plunger face at the home position. x is positive in the direction of wave propagation. z is positive upward. y is positive in the transverse direction towards the east sidewall. Most of the data is taken with wires 1 and 2 at x=10 m, y =(0.0,
0.75) m, respectively, and z=0. Limited data is also taken for x=(25, 40) m and the same (y, z) locations. Wave Elevation. The purpose of the wave elevation test is to procure time histories of wave elevations z in time interval ∆t. The measurement system consists of two capacitance-wire probes and signal conditioners and the carriage PC with AD card for data sampling. The signal conditioners (digital interfaces) were developed at IIHR for making high-resolution, low-noise capacitance-wire wave elevation measurements (Houser et al., 1989). The interface converts water surface elevation (capacitance change) into an analog voltage. The probe consists of a 0.25 mm copper core, 0.025 mm Teflon insulation capacitance wire stretched and held taut in a stainlesssteel support. The probe is electrically connected to the interface with a low-capacitance coaxial cable, with the center wire connected to the sensor wire and the shield connected to the probe support. The probes are fixed to automated traverses in the vertical plane for calibration. The sampled voltages are scaled to length (elevation) units with equation (1): z ( t ) = a 1V ( t ) 2 + a 2 V ( t ) + a 3
(1)
where t is time in seconds, z(t) is wave elevation (cm), V(t) are elevation voltages, and a1-3 are second-order polynomial linear regression (i.e., the polynomial coefficients are not functions of the independent variable) calibration coefficients. An end-to-end calibration is used for the waveelevation test before and after data procurement. The probes, interfaces, and carriage PC AD card are statically calibrated to determine the voltage-elevation relationship. Starting and ending from zero elevation, the calibration is conducted by simulating a range of wave heights while moving the probes up and down about a reference position. Data is sampled at 500 Hz for 4 seconds for each elevation and statistically analyzed, (i.e., average, standard deviation, minimums, maximums, and number of outliers, which are identified and deleted using Chauvenet’s criterion). The two data average values for each elevation increment are averaged, except for the maximum and minimum elevation for which there is only one value. The voltage-elevation relationship appears linear (Figure 3) but repeated curve-fitting tests indicate that a second-order polynomial linear regression curve fit produces the best fit. The curve fit is used to determine the coefficients of the regression equation (a1, 2, 3), which are then used to convert voltage to elevation. The repeatability of the calibration between data procurement cycles is monitored. Data acquisition is done in two steps as shown in Figure 4: (1) voltage from the interfaces is sampled; and
(2) AD conversion in carriage PC. Data is sampled at 135 Hz using 2 channels for 60 seconds (i.e., 4096 samples per channel). Calm-water data is used for the zeroreference value. Data reduction and/or calibration are done two times: (1) AD card output is statistically analyzed; and (2) the wave-elevation time history is converted to cm using the voltage-elevation calibration. Plunger Motion. Limited tests, identified in Table 2, are undertaken to measure the motion of the plunger for one frequency f=0.721 Hz and three wave steepnesses Ak=0.050, 0.100, and 0.150. For these tests, a linearmotion potentiometer with 15 cm range is substituted for the second sensor near the tank sidewall so that wave elevation and plunger motion data can be sampled simultaneously. The potentiometer is fastened to the ram support in the vertical plane with the core half extended and in contact with the frame of the plunger. 5 Uncertainty Assessment The 95% confidence large-sample uncertainty assessment approach is used as recommended by the AIAA Standard (1995) for the vast majority of engineering tests. The approach is derived and explained in detail by Coleman and Steele (1995). The uncertainty assessment is completed for both the wave-elevation and plunger-motion measurement systems. A summary of the results is provided in Table 3. For both measurement systems, bias errors are associated with: (1) the calibration standard; (2) the second-order polynomial linear regression curve fit to the capacitance-wire and potentiometer calibrations; and (3) the installation of the wires/potentiometer. For the first, the calibration standard is the motors/traverses that move the wires/potentiometer up and down in the calibration. This system has a resolution of 6.35e-03 mm. For the second, bias error is introduced from approximating a calibration data set with a curve. The scatter in the data with respect to the curve fit is quantified with the standard error of estimate (SEE) which is a 95% confidence interval on the curvefit. Lastly, the installation of the wires/potentiometer can influence measurement quality if care is not taken to insure that the wires/potentiometer are installed in the vertical plane. Typically, this error source is negligible because the measurement error is proportional to the angle (π, i.e., for h=3 m, λ2.5, IIHR shows a similar trend and is fairly close to Yao (1992), although all values are less than the theory. For λ
