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About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as FORCES, MOMENT AND WAVE PATTERN FOR NAVAL COMBATANT IN REGULAR HEAD WAVES 46 Forces, Moment and Wave Pattern for Naval Combatant in Regular Head Waves L.Gui, J.Longo, B.Metcalf, J.Shao, and F.Stern Iowa Institute of Hydraulic Research (IIHR), The University of Iowa Iowa City, IA 52242, USA ABSTRACT A model-scale naval surface combatant, DTMB 5512, is studied experimentally in steady forward speed and regular head waves with the Iowa Institute of Hydraulic Research (IIHR) towing tank facilities. Unsteady resistance, heave force, pitch moment and free-surface elevations are investigated with different measurement systems for a fairly wide range of test conditions. Test data is procured for validation of RANS CFD codes and for understanding the physics of unsteady ship hydrodynamics. Uncertainty assessments are completed following the AIAA Standard. The results and discussions for the forces and moment cover the time mean values, added resistance and linear and non-linear responses. Results of free surface elevation tests include reconstructed unsteady wave patterns, diffraction wave patterns, and free surface turbulence distributions. 1. INTRODUCTION Rapid advancements in computational fluid dynamics (CFD) have enabled solution of increasingly complex ship hydrodynamics simulations (Arabshahi et al. 1998, Wilson et al. 1998, Landrini et al. 1999, Alessandrini and Delhommeau 1999). For development and validation of CFD codes, much more detailed model-scale, surface ship experiment data is required (Stern et al. 1998, ITTC 1999). To keep pace with the CFD simulations, the experimental fluid dynamics (EFD) community is expected to design and execute experiments that consider more real-world flow conditions and address a variety of physics of interest with advanced measurement techniques. Flowfield measurements are commonly used for CFD validation and flow-physics study on ship hydrodynamics (Hoekstra and Ligtelijn 1991, Bertram et al. 1994, Ogiwara 1994, Suzuki et al. 1998, Van et al. 1998). Toda et al. (1992) and Longo and Stern (1996) applied traditional 5-hole pitot probes to measure the time mean velocities. Laser-Doppler velocimetry (LDV or LDA) was used in towing tanks for reducing probe disturbance effects and measuring mean velocities and Reynolds stresses (Knaack 1992, Longo et al. 1998a). An optical and large-field measurement technique, particle image velocimetry (PIV), has also been applied for high spatial resolution and relatively fast mean velocity and Reynolds stress measurement in towing tanks (Dong et al. 1997, Gui et al. 1999, Roth et al. 1999). For unsteady free-surface flows, experiments are more complex to design and execute and, therefore, limited in number and scope. A phase-averaged measurement of unsteady free-surface flows in an open-channel was conducted by Mezui (1995) with a two-component LDA system and water-wave gauges. Son et al. (1999) used a cinematographic PIV system for unsteady turbulent flow measurements in a wave flume. In addition to flow field measurements in towing tanks, experimental determination of free-surface elevations and measurements of forces and moments are also of great interest, and they are very important aspects for CFD code development and validation in unsteady free-surface flows. Journee (1992) and Rhee and Stern (1998) conducted, respectively, experimental investigations and CFD simulations of unsteady forces and moment for Wigley hullforms. For measuring the unsteady free-surface elevations around a ship model Ohkusu (1990) described two methods, i.e. with wave probes installed on the towing carriage for acquiring data point-by-point and with wave probes fixed in the towing tank for line-by-line measurements. The measurement results were used to predict the added resistance. Kanai (1985) described a grid-projection method for a whole field measurement of the instantaneous wave field. Another optical method was used by Nishio et al. (1998) for mapping the wave height distributions around a ship hull in regular waves. The goal of present work is to support the CFD code development for unsteady ship hydrodynamics through towing tank experiments for forward speed diffraction problem, i.e. ship model advancing in regular head waves, but restrained from motions. Currently, the forward speed diffraction problem plays an important role in engineering approaches, which the authoritative version for attribution. use linear, potential flow, strip theory for ship and

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About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as FORCES, MOMENT AND WAVE PATTERN FOR NAVAL COMBATANT IN REGULAR HEAD WAVES 47 platform motions, and the exciting forces for motions are solution of the forward speed diffraction problem. This model problem can be considered first step in merging of separate fields of resistance and propulsion, seakeeping, and maneuvering. The specific physical problem of interest is a 1:46.6 scale model of a modern naval combatant, DTMB 5512, advancing in regular head waves. The experiments include the measurement of unsteady resistance, heave force and pitch moment for a wide range of incident waves for identification of the effects of the Froude number, wavelength and wave steepness. In addition, a detailed mapping of unsteady free-surface elevations is conducted for a selected test condition. In comparison to previous works, the present study provides much more detailed data with rigorous uncertainty assessment for CFD validation and systematic analyses of the flow physics in ship hydrodynamics covering non-linear responses of forces and moment and distributions of free surface turbulence. Fig. 1: Photos of DTMB model 5512. 2. TEST DESIGN The tests are conducted in the IIHR towing tank, which is 100 m long and 3.048 m wide and deep. The tank is equipped with a drive carriage for housing the carriage controls, computer (PC), and data-acquisition instrumentation and a 3.7-m trailer which is used as a platform for instrumentation and a point of attachment for models. The carriage/trailer are cable driven across level rails by a 15-horsepower motor and can reach speeds of 3 m/s. The carriage speed (Uc) is monitored with an IIHR designed and constructed speed circuit. The details of the carriage speed measurement system and uncertainty assessment are provided in Longo and Stern (1998). A plunger-type wave-maker at the north end of the tank is utilized for generation of regular head waves. The wave-maker is powered by a hydraulic system and controlled through a shore-based PC and National Instruments Labview VI software and MTS controller, and it is capable of generating regular head waves with wavelengths of 0.5~6.0 m and wave steepnesses 0.025~0.3 (Longo et al. 1998b). An automated, moveable sidewall wave-damper system is used in the towing-tank for wave absorption, which enables twenty-minute intervals between carriage runs for steady- and unsteady-flow tests. DTMB model 5512 is selected for the tests (Fig. 1). It has a length of L=3.048 m and was manufactured at DTMB from molded fiber-reinforced Plexiglas and equipped with appendages (brass shafts and struts and wooden rudders) and stainless-steel, twin propellers, although the present tests are for the bare-hull condition. The model is fitted with studs at x=0.05 to initiate transition to turbulent flow. The studs are cylindrical with 1.6 mm height, 3.2 mm diameter, and 10.0 mm spacing and located at x=0.05. The model is rigidly fixed to the carriage using a single-point mount and towed at the dynamic sunk and trimmed condition, which is determined in calm water condition (without wave) for each Froude number. Two right-handed Cartesian coordinate systems are used in the towing tank. The model coordinate system (x, y, z) is attached to the test model with the origin at the intersection of the undisturbed free-surface and forward perpendicular (FP) of the model. The tank coordinate system (X, Y, Z) is fixed in the towing tank. The axes of the coordinate systems are normalized with model length and directed downstream, transverse, and upward, respectively. The unsteady test conditions are determined with Froude number (Fr), wavelength (λ) and wave steepnesses (Ak). Fr the authoritative version for attribution. and Ak are defined as (1) (2) where g is the local gravity acceleration, and A is the amplitude of the incident wave. As shown in Table 1, forces and moment data are procured for a fairly wide range of conditions: low (0.19), medium (0.28), mid-high (0.34), and high (0.41) Froude numbers; small (0.025), small-median (0.05, 0.075), and median (0.10) wave steepnesses; and short (1.524m), median (3.048m), and long (4.572m) wavelengths. The encounter frequency fe varies from low (0.8 Hz) to high (2.5 Hz). For seakeeping, the corresponding H/λ covers very small (1/125), small (1/60), median (1/40) and

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About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as FORCES, MOMENT AND WAVE PATTERN FOR NAVAL COMBATANT IN REGULAR HEAD WAVES 48 mid-large (1/30) values. Since some combinations could not be conducted due to generation of extreme wave amplitudes at the bow, the total number of test cases is 42. The test case for median Fr, small median Ak and median λ (Fr=0.28, Ak=0.05, and λ=3.048m) is chosen for procuring precision limits and assessing total uncertainties, and the results should be representative of most test cases. After observation and analysis of the forces and moment results, a test case of median Fr (0.28), long λ (4.572m) and low Ak (0.025) is selected for the unsteady free-surface elevations, because this condition produces the most manageable linear response, especially, in the farfield region. For all Fr, tests are also conducted without waves, i.e. steady cases. When the test case (i.e. Fr, λ and Ak) is selected, the carriage speed Uc is determined with Fr (Eq. (1)), and the frequency of the regular head wave fw and the frequency of the encounter wave fe are determined with λ as (3) (4) The encounter frequency fe is the dominant frequency of the unsteady responses. The incident wave amplitude A is determined with Ak and λ (Eq. (2)). Table 1: Unsteady test conditions. λ(m) Re[106] Fr Ak fe(Hz) 0.19 3.153 0.025, 0.05, 0.075, 0.1 1.524 1.693 0.025, 0.05, 0.075, 0.1 3.048 1.056 0.025, 0.05, 0.075 4.572 0.811 0.28 4.647 0.025, 0.05, 0.075, 0.1 1.524 2.016 0.025, 0.05, 0.075, 0.1 3.048 1.218 0.025, 0.05, 0.075 4.572 0.919 0.34 5.642 0.025, 0.05, 0.075, 0.1 1.524 2.231 0.025, 0.05, 0.075, 0.1 3.048 1.325 0.025, 0.05, 0.075 4.572 0.991 0.41 6.804 0.025, 0.05, 0.075, 0.1 1.524 2.482 0.025, 0.05, 0.075 3.048 1.451 0.025, 0.05 4.572 1.074 The measurement of free-surface elevations is conducted in the area of −0.25≤x≤1.35, 0≤y≤0.4. This area is divided into two regions: (1) The farfield region beyond the maximum beam of the model (0.08≤y≤0.4), and (2) the nearfield region at the bow and stern (0≤y≤0.08). In the farfield region a longitudinal cut method is employed to determine unsteady free- surface elevations at thousands of points on a constant y-cut in roughly 20 carriage runs. In the nearfield region the free- surface elevations are measured point-by-point with wave probes attached to the moving carriage to obtain detailed information including the free-surface turbulence and high frequency responses. The variables of interest are resistant coefficient (CT), heave force coefficient (CH), pitch moment coefficient (CM) and non-dimensional free-surface elevations (ζT), which are defined as (5) (6) (7) (8) where F x, Fz, My and z are the measured time-varying resistance, heave force, pitch moment and free-surface elevation, respectively; ρ is the towing-tank water density; and S is the design-offsets wetted surface area for the static condition. Since the data acquisition is not synchronized with the wave maker, a time (or phase) reference is needed with the acquired time histories, i.e. the incident wave at x=0, i.e. (9) The amplitude of the reference wave is known, but the initial phase γI is determined through analysis of the incident the authoritative version for attribution. wave time history. In the tests the incident wave records are measured upstream (x ≠ 0) of the model in regions where the waveform is clean with a tank-fixed wave probe (forces and moment, farfield elevations) or a trailer mounted wave probe (nearfield elevations). Thus, a phase shift is necessary to determine the reference phase. Unsteady time histories are reconstructed with FS. When the phase of the reference wave, i.e. the incident

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About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as FORCES, MOMENT AND WAVE PATTERN FOR NAVAL COMBATANT IN REGULAR HEAD WAVES 49 wave at x=0, is set to zero, the FS for time history X (X=CT, CH, C M, ζ T) is determined as follows: (10) (11) (12) (13) (14) (15) wherein XF is the reconstructed time history; Xn is the nth order harmonic amplitude; γn is the corresponding phase; N is the order of the FS and chosen high enough to include all important frequency components. ∆γn is the harmonic phase adjusted with the reference wave, and for forces and moment it is the phase lead relative to the reference wave. Time interval T' is a multiple of the encounter wave period T (=1/fe). Further processing of the test data includes determination of the streaming component of unsteady resistance, i.e. the added resistance C T,ad, and the unsteady perturbation response of unsteady free-surface elevation, i.e. the diffraction wave ζD, and they are defined as (16) (17) where is the time mean of unsteady resistance, CT,st is the steady resistance, is the time mean of the unsteady free-surface elevation. Note that in Eq. (17) ζT is replaced with its first-order FS-reconstruction. 3. MEASUREMENT SYSTEMS 3.1. Forces and moment The measurement system for the forces and moment consists of a four-channel (two force, two moment) strain-gage loadcell and signal conditioner and a carriage-based PC with 12-bit AD card. A shore-based capacitance-wire probe and PC are used to sample the incident wave for determining the reference phase γI. A pair of photoelectric switches is used to synchronize data-acquisition start times for the carriage-based and shore-based measurement systems. The load cell is mounted at the mid-ship of the model (x=0, y=0.5, and the towing height is z=0.0641). A sketch of the measurement system is given in Fig. 2. (18) Fig. 3: Experimental setup for farfield free surface the authoritative version for attribution. Fig. 2: Experimental setup for forces and moment The signals are sampled from the loadcell and the wave probe, amplified and filtered in the signal conditioners, digitized through AD conversion in the carriage and shore-based PC's, and finally converted to time histories of forces and moment (CT(t), CH (t), CM(t)) and incident wave (zI(t)). Each time history consists of 2048 samples producing acquisition times of 30, 10, 15, and 10 seconds for Fr=0.19, 0.28, 0.34, and 0.41 respectively. The phase of the incident wave at the position of the capacitance-wire probe is determined with the first-order FS harmonic phase of time history zI(t), i.e. γz,1. When the data acquisition is started (t=0), the wave probe is in advance of the FP of the model by a distance D (=11.99m). Therefore, a delay of 2πD/λ is required to determine the reference phase:

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About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as FORCES, MOMENT AND WAVE PATTERN FOR NAVAL COMBATANT IN REGULAR HEAD WAVES 50 3.2. Farfie ld free surface elevations A longitudinal wave cut method with two wave probes is used to measure the unsteady farfield freesurface elevations. As shown in Fig. 3, the measurement system consists of a sidewall-mounted boom, servo-type wave probe (probe 1) and signal conditioner, acoustic-type wave probe (probe 2) and signal conditioner, 2D automated traverse system, shore-based PC with 12-bit AD card, carriage-based PC with 12-bit AD card, and a pair of photoelectric switches for external data acquisition triggering. Fig. 5: Spatial distributions of farfield free-surface Fig. 4: Sample time history of farfield free-surface elevations at y=0.082 elevation at y=0.082 Fig. 6: Distribution of the free-surface elevation on the initial phase at one point in a y-cut The measurement of the farfield region is completed with 32 longitudinal (constant-y) cuts, spaced at ∆y=0.0l between the maximum beam of the model and the sidewall damper. The data acquisition is triggered with photoelectric switches 9 seconds prior to the model FP passing the wave probes and ended when the measurement region is completely scanned. The total time interval for data acquisition is 13.3 seconds, and 2700 samples are recorded in every carriage run. 15–25 carriage runs are performed at each constant-y cut to ensure a satisfactory distribution of incident wave phases at the beginning of the raw time histories. As an example, one of the raw time histories (zi(y, t)) taken at y=0.082 is shown in Fig. 4. Note that the incident wave is recorded in the initial 9 seconds, and this information is used to determine the initial phase (γi). In the model coordinate system (x, y, z), the data acquisition at each y-cut is started at x=-D/L, and the wave probe moves in the positive x-direction with constant carriage speed Uc . As such the x-position of the measurement is dependent on the sample time (t). Therefore, the measured raw time histories are converted to spatial distributions of the free-surface elevations with (19) Fig. 5 shows the spatial distributions of free-surface elevation obtained in 14 runs at y=0.082. Based on a group of spatial distributions of the unsteady free-surface elevations at a certain y-cut, a distribution of free-surface elevation on the initial phase is obtained for every x-position. As an example, symbols in Fig. 6 show the distribution of free-surface elevation on the initial phase at x=0.169 in the cut of y=0.082. After the dispersed distribution is fitted with a continuous polynomial curve, see the curve in Fig. 6, FS coefficients are determined with (20) (21) wherein ζp(γ) is the polynomial fit of the dispersed distribution of (ζi, γi), and it depends on position (x, y). According to Eqs. (12), (13), (20) and (21) the FS harmonic amplitude and phase can be computed. For each y-cut, the first point x0 (x0= −D/L, D=14.45m) is upstream and far from the model. Therefore, the first-order FS harmonic phase (γ0) at x0 represent the phase of the local incident wave. A phase delay of 2πD/λ is considered for the incident wave at x=0. In addition, because the data is obtained at different time for different x-positions in each y-cut, a time shift of ∆t=(x−x0)L/Uc should be taken the authoritative version for attribution. into account, and the corresponding phase shift is 2πfe·∆t. Finally, the reference phase is determined with (22) Note that Eq. (22) is valid only for constant y.

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About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as FORCES, MOMENT AND WAVE PATTERN FOR NAVAL COMBATANT IN REGULAR HEAD WAVES 51 Fig. 7: Experimental setup for nearfield free surface 3.3. Nearfield free surface elevations The nearfield measurement system consists of the same equipment as for the farfield measurement system but arranged differently. The two wave-probes are attached to the moving carriage. As shown in Fig. 7, probe 2 is installed forward of the model on the trailer for acquiring the incident wave, and probe 1 is installed on a trailer-mounted automated traverse for measuring the unsteady free-surface elevations. The measurement area is mapped with 22 and 26 variably- spaced (in the x-coordinate) transverse cuts at the bow and stern, respectively. The measurement location spacing in the y- coordinate is variable but mostly ∆y=0.005. Two points are measured in each carriage run with a probe-movement. At each measurement point 3000 samples are acquired in a 9-second time interval. In the data acquisition procedure, time histories for the unsteady free-surface (z(x,y,t)) and incident wave (zI(t)) are obtained. In the post-processing procedure, the reference phase is determined according to the time history of the incident wave, and the FS harmonic amplitudes and phases are computed for unsteady free-surface elevations. The phase of the incident wave at probe 2 is determined with the first harmonic phase of the sampled wave elevation γz,1. Since wave probe 2 is installed at x=−D/L (D=1.905m), a phase delay of 2πD/λ is considered to determine the reference phase: (23) 4. UNCERTAINTY ASSESSMENT Uncertainty assessments are completed for the results on three levels: Raw time histories, FS harmonics and the FS- reconstructed time histories. Following the AIAA Standard (S-017A-1999), the uncertainty of a measurement variable is defined as the root-sum-square (RSS) of the bias limit and precision limit for a 95% confidence level. For a raw time history the bias limit is estimated according to the data-reduction equation and elementary bias limits, and the precision limit is estimated with repeated end-to-end data-acquisition and reduction cycles. The bias limits of the FS harmonics are determined either with the time mean values of the raw-time-history bias limits or with the bias gradient limits. The precision limits of the FS harmonics are determined using the same procedure as for the raw time histories. Finally, the bias limit and precision limit of the FS-reconstructed time history are computed with the bias and precision limits of the FS harmonics according to the RSS method. Detailed descriptions follow. 4.1. Raw time histories Bias limit: For convenience we assume that the measured value X is determined at time t with independent variables Vi for i=1,2,···,M. The data-reduction equation of time history X(t) is represented as: (24) The bias limit for X(t) is determined with (25) where the sensitivity coefficients are determined with (26) and BVi and B t are the elementary bias limits. Respectively for the forces and moment coefficients (CT, CH and C M) and the near and farfield free-surface elevations ( ζFF & ζNF) the data reduction equations are as follows: (27) the authoritative version for attribution. (28) (29) (30) (31) The elementary bias limits BFx, B Fz, BMy and B z are estimated in end-to-end calibration procedures, and Bρ, B Uc, B S, BL are taken from historical uncertainty assessment efforts (Longo and Stern 1998). Bt is provided by manufacturer specifications, and bias limits related to the probe position Bx, B y and B D are estimated during the setup of the measurement systems. Note that the total bias limit BX is a function of time in the unsteady cases.

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About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as FORCES, MOMENT AND WAVE PATTERN FOR NAVAL COMBATANT IN REGULAR HEAD WAVES 52 Precision limit: The precision limit is estimated with multiple end-to-end data-acquisition and reduction cycles. According to the AIAA Standard, the precision limit for a single test of variable X is determined by (32) where K is the coverage factor and equals 2 for a 95% confidence level. The standard deviation σ is defined as (33) where N is the number of multiple tests, and is the mean value of the multiple tests. When is used as the final result, the precision limit is then (34) In unsteady cases the standard deviation and precision limit are computed at each phase. Total uncertainty: The total uncertainty UX is obtained with the RSS method as (35) 4.2. FS harmonics In order to determine the bias limits for the FS harmonic amplitudes and phases, it is assumed that the measured value X deviates from the real value X' with a bias error β. When the random error is not considered, the real and measured value are related with (36) The bias error β is not a constant, and it is usually a function of the measurement value. For simplification, we assume the relation is linear, i.e. (37) where is the bias gradient, and β0 is the constant part of the bias error. The FS harmonic amplitudes and phases (n≠0) for the biased and unbiased cases are related as follows: (38) (39) (40) (41) Wherein a', b', X'n and γ' are for the unbiased case. The bias errors for the FS harmonic amplitudes and phases can then be determined as (42) (43) The above deductions indicate that the bias error of the FS harmonic amplitude does not directly depend on the bias error, but on the bias gradient of the measured variable. Also, the bias error of the FS harmonic phase is independent of the bias error of the measured variable X. According to Eq. (42) The bias limits of the FS harmonic amplitudes can be determined as (44) where is the limit (maximal magnitude) of the bias gradient, which can be calculated with the data-reduction equation and elementary bias limits. The bias limit of the zeroth FS harmonic amplitude is determined as (45) According to Eq. (43) the bias limits of the FS harmonic phases equal zero, i.e. The bias limits of the adjusted are then determined with Eq. (11) and equations for determining the reference phase γI. For example, the bias phases limits of the adjusted harmonic phases for the forces and moment are determined with Eqs (11) and (18) as (46) The precision limit and the total uncertainty for the FS harmonics are determined with the same procedures as for the time histories the authoritative version for attribution. 4.3. FS-reconstructed time histories The data-reduction equation for a FS-reconstructed time history can be represented as (47) where N is order of the FS. For the reconstructed time history, time t is a given value, so it has neither bias nor precision errors. According to the data-reduction equation the bias limit and precision limit are determined with

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About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as FORCES, MOMENT AND WAVE PATTERN FOR NAVAL COMBATANT IN REGULAR HEAD WAVES 53 (48) (49) The sensitivity coefficients are (50) The total uncertainty UXF is obtained with the RSS value of BXF and PXF. 5. RESULTS AND DISCUSSIONS 5.1. Incident wave For all unsteady tests, time histories of the incident head wave (zI) are fundamentally important references for all other measured variables. In Fig. 8a, a sample time history is presented for the median test case, i.e. Fr=0.28, Ak=0.05, λ=3.048 m, where the incident head wave frequency is fw=0.7155 Hz and the encounter frequency fe is 1.2175 Hz. Although this case was chosen for the detailed uncertainty assessment, experience has shown that the other incident waves are similarly repeatable in terms of amplitude and frequency and possess low uncertainty for these two parameters (Longo et al. 1998). Note that the incident wave elevation in the figure represents a nearly perfect first harmonic signal during the initial 8 seconds of the time history but is somewhat distorted in the final 2 seconds due to the closing distance between wave probe and ship model. The zeroth-harmonic amplitude is less than 1% of the first-harmonic amplitude and the uncertainty in wave frequency fw and wave amplitude Aw is 0.7% and 2.65%, respectively, which is based on multiple tests (N=11) and estimates of the bias limits. Also based on multiple tests, the uncertainty of the encounter frequency fe is determined with time histories of CM (Fig. 8d) as 0.4% for the median test case which ensures accuracy in the time domain of the measurements. Note that fe is determined with lower uncertainty than fw, because C M includes more wave periods than zI, i.e. fe>fw. The uncertainty of fw, Aw, and fe for the wave-elevations tests is expected to be at least as good as for the median test case. 5.2. Me dian test case for forces and mome nt Basic results for the forces and moment tests are time histories of resistance (CT), heave force (CH ), and pitch moment (CM) for the 42 test cases. Fig. 8b-d includes the raw data and the first-order FS reconstruction for the median test case. Note that the discussions for this case can generally be applied to most other test cases. The output signals, i.e., C T, C H, CM exhibit strong first harmonic responses at fe , except for some sub-frequency responses for CT and CH (Fig. 8b-c). CT and CH contain limited high-frequency signals at the peaks and troughs, which are associated with carriage vibration transmitted to the single-point mount and loadcell. This noise is absent for C M due to the large inertia of the model for pitching motion. Note that, in Fig. 8, CT, CH, and CM are not in phase with zI, which will be explained later in this section. Fig. 8: Raw and FS-reconstructed time histories for the median test case the authoritative version for attribution. Further investigation of the harmonic content for the forces and moment is shown in Fig. 9, which includes the zeroth, half, and first thru fifth-order FS harmonic amplitudes and the adjusted phases ∆γ. The error bands in the figure are the precision limits

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About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as FORCES, MOMENT AND WAVE PATTERN FOR NAVAL COMBATANT IN REGULAR HEAD WAVES 54 (P=Kσ) obtained with multiple tests (N=11). (Here the bias limits are not provided because they are relatively small and not essential for the discussion). The figures show that the zeroth and first harmonic amplitudes and the first harmonic phases, which are the main focus of the discussions, can be determined with very low uncertainties. Since the corresponding harmonic amplitudes are too small in the median test case, the uncertainties for determining the higher harmonic phases are very high. However, in the case of high-Fr when the higher harmonics have significant amplitudes, see Fig. 16, the phase can also be determined at low uncertainty. Because of the limited recording time (≈10s), the uncertainties for determining phases of the half FS harmonics are very large. Fig. 10: Reconstructed time histories with adjusted start Fig. 9: Amplitudes, phases and precision limits for the phases in the median test case median test case unsteady forces and moment Using the first-order FS harmonics for the median case, the time histories are reconstructed and presented in Fig. 10. The results of the steady test are also plotted in the figure for comparison. Slight differences between the steady results and the mean of the unsteady results for CT, C H, and C M can be observed in Fig. 10. The mean of the unsteady resistance coefficient C T (0.0049) is larger than the steady resistance coefficient CT,st (0.0044), and the difference, i.e. the added resistance C T,ad, will be shown more clearly in Fig. 12. Phase differences between the incident wave ζI and the unsteady responses of C T, CH, and CM can be investigated clearly in the figures, Note that the incident wave signal is determined at x=0 and the wavelength equals the model length in this case. The resistance (CT) and pitch moment (CM) reach maximal values when the peak of the incident wave hit the forebody of the model ship at t/T=0.3 and t/T=0.35, respectively. The heave force becomes maximal when the peak of the wave hit the midbody (t/T=0.5). Uncertainty assessment results for the FS-reconstructed time histories are plotted in Fig. 10 as uncertainty bands. An analysis of the uncertainty assessment results is given in Table 2. The precision limit (85–98%) is the main uncertainty source for the forces and moment coefficients, and the elementary precision limit for ∆γ is the main precision error source (61%–95%). C H has a much larger precision error for determining ∆γ than CT and CM, so that its relative uncertainty (9.76%) is much higher than those of CT (4.23%) and CM (2.93%). Uncertainty assessment the authoritative version for attribution.

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About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as FORCES, MOMENT AND WAVE PATTERN FOR NAVAL COMBATANT IN REGULAR HEAD WAVES 55 results of the FS harmonics for CT, CH, C M are provided in Table 3 with relative contributions of bias and precision components and total uncertainties normalized either with the first harmonic amplitudes for the zeroth and first harmonic and 2π for the phase. Again, the main contribution to the uncertainty in the FS harmonics is the precision limits. The results of the uncertainty assessment for the FS harmonics of C T, CH, C M are also illustrated in Fig. 11, 13, 14 as uncertainty bands and will be discussed later. Table 2: Uncertainty assessment for time histories Term CT CH CM PX,0θX,0 5.46% 4.80% 20.2% PX,1θX,1 15.7% 0.73% 18.9% P∆γ,1θ∆γ,1 78.8% 94.5% 60.9% BX 11.3% 14.1% 2.12% PX 88.7% 85.9% 97.9% UX 4.23% * 9.76% * 2.93% * ( : Normalized with X1) Table 3: Uncertainty assessment for FS harmonics Term CT CH CM BX0 38.2% 11.7% 2.21% PX0 61.8% 88.3% 97.8% UX0 1.08%* 12.3%* 2.80% * BX1 15.5% 18.1% 14.1% PX1 84.5% 81.9% 85.9% UX1 3.83%* 3.18%* 4.25% * B∆γ1 0.45% 0.26% 0.70% P∆γ1 99.5% 99.7% 99.3% U∆γ1 3.62% ** 6.24% ** 2.32% ** 5.3. Linear response for forces and mome nt Since the regular head waves generated by the IIHR wave maker are typical first-order harmonic waves, the encountered waves by the ship hull with a constant forward speed are also first-order harmonics. When likening the ship hull and the encounter wave system to a dynamic (oscillating) system, the output signals (measured variables CT, CH, C M) can be considered as linear responses, if they are also first-order harmonics. The unsteady responses in the median test case are linear because the measured variables are dominated by first-order FS harmonics. In cases of non-linear responses, the first-order FS harmonics represent the linear portion of the total unsteady responses. In the following the linear portions of the unsteady responses, i.e. the zeroth and first harmonic amplitudes and the first harmonic phases, are discussed for all test cases. Fig. 11: Zeroth and first FS harmonic amplitude and the first FS harmonic phase for CT The zeroth and first FS harmonics of C T are shown in Fig. 11. For comparison, the zeroth FS harmonic amplitude of CT for the steady (without wave) case is also plotted in Fig. 11a. The zeroth FS amplitude C T,0 initially decreases with increasing Fr and then increases with increasing Fr beyond Fr=0.28 (Fig. 11a). Not surprisingly, CT,0 approaches the steady the authoritative version for attribution. case for decreasing Ak (Fig. 11a). In addition, CT,0 increases with increasing Ak (Fig. 11a, d) or λ (Fig. 11d). The first FS amplitude CT,1 decreases nonlinearly with increasing Fr, with the steepest descents for increasing Fr at the highest Ak (Fig. 11b). With increasing Ak or λ, CT,1 increases rapidly (Fig. 11b, e). The phase lead of CT, ∆γCT,1 is mostly constant versus Fr and Ak, but increases with increasing λ (Fig. 11c, f). In Fig. 11a, obvious difference between the unsteady and steady CT,0, i.e. double of the added resistance, is investigated, especially for low Fr and high Ak. As shown in Fig. 12 the added resistance CT,ad decreases with increasing Fr but increases with increasing Ak or λ.

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About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as FORCES, MOMENT AND WAVE PATTERN FOR NAVAL COMBATANT IN REGULAR HEAD WAVES 56 Fig. 13: Zeroth and first FS harmonic amplitude and the first FS harmonic phase for CH Fig. 12: Dependencies of the added resistance (CT,ad) on Fr, Ak, and λ The zeroth and first FS harmonics of the heave coefficient are plotted in Fig. 13. No differences are observed for CH,0 between the steady and unsteady cases (Fig. 13a). C H,0 decreases linearly with increasing Fr, but it is generally constant versus Ak and λ (Fig. 13a, d). CH,1 decreases for increasing Fr (Fig. 13b), but it increases with increasing Ak or λ (Fig. 13b, e). The phase lead of CH , ∆γCH,1 is mostly constant versus Fr and Ak but increases with increasing λ (Fig. 13c, f). the authoritative version for attribution. Fig. 14: Zeroth and first FS harmonic amplitude and the first FS harmonic phase for CM The zeroth and first FS harmonics of the pitch moment coefficient are plotted in Fig. 14. Only slight differences are observed for CM,0 between the steady and unsteady cases at low Fr (Fig. 14a). CM,0 increases nonlinearly with increasing Fr and slightly with increasing Ak at low Fr (Fig. 14a), but it is generally constant versus λ (Fig. 14d). C M,1 decreases for increasing Fr (Fig. 14b), but increases with increasing Ak and λ (Fig. 14b, e). The phase lead of CM, ∆γCM,1 is mostly constant versus Fr and Ak but increases with increasing λ (Fig. 14c, f). In traditional studies based on the strip theory for ship motions (Gerritsma and Beukelman 1967, Lewis 1989, Journee 1992,), the exiting forces for surge, heave and pitch are the first harmonics of the resistance, heave force and pitch moment, whose amplitudes are usually normalize as follows:

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About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as FORCES, MOMENT AND WAVE PATTERN FOR NAVAL COMBATANT IN REGULAR HEAD WAVES 57 (51) (52) (53) where ∇ is the volume of displacement, Aw is the waterplane area, IL is the longitudinal moment of inertia of water- plane area about y axis, ζI,1, Fx,1, Fz,1 and My,1 are the first FS harmonic amplitudes for incident wave, heave force and pitch moment, respectively. According to previous studies the non-dimensional exiting forces depend mainly on the wave length, and their amplitudes approaches 1 when L/λ equals zero, i.e. when λ is unlimited large. Fig. 15: Exciting force amplitudes for three ship models Fig. 16: Time histories and FT results of unsteady pitch moment for two typical cases The non-dimensional exciting force amplitudes F'x, F'z and M'y are computed for DTMB 5512 at three Fr numbers and presented in Fig. 15 together with data taken by Journee (1992) for a Wigley model at Fr=0.30 and by Gerritsma and Beukelman (1967) for a ship model. The dependences of the non-dimensional exciting force amplitudes on the relative wavelength are similar for the three models, and the observed differences may result from the model geometry variations. 5.4. Non-linear response for forces and mome nt In above discussions the first-order harmonic responses in the present ship hull and wave system are considered as the authoritative version for attribution. linear responses. That implies that all the sub- and super harmonics in the test results are referred to non-linear responses. According to the analysis in subsection 5.2., the unsteady responses of CT, CH are CM are mostly linear in the median test case because the sub-harmonics are considered to be noises and the super harmonics can be neglected. In consideration of other test cases, the time histories and the corresponding FT results of CM are given in Fig. 16

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About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as FORCES, MOMENT AND WAVE PATTERN FOR NAVAL COMBATANT IN REGULAR HEAD WAVES 58 for a long-wave/low-Fr case (Fr=0.19, Ak=0.025, λ =4.572 m) and a short-wave/high-Fr case (Fr=0.34, Ak=0.075, λ=1.524 m). Both the time history in Fig. 16a and FT result in Fig. 16b suggest nearly perfect first harmonic unsteady response for the former test case. Although a strong first harmonic unsteady response is also observed for the latter short-wave case, a super-harmonic response at 2fe is also present in Fig. 16d. Similar tendencies in the harmonics are also observed for CT and CH but not shown here. Amongst the tests, the super-harmonic responses are only investigated in the short-wave cases, i.e. for λ=1.524 m. Fig. 17: FS harmonic amplitudes for a short wavelength (λ=1.524 m) versus Fr and Ak Detailed investigation of unsteady responses for the short-wave case through analysis of the 1st, 2nd and 3rd FS harmonic amplitudes for C T and CH versus Fr and Ak is provided in Fig. 17. The FS harmonic amplitudes for n=1, 2, 3 generally increase with increasing Ak, and they are roughly linear functions of Ak except for cases at Fr=0.41 which appear to be parabolic. The super harmonics appear to have significant magnitudes for Fr=0.34 and 0.41. The tendencies in the FS harmonics noted above are similar for CM but not shown here. The conclusions from Figs. 16 and 17 point to non- linear unsteady responses in the forces and moment coefficients but only for combinations of short λ and mid-high and high Fr. Further investigation of the super harmonics are shown in Fig. 18, in which the dependencies of the FS harmonic amplitudes on Fr for Ak=0.1 and λ=1.524 are given. For CT, CH and C M, the first harmonic amplitudes decrease with increasing Fr, and the third harmonic amplitudes are relatively very small. Interestingly, for all three variables the second harmonic amplitude has a maximum near Fr=0.34. Fig. 18: Dependencies of FS harmonic amplitudes on Fr Fig. 19: Raw and reconstructed time histories of CM for for λ=1.524 m and Ak=0.1 Fr=0.34, λ=1.524m and Ak=0.1 the authoritative version for attribution. The raw and reconstructed time histories of the pitch moment coefficient CM are given in Fig. 19 for the most non- linear case, i.e. Fr=0.34, λ=1.524m and Ak=0.1. The reconstructed time history includes the second-order FS and reflects a typical non-linear response. In Fig. 19, the raw time history is different in

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About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as FORCES, MOMENT AND WAVE PATTERN FOR NAVAL COMBATANT IN REGULAR HEAD WAVES 59 different encounter periods due to some sub-frequency content. Because of the limited data-acquisition time (10~15s), the sub-frequency content cannot be determined correctly with the current data. Fig. 20: The 0th (a) and 1st (b) harmonic amplitude and the 1st harmonic phase (c) for the unsteady free-surface elevation Fig. 21: Unsteady wave patterns at t/T=0, 1/4, 1/2, 3/4 5.5. Free surface elevations The free-surface elevation data provided for CFD validation includes the FS-reconstructed unsteady free-surface elevations and uncertainty assessment results. Detailed analysis of time histories at select locations in the wavefield have verified that the unsteady wavefield exhibits a strong first-harmonic response and, therefore, can be represented with a first-order FS. The zeroth and first FS harmonic amplitudes and the first FS harmonic phase are computed in both far- and nearfield regions and shown in Fig. 20. The zeroth harmonic amplitude (Fig. 20a) of the wavefield displays the typical wave pattern characteristics of a fine hull form advancing in calm water, including diverging and transverse waves and a dominant fore-shoulder wave. The zeroth harmonic amplitude is, in fact, two times of the mean unsteady free surface elevation. According to the test results the difference between the mean unsteady free surface elevation and the steady free surface elevation is within the uncertainty band. The amplitude of the incident wave (0.006) is 43% of the dynamic range of the steady free surface elevation (0.014). Fig. 20b includes contours of the first FS harmonic amplitude in the wavefield. Note that the contours are contained in a wedge-shaped region with semiangle of 24.5°. A dominant crestline is observed swept backward from the forebody shoulder, and a weaker troughline emanates from the transom corner. The maximum of the first harmonic amplitude (0.01) is 1.7 times of the incident wave amplitude. Fig. 20c shows contours of the first FS harmonic phase. Interestingly, the two regions where the contour lines are most affected seem to be associated with the crest and troughlines of the first FS harmonic amplitude. In comparison to the uniform phase distribution of the incident wave (−2πxL/λ), phase leads and lags are present at the forebody shoulder and transom corner, respectively, and the dynamic range is about π/3. Distributions of the zeroth and first FS harmonic amplitude and the first harmonic phase are used to reconstruct the unsteady wave patterns. Examples are shown in Fig. 21 at four instants in the encounter period (t/ T=0, 0.25, 0.5, 0.75). The unsteady perturbation response of the free-surface elevation, i.e. the diffraction wave, is computed with the reconstructed unsteady free-surface elevation and the incident wave pattern (Eq. (17)). Since the unsteady free-surface elevation is reconstructed with the first-order FS, the diffraction wave contains only first-order FS harmonics. The distributions of the harmonic amplitude and phase are shown in Fig. 22. the authoritative version for attribution.

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About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as FORCES, MOMENT AND WAVE PATTERN FOR NAVAL COMBATANT IN REGULAR HEAD WAVES 60 The contour patterns of the diffraction wave amplitude (Fig. 22a) look similar to that of the first-order FS amplitude of the unsteady free-surface elevation (Fig. 20b). Two maximums of the diffraction wave amplitude initiate at the forebody shoulder and transom corner and diverge from the model at 24.5° with respect to the centerplane. The maximal amplitude of the diffraction wave (0.004) is about 40% of that of the unsteady free surface elevations. There are two peaks in the phase distribution of the diffraction wave (Fig. 22b): one is near the forebody shoulder (x=0.35); the other is inboard of the diverging stern wave crest (x=1.09). This implies that the diffraction waves originate, in principle, from the forebody and stern regions of the model. This can also be seen in the time history of the diffraction wave (Fig. 23). Note that in Fig. 22b large errors exist for the phase in regions of very low amplitude. Fig. 22: Amplitude (a) and phase (b) distributions of the diffraction wave Fig. 23: Diffraction wave patterns (ζD) at four instants Table 4: Uncertainty for farfield free-surface Term Steady, y=0.082 Unsteady, y=0.232 Magnitude (%) Magnitude (%) 3.0806×10−4 (79.3) 4.9762×10−4 (84.0) BUcθUc 1.4364×10−7 (0.04) 2.3203×10−7 (0.04) Btθt 2.2898×10−5 (5.89) 3.6988×10–5 (6.24) BDθD 2.4636×10−5 (6.34) 2.5024×10−5 (4.22) Byθy 3.2808×10−5 (8.44) 3.2808×10−5 (5.54) Bzθz 3.12×10−4 (59.0) 5.01×10−4 (43.3) Bζ 2.17×10−4 (41.0) 6.55×10−4 (56.7) Pζ 3.80×10−4 (1.50)* 8.24×10−4 (3.25)* Uζ (*: Normalized with maximal ζT,1) A summary of the uncertainty assessments for the farfield free-surface elevations is provided in Table 4 at y=0.082 and y=0.232 for the steady and unsteady case, respectively. For the unsteady case precision limits are determined at six phases and averaged. For both the steady and unsteady cases, the values are spatially averaged in the region of x=0~1 and also time averaged for the unsteady case. Table 4 shows that the bias and precision limits are nearly the same order for both the steady and unsteady case. In the steady case the bias limit is larger than the precision limit, but switched for the unsteady case. For both the steady and unsteady cases the main bias error source is from Uc. The uncertainty levels (1.5% and 3.3%) are reasonable. Uncertainty assessment results for the nearfield free-surface elevation measurements are conducted at two points in the the authoritative version for attribution. wavefield corresponding to high (x=1.075, y=0; HTR) and low (x=0.05, y=0.07; LTR) free-surface turbulence regions and summarized in Table 5. Note that for the unsteady cases uncertainty assessments are completed for the FS-reconstructed time histories, and the results are time-averaged. For both steady and unsteady cases, precision limits are obtained with multiple tests (N=10). Results for all cases demonstrate reasonable uncertainty levels of 1.1–4.2%. For the LTR, bias and precision limit contributions are equally weighted for the steady case

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About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as FORCES, MOMENT AND WAVE PATTERN FOR NAVAL COMBATANT IN REGULAR HEAD WAVES 61 but for the unsteady case, the uncertainty value is dominated by precision limit (84%). For the HTR and both steady and unsteady cases, the uncertainty values are dominated by precision limit, 75% and 87%, respectively. Table 5: Uncertainty for nearfield free-surface Steady (Fr=0.28) Term x=0.05, y=0.07 x=1.075, y=0 Magnitude (%) Magnitude (%) 3.2808×10−5 (52.6) 3.2808×10−5 (25.2) Bξ 2.9600×10−5 (47.4) 9.7200×10−5 (74.8) Pξ 4.4187×10−5 (1.10) 1.0259×10−4 (1.90) Uξ Unsteady (Fr=0.28, λ=4.572 m, Ak=0.025) Term x=0.05, y=0.07 x=1.075, y=0 Magnitude (%) Magnitude (%) 1.5754×10−4 (65.7) 1.5520×10−4 (40.1) Pξ,0θξ,0 5.2452×10−5 (21.9) 1.1498×10−4 (29.7) Pξ,1θξ,1 2.9945×10−5 (12.4) 1.1704×10−4 (30.2) P∆γ,1θ∆γ,1 3.2808×10−5 (16.3) 3.2808×10−5 (12.7) Bξ 1.6872×10−4 (83.7) 2.2584×10−4 (87.3) Pξ 1.7188×10−4 (2.86) 2.2821×10−4 (4.23) Uξ ( : Normalized with local ζ T,1) With data from the nearfield free-surface test, the harmonic content and free-surface turbulence are investigated to determine the characteristics of the unsteady wavefield. Eight measurement points located in regions of high (x=1.0148, y=0~0.03) and low (x=1.0148, y=0.05~0.08) free-surface turbulence are selected for the detailed investigations. FT results of the time histories at each location are presented in Fig. 24. On and near the center plane (Fig. 24a-d), the FT record contains a spike at fe and abundant sub- and super-harmonic frequency content associated with the naturally turbulent topography of the transom wavefield. Moving further from the centerplane transversely (Fig. 24e-h), the FT records abruptly become very clean in the higher-frequency region, leaving a dominant spike at fe surrounded by a small local region of FT content probably associated with the coarse resolution of the FT for the limited data-acquisition time (≈ 9 s). Fig. 23 indicates that the majority of the wavefield exhibits a strong first-harmonic (linear) response and provides support for representation of the unsteady wavefield with a first-order FS. The free-surface turbulence level in the steady case is usually described with the RMS value of free-surface fluctuations around the mean value. Similarly, the unsteady free-surface turbulence level is here defined with the RMS value of the free-surface fluctuations around the reconstructed free-surface elevations (first-order FS). Fig. 25 shows the comparisons of mean and RMS fluctuation of free-surface elevations for steady and unsteady cases at the stern of the model. The steady free-surface elevation (ζst) and the mean of unsteady free-surface elevation (ζT,0 /2) are compared in Fig. 24a, and the figure shows that the contour patterns and the magnitudes are very similar. The RMS values of the steady and unsteady free-surface fluctuations have similar contour patterns, and their maximal values are of the same order. However, away from the high turbulence center, the RMS fluctuation is higher for the unsteady case than the steady case. Fig. 24: FT results of unsteady free-surface elevations at 8 selected locations near the model stern 6. SUMMARY AND CONCLUSIONS the authoritative version for attribution. Present investigations are aimed at procuring validation data for RANS CFD codes and explication of flow physics regarding DTMB model 5512 in

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About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as FORCES, MOMENT AND WAVE PATTERN FOR NAVAL COMBATANT IN REGULAR HEAD WAVES 62 regular head waves. Unsteady resistance, heave force, and pitch moment are procured at a fairly wide range of test conditions of interest. Unsteady free-surface elevations are mapped in a case of median Froude number, long wavelength and low wave steepness. The test uncertainties assessed following the AIAA Standard (1999) are in reasonable levels. The mean of the unsteady resistance coefficient is larger than the steady resistance coefficient, especially at low Froude number and high wave steepness, and the difference, i.e. the added resistance coefficient, decreases with increasing Froude number but increases with increasing wavelength or wave steepness. The mean of the unsteady heave force coefficient is almost the same as the steady heave force coefficient, and it decreases linearly with increasing Froude number without dependencies on the wave steepness and wavelength. The mean of the unsteady pitch moment coefficient is nearly the same as the steady pitch moment coefficient, but it is slightly larger at low Froude numbers. Test results for unsteady forces and moment demonstrate mostly linear responses in cases of median and long wavelength, which agree with the previous experiments and analyses basing on the traditional strip theory for ship motions. For the linear responses, the amplitudes of the exciting forces (or the first harmonics) increase linearly with increasing wave steepness at the same Froude number and wavelength. However, nonlinear responses are investigated in cases of short wavelength and high Froude number. The non-linear responses contain significant second-order harmonics, and their amplitudes increase non-linearly with increasing wave amplitude. Generally, the first order harmonic amplitudes of the forces and moment coefficients increase with increasing wavelength or wave steepness and decrease with increasing Froude number. Relative to the incident wave at the forward perpendicular of the model, phase lags exist and only depend on the wavelengths. The unsteady response of the free-surface elevation is linear in the case of median Froude number and long wavelength, except for a small area near the ship hull at the stern in the transom wave field. The mean of the unsteady free surface elevation shows the same patterns as the diverging and transverse waves in the steady case. The reconstructed unsteady free surface elevation has maximal amplitude of 1.7 times of the incident wave amplitude. Relative to the incident wave patterns, phase leads and lags are present in the range of π/3 at the forebody shoulder and transom corner, respectively. The free-surface turbulence levels of the steady and unsteady cases are nearly the same in the high-turbulence region at the wake center, but in the low-turbulence region off the wake center the turbulence level of the unsteady case is higher. The maximal amplitude of the diffraction wave is about 40% of that of the unsteady free surface elevation. The phase distribution indicates that the diffraction waves originate from the forebody and stern regions of the model. Results of uncertainty assessments indicate that the main uncertainty source for the forces, moment, and nearfield free-surface elevation measurements is the precision error. The precision error can be reduced in the future by improving the stability of the measurement systems and by increasing the recording time for unsteady signals. For the farfield free- surface measurement the bias limit is as significant as the precision limit, and the main bias error results from the carriage speed. Therefore, the speed of the carriage should be controlled better for future unsteady tests. The test data and the uncertainty results is being used for CFD validation in the IIHR, and it will be archived at “http://www.uiowa.edu/~towtank” for general dissemination. For future tests, phase-averaged PIV measurements of the unsteady flowfield are being conducted in the IIHR towing tank using the same test condition as for the unsteady free- surface tests, and the results will appear soon. Fig. 25: Nearfield free-surface elevation at the stern: (a) Steady and mean of unsteady, (b) RMS ACKNOWLEDGMENTS This research was sponsored by Office of Naval Research under Grant N00014–96–1–0018 under the administration of Dr. E.P.Rood. The generous loan of the servo-type and acoustic wave probes by Prof. Yasuyuki Toda, Department of Global Engineering, the authoritative version for attribution.

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About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as FORCES, MOMENT AND WAVE PATTERN FOR NAVAL COMBATANT IN REGULAR HEAD WAVES 63 The University of Osaka, Osaka, Japan is gratefully acknowledged. REFERENCES AIAA Standard (1999), Assessment of Experimental Uncertainty with Application to Wind Tunnel Testing. AIAA S-017A-1999 Ale ssandrini B, De lhommeau G (1999), A fully coupled Navier-Stokes solver for calculation of turbulent incompressible free surface flow past a ship hull. 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Physics of Fluids, vol. 11, pp. 3512–3523 Son SY, Kihm KD, Cox D T (2000), Evaluation of unstationary turbulent flow fields using cinematographic particle image velocimetry (PIV), to be published in Exp. Fluids Stern F, Longo J, Maksoud M, Suzuki T (1998), Evaluation of Surface-Ship Resistance and Propulsion Model-Scale Database for CFD Validation. 1st Symposium on Marine Applications of Computational Fluid Dynamics, McLean, VA. Stern F, Longo J, Pe nna R, Oliviera A, Ratcliffe T, Cole man H (2000), International Collaboration on Benchmark CFD Validation Data for Naval Surface Combatant. 23rd ONR Symposium on Naval Hydrodynamics, Val de Reuil, France, 17–22 September. Suzuki H, Miyazaki S, Suzuki T, Matsumura K (1998), Turbulence Measurements in Stern Flow the authoritative version for attribution.

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About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as FORCES, MOMENT AND WAVE PATTERN FOR NAVAL COMBATANT IN REGULAR HEAD WAVES 64 Field of Two Ship Models. Proceedings 3rd Osaka Colloquium on Advanced CFD Applications to Ship Flow and Hull Form design, Osaka, Japan Toda Y, Stern F, Longo J (1992), Mean-Flow Measurements in the Boundary Layer and Wake and Wave Field of a Series 60 CB =0.60 Ship Model. Journal of Ship Research, Vol. 36, No. 4, pp. 360–377. Van SH, Kim WJ, Yim GT, Kim DH, Lee CJ (1998), Experimental Investigation of the Flow Characteristics Around Practical Hull Forms. Proceedings 3rd Osaka Colloquium on Advanced CFD Applications to Ship Flow and Hull Form design, Osaka, Japan Wilson R, Paterson E, Stern F (1998), Unsteady RANS CFD Method for Naval Combatant in Waves. 22nd ONR Symposium on Naval Hydro, Washington DC. the authoritative version for attribution.

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About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as FORCES, MOMENT AND WAVE PATTERN FOR NAVAL COMBATANT IN REGULAR HEAD WAVES 65 DISCUSSION R.Beck University of Michigan, USA You mentioned that the diffractial wave field was 200% of the incident wave, Since the diffracted waves against a wall is double the incident wave height (100%), can you explain why you found such large diffractial waves? AUTHOR'S REPLY The diffraction waves are 67% of the incident wave height, i.e., (0.004/0.006) DISCUSSION H.Bingham Technical University of Denmark, Denmark What theory are you using to generate your nonlinear incident waves? Have you checked that you can indeed produce a steady nonlinear wave? AUTHOR'S REPLY The incident waves are first-harmonic linear waves. DISCUSSION R.Penna Instituto Nazionale per Studi ed Esperienze di Architettura Navale, Italy In order to study the unsteady flow in the wake produced by the waves, I would like to know if you've scheduled experiments using PIV in a tank. AUTHOR'S REPLY Yes. Current efforts in the IIHR towing are concerned with the experimental setup and measurement by PIV of the unsteady flowfield at several constant-x stations of the 5512 model. Measurements will begin at x=0.935 (propeller plane) and then proceed to forebody and wake stations. the authoritative version for attribution.