NSWC Carderock Division

A higher-order algorithm for the numerical integration of one-variable, additive, white-noise equations is developed. The method of development is to extend standard deterministic Runge-Kutta algorithms to include stochastic terms. The ability of the algorithm to generate proper correlation properties is tested on the Ornstein-Uhlenbeck process, showing higher accuracy even with longer step size.

Experimental measurements of the frequency spectra and frequency cross-spectra of the wall pressure fluctuations beneath a turbulent boundary layer were made in a low-noise flow facility. The data, taken over a range of flow speeds, clearly display a dimensionless frequency (ωδ/uτ=50) at which the spectra achieve a maximum and a low-frequency range with an approximately ω2 rolloff. The scaling laws for the low-, mid-, and high-frequency regions of the spectrum are established. The cross-spectral data, obtained over a range of streamwise separations (0.21≤ξ/δ≤16.4), allow for the computations of the decay Γ(ξ,ω) and convection velocity Uc(ξ,ω) of the wall pressure field. These data show the existence of two distinct wave number groups: a high wave number group that scales on the similarity variable k1ξ=ωξ/Uc(ξ,ω) associated with turbulent sources in the log region of the boundary layer, in which eddies decay in proportion to their size, and a low wave number group that defines the cutoff for the large-scale turbulence contributors in the outer region of the boundary layer. The convection velocity data support the conjecture that the major turbulent contributions to the low and high wave number groups come from the outer and inner layers, respectively. These new results, when examined collectively, firmly establish the spectral features of the wall pressure fluctuations, including the low-frequency range, which is highly sensitive to (passive) structures in the outer flow. The locations for the turbulent sources of the wall pressure field are proposed.

Electrochemical impedance results are presented for 550 day exposures of organic‐coated carbon steel samples. Coatings consisted of translucent pigmented and unpigmented epoxy and conventional opaque epoxy polyamide systems. Coating thicknesses ranged from 20 to 185 μm. Specimens were exposed under freely corroding conditions and at two cathodic polarization levels (−850 and −1250 mV vs. SCE) in ASTM artificial ocean water. The objective was to identify impedance parameters which measure subcritical coated‐metal system property changes at early exposure times that predict significant long‐term coating deterioration. Impedance data developed at early times, including coating resistance, coating capacitance, the increase in frequency for the coating's 45° phase angle, and low frequency impedance data, are compared to the coating system's performance after 550 days exposure. Coating performance at 550 days is visually evaluated using ASTM Method D‐610, and a modification of ASTM D‐714. In particular, coating resistance, changes in the frequency for the coating's 45° phase angle, and low frequency impedance data determined at exposure times ranging from 2 to 200 days were found to predict the 550 day coating performance. Relative changes in the electrochemically active surface area were correlated with the frequency of the coating 45° phase angle.

'I'his paper investigates the gains in structural efficiency that can be achieved by aligning the fibers in some or all of the layers in a laminate with the principal stress directions in those layers. The name curvilinear fiber format is given to this idea. The problem studied is a plate with a central circular hole subjected to a uniaxial tensile load. An iteration scheme is used to find the fiber directions at each point in the laminate. Two failure criteria are used to evaluate the tensile load capacity of the plates with a curvilinear format, and for comparison, counterpart plates with a conventional straightline fiber format. The curvilinear designs for improved tensile capacity are then checked for buckling resistance. It is concluded that gains in efficiency can be realized with the curvilinear format.

A new computational capability is described for calculating the sound-pressure field radiated or scattered by a harmonically excited, submerged, arbitrary, three-dimensional elastic structure. This approach, called nashua, couples a nastran finite element model of the structure with a boundary element model of the surrounding fluid. The surface fluid pressures and normal velocities are first calculated by coupling the finite element model of the structure with a discretized form of the Helmholtz surface integral equation for the exterior fluid. After generation of the fluid matrices, most of the required matrix operations are performed using the general matrix manipulation package available in nastran. Farfield radiated pressures are then calculated from the surface solution using the Helmholtz exterior integral equation. The overall capability is very general, highly automated, and requires no independent specification of the fluid mesh. An efficient, new, out-of-core block equation solver was written so that very large problems could be solved. The use of nastran as the structural analyzer permits a variety of graphical displays of results, including computer animation of the dynamic response. The overall approach is illustrated and validated using known analytic solutions for submerged spherical shells subjected to both incident pressure and uniform and nonuniform applied mechanical loads.

The breakpoint frequency method, which allows determination of the electrochemically active area of a coated metal in seawater, is described. A computer model is used to explain the basis of the breakpoint method, and the model is compared to impedance and visual data from epoxy‐coated steel panels in ASTM artificial seawater with and without an intentional defect of known area. The breakpoint frequency method was found to be extremely useful in determining the electrochemically active area of coated steel in seawater. The equivalent circuit model used in this analysis was found capable of fitting actual data on coated steel panels with and without an intentional defect. A correlation was obtained between the breakpoint frequency and visually estimated electrochemically active area on epoxy coatings of a variety of thicknesses. This method offers a simple alternative to determination of defect areas via the use of the pseudocapacitance from difficult‐to‐analyze low‐frequency impedance data. This approach also can detect the beginnings of coating breakdown long before visual indications are present.

In an attempt to develop a systematic series of wave spectra covering a variety of spectral shapes observed in the ocean, this paper presents a newly developed series of wave spectra which involves six parameters. In the development of the six-parameter wave spectra, the spectra are decomposed into two parts. Each part is expressed by a mathematical formula with three parameters, and the total spectrum is expressed by the combination of two sets of three-parameter spectra. Results of analysis have shown that the six-parameter wave spectra thus derived appear to represent almost all stages of development of a sea during a storm. Then, from the statistical analysis of 800 spectra observed at the North Atlantic Ocean, the values of the six-parameters are expressed in terms of significant wave height so that a family of spectra for a desired sea severity can be generated.

The effects of transverse compressional damping on the vibratory response of three-layer elastic-viscoelastic-elastic beams are considered both analytically and experimentally in a mechanical impedance format. The relative importance of this type of damping is assessed by comparison to shear damping mechanisms inherent in the composite using the Mead and Markus model. Results suggest the effects from compressional damping have a relatively narrow frequency bandwidth centered at the compressional (delamination) frequency, omega sub c, of the composite. Compressional damping is shown to have a minimal effect on the transverse damping response of thin three-layer damped beams for frequencies significantly less than omega sub c, where a shear damping model provides a better description of dynamic response. (Author)

A flow circulation in a closed circular-cylindrical container is produced by a rotating lid. After a transient phase from an initial state at rest a steady-flow situation is reached for a certain parameter range. In a subspace of this parameter range an undulating meridional flow occurs that may exhibit at the axis of rotation one or several separation bubbles which are interpreted as vortex breakdown. Numerical calculations on the basis of the Navier-Stokes equations for incompressible homogeneous and Boussinesq fluids enable the study of the influence of various flow parameters on the properties of these separation bubbles. The parameters varied are the Reynolds, Prandtl, Rayleigh, and Eckert numbers together with the ratio of height to radius of the container. The numerical results are in good agreement with experiments performed by Vogel, Ronnenberg, and Escudier. The stability of the fluid motions in these experiments with respect to non-axisymmetric disturbances strongly suggests that the corresponding axisymmetric solutions of the Navier-Stokes equations are stable configurations.

Both a second-order and a fourth-order stochastic extension of standard Runge-Kutta algorithms are developed for colored-noise equations. These algorithms are tested by computing mean first-passage times in a bistable potential driven by colored noise.

Advances in second-order near-wall turbulence closures are summarized. All closures under consideration are based on high-Reynolds-number models. Most near-wall closures proposed to date attempt to modify the high-Reynolds-number models for the dissipation function and the pressure redistribution term so that the resultant models are applicable all the way to the wall. The asymptotic behavior of the near-wall closures is examined and compared with the proper near-wall behavior of the exact Reynolds-stress equations. It is found that three second-order near-wall closures give the best correlations with simulated turbulence statistics. However, their predictions of near-wall Reynolds-stress budgets are considered to be incorrect. A proposed modification to the dissipitation-rate equation remedies part of those predictions. It is concluded that further improvements are required if a complete replication of all the turbulence properties and Reynolds-stress budgets by a statistical model of turbulence is desirable.

Many shipyards now employ line-heating processes to form metal by controlled heating and cooling. The benefits of line-heat forming include improved accuracy and productivity. The current line-heating method utilizes an oxyacetylene torch as the heat input. A new forming technique that uses a high-power laser as the heat source is being researched. The feasibility of forming mild-and high-strength steels with a laser heat input is reviewed. The primary incentives for using a laser are the capability to accurately control the forming process; the capability to minimize the material degradation; the capability to form high-strength steels; and the increased compatibility with other advanced manufacturing systems. In summary, by manipulating the laser power, laser beam diameter, and plate travel speed, one may form metal plates to a predetermined shape in a repeatable manner.

This study examines the feasibility of predicting the fracture toughness for structurally relevant situations (shallow cracks in thick plates) based on toughness values measured with experimentally convenient specimen geometries (deep cracks in small specimens). The cleavage fracture toughness, Jc, of ASTM A515 Grade 70 steel plate was measured using single edge notch bend specimens. Specimen size and initial crack depth were varied to obtain Jc values over a range of constraint conditions. The results of these experiments indicate that crack depth and thickness cannot be traded off against each other to achieve the same constraint and thereby the same fracture toughness. The absence of this simple trade-off is due to the greater effect of crack depth than of specimen size on Jc and to the scatter in fracture toughness data characteristic of temperatures in the transition range. Alternative techniques for determining structurally relevant toughness measures from specimens based on recently proposed constraint parameters were therefore examined. These various parameters divide into two categories: those which index constraint and those which correct for constraint. Application of these constraint parameters to the A515 data indicate that all of the currently proposed techniques can account for the constraint-induced changes in cleavage fracture toughness. However, the feasibility of applying these techniques during a structural fracture safety assessment depends upon the experimental complexity and cost associated with fracture toughness determination and the ease with which the constraint parameter can be calculated for a structure.

Recent experimental and flight test programs have developed and confirmed the high lift capability of the Circulation Control Wing (CCW) concept. These CCW airfoils employ tangential blowing of engine bleed air over circular or near circular trailing edges, and are capable of usable lift coefficients triple those of simple mechanical flaps. Earlier versions of these blown airfoils made use of relatively complex leading and trailing edge devices which would have to be retracted mechanically for cruise flight. In a continuing program to reduce the complexity, size and weight of the CCW system, several series of advanced CCW airfoils have been developed which can provide STOL capability for both military and commercial aircraft using much smaller, less complex high lift systems. This paper describes these configurations and presents the experimental results confirming their aerodynamic characteristics. Comparisons to previous CCW and more conventional high lift systems are provided.

The Naval Sea Systems Command has recently certified a lower-cost alternative steel to the HY-80 steel presently used in construction of naval surface ships. This alternative steel is based on the commercial development of high strength low alloy (HSLA) steels originally directed to the offshore oil exploration platform and gas line transmission industries. The certification is a result of an ongoing research and development program begun in 1980. This paper addresses several aspects of the HSLA steel development effort, including a discussion of the properties and metallurgy of this steel, and the cost savings which are achievable. Finally, the status of the current and planned Navy HSLA usage and the R&D program is described.

Work and power optimization of a Brayton cycle are analyzed with a finite-time heat transfer analysis. This work extends the recent flurry of publications in heat engine efficiency under the maximum power condition by incorporating nonisentropic compression and expansion. As expected, these nonisentropic processes lower the power output as well as the cycle efficiency when compared with an endoreversible Brayton cycle under the same conditions.

This study presents a simple, accurate, and efficient method for numerically evaluating the Green function, and its gradient, of the theory of water-wave radiation and diffraction. The method is based on five expressions for the Green function that are useful in complementary regions of the quadrant in which the Green function is defined. These expressions consist of asymptotic expansions, ascending series, two complementary Taylor series, and a numerical approximation based on a modified form of the Haskind integral representation. The four series representations are refinements of the series obtained previously in Noblesse [1].2 These series express the Green function and its gradient as sums of power series and terms involving functions of only one variable. The power series can be evaluated quickly by using recurrence relations; and the functions of one variable, by using rational approximations. The method permits the Green function and its gradient to be evaluated with an absolute error smaller than 10–6 very efficiently (with computing time less than 6 × 10–5 sec on a CDC CYBER 176 computer). A listing of the FORTRAN subroutine is included in the paper.

The identification of power flow paths in dynamically loaded structures is an important, but currently unavailable, capability for the finite element analyst. For this reason, methods for calculating power flows and mechanical intensities in finite element models are developed here. Formulations for calculating input and output powers, power flows, and mechanical intensities for beam and plate/shell element types are derived. NASTRAN is used to calculate the required velocity, force, and stress results of an analysis, which a post-processor then uses to calculate power flow quantities. Test models include a simple truss and a beam-stiffened cantilever plate. Both test cases showed reasonable power flow fields over low to medium frequencies.

Three indirect methods for characterizing the drag of an arbitrarily rough surface on a flat plate are derived or rederived from the similarity laws of turbulent shear flows. These are:the well-known procedure using displacement thickness;the probably not-so-well-known procedure using total drag; anda proposed new procedure using only the freestream velocity and a local shear stress. The classical indirect procedure for pipe flow is also derived to show a commonality with the flat-plate methods.

Experiments were performed to investigate some aspects of turbulence in rotating and non-rotating fluid systems where the turbulence was induced by a horizontal grid oscillating vertically. An earlier theory by the second author made use of a planar source of energy, which appeared to be similar to the energy source of the grid, in determining the characteristics of the turbulence at points some distance away. The simplicity of the theory was in the parameterization of the grid ‘action’ by a single quantity K , with dimensions and characteristics of eddy viscosity. The experimental results provide additional confirmation of the theory in the non-rotating case, and indicate the usefulness of the idealized energy source in the rotating case. In the latter, we measured the propagation of the front separating disturbed and undisturbed fluid, moving along the axis of rotation. The thickness d(t) of the disturbed region increases at first as ( Kt ) ½ , as in a non-rotating fluid, until the Rossby number K /Ω d 2 k becomes of order unity. Beyond this the disturbances are wavelike and rotationally dominated, and the thickness now increases linearly with time, yielding a speed of propagation for the front proportional to the wave speed ( K Ω) ½ . Finally, the disturbances reach the bottom and the vessel is in statistical steady state. Then a region of thickness d k independent of time is found, and it contains motion that resembles ordinary, three-dimensional turbulence. d k ∼ ( K /Ω) ½ is analogous to the depth of the turbulent Ekman layer H ∼ ( K /Ω) ½ , where K is taken as an eddy viscosity. McEwan constructed a similar rotating experiment, although with a different energy source, and observed vortices parallel to the axis of rotation, provided that the Rossby number was less than a critical value. Our observations and theory indicate that the disappearance of the vortices corresponds to h < d k , where h is the total depth of the fluid. At that point, the whole tank is filled with three-dimensional turbulence.