An asymmetric truncated concave parabolic fin is analyzed using a two-dimensional analytical method. In this analysis, the variation in the ratio of the top surface temperature to the bottom surface temperature along the fin length is presented. Heat loss from each surface and that from the fin are shown as a function of the convection characteristic number and the fin base height. The ratios of heat loss from each surface to that from the fin are given as a function of the actual fin length. The relationship between the convection characteristic number and the fin base height, as well as that between the actual fin length and the fin base height, are presented for equal amounts of heat loss. One of the results shows that the effect of fin base height variation on heat loss from the fin bottom surface and on heat loss from the fin tip surface is negligible when the actual fin length is fixed.

A concave parabolic fin with vertically cutting fin tip and variable fin base thickness is analyzed using a two-dimensional analytic method. Heat loss is presented as a function of the actual fin length, the ratio of the actual fin length to the imaginary fin length, the fin base height, and the convection characteristic number. Also, heat loss is shown as a function of the fin base thickness for both the fixed actual fin length and the fixed actual fin tip length. For equal amounts of heat loss, the relationships are presented between 1) the convection characteristic number and the fin base height, 2) the fin base thickness and the fin base height, and 3) the fin base thickness and the actual fin tip length. One of the results shows that the heat loss for the fixed actual fin tip length decreases more remarkably than that for the fixed actual fin length as the fin base thickness increases. (C) 2021 Elsevier Ltd. All rights reserved.

: Heat loss and fin efficiency of symmetric and asymmetric trapezoidal fins with variable slope of fin's top surface are obtained by using a two-dimensional analytic method. Shapes of symmetric and asymmetric fins are changed from rectangular through trapezoidal to triangular by adjusting the fin shape factor. The ratio of symmetric trapezoidal fin length to asymmetric trapezoidal fin length is presented as a function of fin base height and convection characteristic number. The ratio of symmetric trapezoidal fin efficiency to asymmetric trapezoidal fin efficiency is presented as a function of the fin base height and fin shape factor. One of results shows that asymmetric trapezoidal fin length is shorter than symmetric trapezoidal fin length (i.e., asymmetric trapezoidal fin volume is smaller than symmetric trapezoidal fin volume) for the same heat loss when the fin base height and fin shape factor are the same. Key words : Symmetric trapezoidal fin(대칭 사다리꼴 핀), Asymmetric trapezoidal fin(비대칭 사다리꼴 핀), Convection characteristic number(대류특성계수), Fin shape factor(핀 형상계수), Fin efficiency(핀 효율)

Numerical simulations using computational fluid dynamics are frequently applied to analyze complex flow fields. However, they have to be validated by matching simulation results to those from canonical flows or experimental measurements. The objective of the present research is to compare results from numerical simulations and wind tunnel measurements for air wakes generated behind ships' superstructures to those from direct in situ measurements. Numerical simulations are performed using COBALT on an unstructured grid system, wind tunnel data are collected from a 4%-scale model, and in situ measurement data are sampled using ultrasonic anemometers mounted above an aft flight deck on a 32.9-m (108 ft)-long research vessel. Reynolds numbers are closely matched for all three approaches concurrently. Two different incoming velocity conditions are compared: a head wind condition and wind 15 degrees off the starboard bow (beta = 0 degrees,-15 degrees, respectively, where beta is the wind yaw angle). Differences in velocity and boundary layers between the three approaches are resolved using unique velocity normalization. The flow structures between beta = 0 degrees and beta = -15 degrees are quite different, i.e., there appears to be strong asymmetric vortical structures over the flight deck for beta = -15 degrees. In general, in situ, computational, and wind tunnel data all show large-scale recirculation motion behind the ship's hangar. However, there are nonnegligible differences between the simulations and wind tunnel measurements compared to the in situ measurements. Differences in velocity angles increase with the yaw angle of the incoming flow.

Geometrically asymmetric trapezoidal fins with variable slope of fin’s top surface are optimized for fixed fin volumes. Convection from the inside fluid to the inside wall, conduction from the inside wall to the fin base and conduction through the fin base are considered simultaneously for the fin base boundary condition. For fixed fin volumes, the optimum heat loss, the corresponding optimum fin length, and fin base height are presented as functions of the fin base thickness, inside fluid convection characteristic number, fin volume, fin shape factor, and ambient convection characteristic number. The optimum values between 1-D and 2-D analyses are compared. One of the results shows that both the optimum fin length and fin base height decrease with the increase of the fin shape factor.

This paper describes a set of turbulence measurements at sea in the area of high flow distortion in the near-wake and recirculation zone behind a ship's superstructure that is similar in geometry to a helicopter hangar/flight deck arrangement found on many modern U.S. Navy ships. The instrumented ship is a 32-m-long training vessel operated by the United States Naval Academy that has been modified by adding a representative flight deck and hangar structure. The flight deck is instrumented with up to seven sonic anemometers/thermometers that are used to obtain simultaneous velocity measurements at various spatial locations on the flight deck, and one sonic anemometer at bow mast is used to characterize inflow atmospheric boundary conditions. Data characterizing wind over the deck at an incoming angle of 0 degrees (head winds) and wind speeds from 2 to 10 m s(-1) obtained in the Chesapeake Bay are presented and discussed. Turbulent statistics of inflow conditions are analyzed using the Kaimal universal turbulence spectral model for the atmospheric surface layer and show that for the present dataset this approach eliminates the need to account for platform motion in computing variances and covariances. Conditional sampling of mean flow and turbulence statistics at the flight deck indicate no statistically significant variations between unstable, stable, and neutral atmospheric inflow conditions, and the results agree with the published data for flows over the backward-facing step geometries.

This paper provides an update on a multiyear research project that involves the systematic investigation of ship air wakes using an instrumented research vessel. The object is to validate Computational Fluid Dynamics (CFD) tools that will be useful in determining ship air wake impact on rotary wing aircraft. Currently, ship launch and recovery wind limits and envelopes are primarily determined through at-sea in situ flight testing that is expensive and frequently difficult to schedule and complete. The 108-foot long research vessel is modified to include a flight deck and hangar-like structure to produce air wake data similar to that from a modern destroyer. The research vessel is equipped with three-component ultrasonic anemometers to collect air wake data. Repeated underway testing has been performed to collect in situ data while wind tunnel testing has been also performed on a 4% scale model of the research vessel. Comparison of in situ data from above the flight deck, with similar data from wind tunnel testing and CFD simulations, shows good agreement in velocity direction for a headwind condition and for winds 15 and 30 off the starboard bow. Off-ship air turbulence data collected with an instrumented radio-controlled helicopter shows that an off-ship air wake is present where predicted by CFD simulations. Analysis indicates that CFD simulations likely require modeling of the atmospheric boundary layer to improve simulation accuracy.

In situ air velocity measurements in the near wake of a Navy training ship are presented for an inflow of 15 to starboard. This data is required for the validation of ship airwake simulations, which are used to determine the launch and recovery envelopes for shipborne rotorcraft and for use in piloted flight simulations. The measurements are taken primarily above an aft flight deck, which sits immediately behind a step-like hangar structure. A description of the mean flow structure is included, as well as the Reynolds stresses at numerous points along the ship centerline. Comparisons are made between the present 15 case and the case of a direct headwind, presented previously. Compared to the 0 inflow condition, the flow symmetry is clearly broken with a cross-wind. The port and starboard sides of the deck have very different mean flow profiles and turbulent stress components. An updraft is visible over much of the starboard side of the flight deck, which is not found on the port side, or on either side under a headwind. Along the centerline, the streamwise normal component of the turbulent stresses are much larger in the cross-wind case than in the headwind case, while the shear components have similar magnitudes. This suggests that the wake turbulence is similar, but that in the cross-wind case the flight deck is more heavily burdened by inflow fluctuations from the atmosphere.

The temperature distribution of an asymmetric trapezoidal fin with various upper lateral surface slopes is investigated by using the two-dimensional analytic method. For this asymmetric fin, convection from the inner fluid to the inner wall, conduction from the inner wall to the fin base and conduction through the fin base are considered simultaneously. The temperature profile with the variation of dimensionless fin length and height coordinates is shown. Also, the temperature variation at the bottom tip of the fin is presented as a function of the fin shape factor. Heat losses through the fin base and from each side are compared for variations in fin length. One of the results shows that temperature at the fin bottom tip decreases linearly as the fin shape factor increases.

For large wind farms, kinetic energy must be entrained from the flow above the wind turbines to replenish wakes and enable power extraction in the array. Various statistical features of turbulence causing vertical entrainment of mean-flow kinetic energy are studied using hot-wire velocimetry data taken in a model wind farm in a scaled wind tunnel experiment. Conditional statistics and spectral decompositions are employed to characterize the most relevant turbulent flow structures and determine their length-scales. Sweep and ejection events are shown to be the largest contributors to the vertical kinetic energy flux, although their relative contribution depends upon the location in the wake. Sweeps are shown to be dominant in the region above the wind turbine array. A spectral analysis of the data shows that large scales of the flow, about the size of the rotor diameter in length or larger, dominate the vertical entrainment. The flow is less incoherent below the array, causing decreased vertical fluxes there. The results show that improving the rate of vertical kinetic energy entrainment into wind turbine arrays is a standing challenge and would require modifying the large-scale structures of the flow. Such an optimization would in the future aid recovery of the wind turbine wake towards conditions corresponding to the undisturbed atmospheric boundary layer.

Two-dimensional Particle Image Velocimetry (2-D PIV) measurements were performed to study the effect of free-stream turbulence on the flow around a smooth and rough surface airfoil, specifically under stall conditions. A 0.25-m chord model with an S809 profile, common for horizontal-axis wind turbine applications, was tested at a wind tunnel speed of 10 m/s, resulting in Reynolds numbers based on the chord of Re c ≈ 182,000 and turbulence intensity levels of up to 6.14%. Results indicate that when the flow is fully attached, turbulence significantly decreases aerodynamic efficiency (from L/D ≈ 4.894 to L/D ≈ 0.908). On the contrary, when the flow is mostly stalled, the effect is reversed and aerodynamic performance is slightly improved (from L/D ≈ 1.696 to L/D ≈ 1.787). Analysis of the mean flow over the suction surface shows that, contrary to what is expected, free-stream turbulence is actually advancing separation, particularly when the turbulent scales in the free-stream are of the same order as the chord. This is a result of the complex dynamics between the boundary layer scales and the free-stream turbulence length scales when relatively high levels of active-grid generated turbulence are present.

위 측면 표면 기울기가 변화하는 비대칭 사다리꼴 핀의 최적화가 2차원 해석적 방법을 사용하여 수행된다. 고정된 핀 바닥 높이에 대하여 최적 열손실, 핀 길이 그리고 유용도가 내부유체 대류특성계수, 핀 바닥 두께, 핀 바닥 높이, 핀 형상계수 그리고 주위 대류특성계수의 함수로 나타내어진다. 이러한 최적화 절차를 위해서 핀으로부터의 최대 열손실 값의 95%를 최적 열손실 값으로 정의하였다. 결과 중 하나는 최적 열 손실과 유용도는 핀 형상계수의 변화에 독립적으로 보이는 반면 최적 핀 길이는 핀 형상계수가 증가함에 따라 거의 선형적으로 감소함을 보여주고 있다. Optimization of the asymmetric trapezoidal fin with various upper lateral surface slope is made using a two-dimensional analytic method. For the fixed fin base height, the optimum heat loss, fin length and effectiveness are represented as inner fluid convection characteristic number, fin base thickness, fin base height, fin shape factor and ambient convection characteristic number. For this optimum procedure, the optimum heat loss is defined as 95% of the maximum heat loss from the fin. One of the results shows that optimum heat loss and effectiveness seems independent of the fin shape factor while optimum fin length decreases almost linearly as the fin shape factor increases.

An experimental study of interactions between a high Reynolds number fluid flow and multi-scale, fractal, objects is performed. Studying such interactions is required to improve our current understanding of wind or ocean current effects on vegetation elements, which often display fractal-like branching geometries. The main objectives of the study are to investigate the effects of the range of scales (generation numbers) of the fractal object and of the incoming flow condition on the drag force and drag coefficient, and to observe flow features in the near wake region resulting from the interaction. In this study, Sierpinski carpets and triangles with the scale ratios of 1/3 and 1/2, respectively, are employed. The fractal dimensions of the Sierpinski carpet and triangle are D = 1.893 and 1.585, respectively. Each pre-fractal object is mounted on a load cell at the centerline in a wind tunnel. Two types of inflow conditions are considered: laminar flow and high-turbulence level, active-grid-generated, flow. As a first approximation, we find the drag coefficients are approximately constant of order unity, and do not depend upon generation number of the pre-fractal when defined using the actual frontal area that varies as function of generation number. Still, the drag coefficient of the Sierpinski carpet increases weakly with number of generations indicating that the drag force decreases less than the cross-sectional area. For the Sierpinski triangle a similar trend is observed at large scales. However, the drag coefficient displays a peak at the third generation and then shows a decreasing trend as smaller scales are included for higher generation cases. The drag coefficient for the turbulent flow is larger than that for the laminar flow for all the fractal generations observed. Flow features (mean velocity, mean vorticity, and turbulence root-mean-square distributions) are measured by using stereoscopic Particle Image Velocimetry to observe various scales of the motion in the near wake of the pre-fractal objects. Strong shear layers are formed behind the fractal objects depending on the hole locations of different generations, which results in the formation of various length scales of the dominant turbulence structures. The smaller scale wakes are found to merge behind the Sierpinski carpet, whereas they are merely damped behind the Sierpinski triangle.

Velocity measurements in a ship airwake are obtained in situ aboard a 108 ft naval training vessel. The measurements and analyses aremotivated by the need for validation data for airwake computational fluid dynamics simulations. Three-component anemometers are placed above the bow of the ship and at numerous locations above a flight deck at the stern of the ship. Data are presented for a direct headwind (nominally 0 deg wind-over-deck). The mean velocity field shows a clear structure to the flow, dominated by a recirculation region in the near-wake of a hangar-like backward-facing step. The location of this primary vortex and the reattachment point on the flight deck are estimated. Reynolds stresses are presented to quantify the turbulent fluctuations, which are required for the prediction of unsteady loading on rotorcraft operating in this environment. Significant anisotropy is measured in the wake, both within the primary vortex and in the far field. The peak Reynolds shear stress is located in the recirculation region, while the streamwise normal stress is found to increase with height throughout the measurement domain. Finally, autoand two-point velocity correlations from the flight deck provide an estimate of flow scales, showing the potential influence of turbulence on piloted helicopter operations.

This paper provides an overview of a multi-year research project that involves the systematic investigation of ship air wakes using an instrumented United States Naval Academy (USNA) YP (Patrol Craft, Training). The objective is to validate and improve Computational Fluid Dynamics (CFD) tools that will be useful in determining ship air wake impact on naval rotary wing vehicles. This project is funded by the Office of Naval Research and includes extensive coordination with Naval Air Systems Command. Currently, ship launch and recovery wind limits and envelopes for helicopters are primarily determined through at-sea in situ flight testing that is expensive and frequently difficult to schedule and complete. The time consuming and potentially risky flight testing is required, in part, because computational tools are not mature enough to adequately predict air flow and wake data in the lee of a ship with a complex superstructure. The top-side configuration of USNA YPs is similar to that of a destroyer or cruiser, and their size (length of 108 ft and above waterline height of 24 ft) allows for collection of air wake data with a Reynolds number that is the same order of magnitude as that of modern naval warships, an important consideration in aerodynamic modeling. A dedicated YP has been modified to add a flight deck and hangar structure to produce an air wake similar to that on a modern destroyer. Three axis acoustic anemometers, fog generators and an inertial measurement unit have been installed. Repeated testing on the modified YP is being conducted in the Chesapeake Bay, which allows for the collection of data over a wide range of wind conditions. Additionally, a 4% scale model of the modified YP has been constructed and tested in the 42×60×120 inch USNA wind tunnel. The project involves USNA midshipmen who are participating in test planning, collecting and analyzing data, and in CFD modeling, providing the midshipmen with valuable professional and research experience. Comparison of YP in situ data with similar data from wind tunnel testing and CFD simulations shows reasonable agreement for a headwind condition and for wind 15° off the starboard bow.

This paper provides current results of a multi-year research project that involves the systematic investigation of ship air wakes using an instrumented United States Naval Academy (USNA) YP (Patrol Craft, Training). The objective is to validate and improve Computational Fluid Dynamics (CFD) tools that will be useful in determining ship air wake impact on naval rotary wing vehicles. This project is funded by the Office of Naval Research and includes extensive coordination with Naval Air Systems Command. Currently, ship launch and recovery wind limits and envelopes for helicopters are primarily determined through at-sea in situ flight testing that is expensive and frequently difficult to schedule and complete. The time consuming and potentially risky flight testing is required, in part, because computational tools are not mature enough to adequately predict air flow and wake data in the lee of a ship with a complex superstructure. The top-side configuration of USNA YPs is similar to that of a destroyer or cruiser, and their size (length of 108 ft and above waterline height of 24 ft) allows for collection of air wake data with a Reynolds number that is the same order of magnitude as that of modern naval warships, an important consideration in aerodynamic modeling. A dedicated YP has been modified to add a flight deck and hangar-like structure to produce an air wake similar to that on a modern destroyer. Three-axis acoustic anemometers, fog generators and an inertial measurement unit have been installed. Repeated testing on the modified YP is being conducted in the Chesapeake Bay, which allows for the collection of data over a wide range of wind conditions. Additionally, a 4% scale model of the modified YP has been constructed and tested in the 42×60×120 inch USNA wind tunnel. Comparison of YP in situ data with similar data from wind tunnel testing and CFD simulations shows reasonable agreement for a headwind condition and for a relative wind 15° off the starboard bow. Analysis of in situ data and wind tunnel data for a 30° relative wind also show reasonable agreement, though with a greater deviation than in the 15° relative wind condition. Furthermore, analysis indicates that CFD simulations require modeling the velocity profile in the atmospheric boundary layer to improve simulation accuracy.