VORTEX GENERATOR SYSTEM AND METHOD FOR SHIP FORM DRAG REDUCTION

Abstract

A vortex generation system and method for reducing hydrodynamic drag in ships with high block coefficients is disclosed. The system includes a hull and a plurality of vortex generators affixed circumferentially to the hull at locations determined relative to the point of detachment of the boundary layer. Each vortex generator features substantially triangular surfaces with dimensions, such as height, width, and surface area, optimized using a data-driven methodology employing Gaussian Process Regression (GPR). The method iteratively analyzes computational fluid dynamics (CFD) models to identify optimal design parameters, including wedge angle, longitudinal position, and density of vortex generators, which minimize form drag while maintaining low skin friction coefficients. This system significantly enhances fuel efficiency and operational performance by addressing the moving detachment point dilemma and optimizing vortex generator configurations. Applications include marine vehicles and submerged structures, with scalability ensured through calculated scaling factors for full-scale implementation.

Claims

1. A wedge-shaped vortex generator for reducing hydrodynamic drag in a marine fluid environment, comprising: a monolithic body having: an upper face configured with a convex curvature, a base face, a rear face, and a pair of laterally opposed side faces; wherein the body is defined by at least one of: a wedge angle, a wedge elevation angle, a tip-to-base length, and a base bottom width; and wherein the convex upper face is shaped to promote the generation of streamwise vortices by re-energizing an adjacent fluid boundary layer to delay flow separation.

2. The wedge-shaped vortex generator of claim 1, wherein the wedge angle is between 25 degrees and 35 degrees.

3. The wedge-shaped vortex generator of claim 1, wherein the wedge elevation angle is between 15 degrees and 20 degrees.

4. The wedge-shaped vortex generator of claim 1, wherein the tip-to-base length is between 1.0 meters and 1.5 meters.

5. The wedge-shaped vortex generator of claim 1, wherein the base bottom width is between 0.5 meters and 1.0.

6. The wedge-shaped vortex generator of claim 1, wherein the height of the body is between 20% and 40% of a local boundary layer thickness at the mounting location on the hull.

7. The wedge-shaped vortex generator of claim 1, wherein the upper face is convex in a longitudinal direction from the tip to the base.

8. The wedge-shaped vortex generator of claim 1, wherein the monolithic body is formed from a corrosion-resistant metal or composite material.

9. The wedge-shaped vortex generator of claim 1, wherein the base face is configured for direct attachment to a marine hull using mechanical fasteners or welding.

10. The wedge-shaped vortex generator of claim 1, wherein at least one dimension of the body is scaled according to a boundary layer thickness scaling factor.

11. A vortex generator system for reducing hydrodynamic drag in a marine vessel, comprising: a hull; a plurality of wedge-shaped vortex generators affixed to the hull, each vortex generator comprising: a monolithic body having an upper face with a convex curvature, a base face, a rear face, and a pair of laterally opposed side faces, wherein the body is defined by a wedge angle, a wedge elevation angle, a tip-to-base length, and a base bottom width; wherein the plurality of vortex generators are circumferentially arranged around the hull at a predetermined longitudinal position relative to the flow detachment region, and are configured to generate streamwise vortices that re-energize the boundary layer, delay flow separation, and reduce form drag on the hull.

12. The vortex generator system of claim 11, wherein the plurality of vortex generators are spaced circumferentially around the hull at uniform intervals.

13. The vortex generator system of claim 11, wherein the monolithic body of each vortex generator is formed from a corrosion-resistant material selected from the group consisting of stainless steel, aluminum alloys, and composite materials.

14. The vortex generator system of claim 11, wherein the plurality of vortex generators are affixed to the hull using mechanical fasteners, welding, or adhesive bonding.

15. The vortex generator system of claim 11, wherein the longitudinal position of the plurality of vortex generators is determined relative to a point of flow detachment on the hull using a data-driven optimization methodology.

16. The vortex generator system of claim 11, wherein the dimensions of each vortex generator are scaled according to a boundary layer thickness scaling factor.

17. The vortex generator system of claim 11, wherein the number of wedge-shaped vortex generators is calculated as a ratio of a function of a circumference of the hull at the mounting location divided by a base width of an individual vortex generator.

18. A computer-implemented method for optimization of a vortex generation system, comprising: receiving one or more models of the vortex generation system; iteratively analyzing the one or more models utilizing a computational fluid dynamics analysis to determine one or more performance parameters for each of the one or more models; comparing the one or more performance parameters of each of the one or more models; selecting at least one model having a performance parameter of the one or more performance parameters exceeding a first threshold; optimizing one or more dimensions of the at least one model, wherein in the optimizing further comprising: iteratively, varying the one or more dimensions of the at least one model; and testing the varied one or more dimension resulting in at least one performance characteristic for each of the one or more dimensions; and outputting, the one or more dimensions having the at least one performance characteristic exceeding a second threshold.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0016] FIG. 1 is a flowchart of a method of optimizing one or more parameters for Vortex Generator designs, according to aspects of the present invention.

[0017] FIG. 2A is a graphical representation of flow visualization of a bare hull.

[0018] FIG. 2B is a graphical representation of flow visualization of a hull with delta vortex generators.

[0019] FIG. 2C is a graphical representation of flow visualization of a hull with wedge-shaped vortex generators, according to aspects of the present invention.

[0020] FIG. 3A is a schematic diagram of a first Vortex Generator System, according to aspects of the present invention.

[0021] FIG. 3B is a schematic diagram of a second Vortex Generator System, according to aspects of the present invention.

[0022] FIG. 3C is a schematic diagram of a third Vortex Generator System, according to aspects of the present invention.

[0023] FIG. 4 is a front perspective view of a Vortex Generator, according to aspects of the present invention.

[0024] FIG. 5 is a rear perspective view of a Vortex Generator, according to aspects of the present invention.

[0025] FIG. 6 is a view of a first view of a Vortex Generator System, according to aspects of the present invention.

[0026] FIG. 7 is a view of a second view of a Vortex Generator System, according to aspects of the present invention.

DETAILED DESCRIPTION OF THE INVENTION

[0027] The following detailed description is of the best currently contemplated modes of carrying out exemplary embodiments of the invention. The description is not to be taken in a limiting sense but is made merely for the purpose of illustrating the general principles of the invention, since the scope of the invention is best defined by the appended claims.

[0028] Ships, or vessels, possessing a high block coefficient suffer from form drag at their stern, a necklace vortex at their bow, and increased resistance due to trim. Increased drag and/or resistance results in increased utilization of fuel to overcome drag forces. As stated above, vortex generators (VG) can be utilized to reduce drag, however, a plurality of design parameters must be considered in order to provide appropriate form drag reductions. The plurality of design parameters includes a shape, or geometry of a vortex generator, a requisite number of vortex generators to complete the circumference of a hull of the ship, and critically, a longitudinal location of the plurality of vortex generators relative to the point of detachment on the hull, for the plurality of vortex generators. The most critical design parameter with respect to reducing hydrodynamic drag is the relative position of the vortex generators concerning the point of detachment.

[0029] Broadly, an embodiment of the present invention provides a vortex generation system and methods for reducing form drag in a ship traveling through a fluidic environment. The system includes a plurality of vortex generators affixed to the hull of the ship which significantly reduces hydrodynamic drag. Additionally, a data-driven method is provided to determine the most appropriate design parameters, such as wedge angle of a vortex generator, a requisite number of vortex generators to complete the circumference of a hull of the ship, and critically, a longitudinal location of the plurality of vortex generators relative to the point of detachment on the hull, for the plurality of vortex generators. The data-driven method utilizes Gaussian Process Regression (GPR) as the backbone of the data-driven approach. Specifically, a series of iterative computations can be conducted to elucidate the intricate relationship between the plurality of vortex generators design parameters and the ensuing hydrodynamic drag. The GPR model can facilitate a nuanced understanding of the complex interplay between these parameters, effectively addressing the moving detachment point dilemma and aiding in the identification of an optimal design configuration that significantly reduced hydrodynamic drag.

[0030] The data-driven methodology employed in this analysis provided a robust framework for substantiating the optimal configuration of VGs, thereby rendering a clear pathway towards substantially enhancing the hydrodynamic performance of marine vehicles. This invention marks a significant stride in hydrodynamic drag management, showcasing a precedent for employing data-analytic methodologies in marine and hydraulic engineering design processes. The optimized VG configuration, validated through this rigorous analytical approach, promises improved fuel efficiency and operational efficacy in the relevant engineering domains. A submerged axisymmetric body was used for simplicity to demonstrate the principles of VG design, but the methodology is directly applicable to ships and a great variety of surface and submerged vehicles and structures.

[0031] In some embodiments, the configuration of the vortex generators may be adaptable. Vortex generators are inspired from delta wing configurations and have been utilized to move high-speed fluid toward the boundary layer, which can delay or mitigate the thickening of the boundary layer in turbulent regimes. Vortex generators are protrusions with sharp edges, such as wings, or winglets, or wedges, whose surfaces form an angle of attack with respect to the flow, and can generate a streamwise vortex in fluids that re-energize the boundary layer, preventing flow separation and delaying the thickening of the boundary layer. In embodiments, vortex generators can produce streamwise vortices strong enough to overcome the flow separation or thickening at the boundary layer.

[0032] Referring now to FIG. 1, a method of selection and optimization of a vortex generator system 100 is illustrated, according to aspects of the present invention. Vortex generators can vary in one or more parameters related to their design, which impact their ability to reduce drag for the ship on which they are installed. In embodiments, the one or more parameters include, but are not limited to: an overall size of a vortex generator, a height of the vortex generator, a longitudinal position of the vortex generator on the hull, orientation of the vortex generator, a vortex generator density, a hull tail type and/or a location of the vortex generator on the hull.

[0033] As a first step 102, one or more models are generated, including a plurality of hulls, such as an axisymmetric hull, and a plurality of vortex generators, each of the plurality of vortex generators having one or more parameters of the design needing to be analyzed. In embodiments, each of the plurality of hulls have a plurality of vortex generators thereon, wherein the one or more parameters of the plurality of vortex generators varies from hull to hull, but not within a hull. In an exemplary embodiment, the plurality of models include: an axisymmetric hull having no vortex generators, i.e. a bare hull, an axisymmetric hull having a plurality of vortex generators of a first shape, i.e. delta wing vortex generators, and an axisymmetric hull having a plurality of vortex generators of a second shape, i.e. wedge vortex generators. Advantageously for experimentation, an axisymmetric hull model is viewed as a double hull of a surface ship, and can be submerged well below the surface of the water so as not to produce waves, making the investigation much easier as one does not have to deal with the wave resistance.

[0034] As a second step 104, the one or more models are iteratively analyzed utilizing one or more computation fluid dynamics (CFD) analyses to determine one or more performance parameters of the one or more models. In embodiments, the one or more CFD analyses are a Detached Eddy Simulation (DES), and the one or more performance parameters are a skin friction coefficient, Cf. In embodiments, one or more outputs associated with CFD analysis of the one or more models are provided. In embodiments, the one or more outputs are graphical outputs showing the one or more performance parameters of the one or more models. In an exemplary embodiment, FIGS. 2A-2C illustrate the one or more outputs as a flow visualizations of the one or more models and their corresponding skin friction coefficient(s), Cf. Specifically, FIG. 2A illustrates the bare hull model showing very low Cf, reflecting detached flow, and a resulting wake that forms containing unsteady patterns, thereby negatively impacting the performance the hull. Additionally, FIG. 2B, illustrates a hull model with delta wing VGs, which also exhibits a nearly attached flow to the trailing edge and smooth velocity distribution, but with increased skin friction coefficient. Finally, FIG. 2C illustrates hull model with wedge VGs showing an attached flow almost to the trailing edge, combined with low skin frictional coefficient, indicating superior performance when compared to the other models.

[0035] As a third step 106, one or more hull model(s) with a plurality of vortex generators having a performance parameter exceeding a threshold level are validated, utilizing one or more experimental testing methods, such as force and drag measurement, in tow tank testing, to validate performance characteristics. As a result of performance validation, a vortex generator having at least one of the one or more parameters, that perform best according to the performance parameter, is selected for further optimization. In embodiments, the at least one of the one or more parameters is an overall shape of a vortex generator having the higher performance parameter.

[0036] As a fourth step 108, the selected vortex generator has one or more optimization(s) is performed thereon. In embodiments, the one or more optimizations includes varying, iteratively, one or more of: an overall size of the selected VG, a height of the selected VG, a longitudinal position of the selected VG on the hull, orientation of a VG, a VG density, a hull tail type and/or a location of the selected VG on the hull, as illustrated in FIGS. 3A-3C. Optimization is performed using one or more scale hull models having a plurality of scale vortex generators, having the one or more parameters. Additionally, optimization is measured, during each iteration, using one or more optimization parameters, such as net drag reduction.

[0037] As a fifth step 110, each of the one or more optimizations is tested, such as by towing the optimization in a tow tank, measuring one or more parameters, one or more calculations is made and/or visualizing one or more performance parameters. In embodiments, a towing speed is varied, and one or more performance parameters is measured, such as a drag (average, net, or otherwise), which is compared to a baseline configuration, i.e. a bare hull, to determine the one or more calculations, such as a drag reduction percentage for a given optimization of the one or more optimizations.

[0038] As a seventh step 112, the one or more optimizations having desired performance characteristics, such as a desired amount of drag reduction percentage is selected for utilization as the novel vortex generator, illustrated in FIG. 3C. In embodiments, the one or more optimizations are parameters of the novel vortex generator, having the highest overall performance and include, but are not limited to: an overall size of the selected VG, a height of the selected VG, a longitudinal position of the selected VG on the hull, orientation of a VG, a VG density, a hull tail type and/or a location of the selected VG on the hull.

[0039] Because the novel vortex generator is modeled, tested, and optimized, using one or more scale models, including at least one scaled hull and at least one plurality of scaled vortex generators, one or more scaling factors are determined, in order to implement the novel vortex generator. In embodiments, one or more scaling factors are employed to project one or more parameters of the novel vortex generator at full scale. In embodiments, a first scaling factor, , represents the ratio of the length of a full scale vessel, L.sub.S, or ship, to the length of the model, L.sub.M, used for testing, experimentation, and optimization, and is given by:

[00002]$=\frac{L_S}{L_M}.$

[0040] As long as the one or more hull models are double Hull submerged bodies, Froude scaling is not needed, and thus a separate scaling factor, .sub.U, representing the ratio of the full scale vessel speed U.sub.S, to the model speed U.sub.M, is utilized. Using the factors above and the kinematic velocity of the fluid, v, Reynolds numbers for the full scale vessel, R.sub.S, and for the model, R.sub.M are calculated as follows:

[00003]$R_S=\frac{U_S*L_S}{v},\mathrm{and}{R}_M=\frac{U_M*L_M}{v}$

[0041] Reynold's numbers are utilized to estimate a turbulent boundary layer thickness, , for both the full scale vessel, .sub.S, and the model, .sub.M, and is calculated, generally, as follows:

[00004]$0.38\left(\frac{L}{R^{\frac{1}{5}}}\right),$

and .sub.S is related to .sub.M as follows: .sub.S=.sub.M .sup.4/5 .sup.1/5.

[0042] Frictional coefficients for the full scale vessel, C.sub.fS, and for the model, C.sub.fM, are calculated as follows:

[00005]$C_{\mathrm{fS}}\frac{0.0592}{{R_S\left(x\right)}^{\frac{1}{5}}}\mathrm{and}{C}_{\mathrm{fM}}=C_{\mathrm{fS}}\left({}^{\frac{1}{5}}{}_U^{\frac{1}{5}}\right),$

where R.sub.S(x)=Reynolds number a distance, x, from the bow.

[0043] The scaling factor that determines the size, or dimensions of the vortex generators is the boundary layer thickness, .sub.S, at the location of the vortex generator on the vessel's hull. In embodiments, the dimensions of the ship hull scale as , while the VG dimensions scale according to the thickness of the boundary layer . Likewise, the area of the VGs scales as the square of delta, etc. As a result, the VGs in full scale are smaller in proportion to the ship length than at model scale, while more VGs are required overall, in order to keep the relative distance between adjacent VGs in proportion to the model VGs.

[0044] Additionally, the number of vortex generators needed are given by, N, which is a ratio of the number needed at full scale, N.sub.S, and a number need at model scale, N.sub.M, as follows:

[00006]$\frac{N_S}{N_M}=\frac{\sqrt[5]{\left({}_U\right)}}{2}.$

[0045] In an exemplary embodiment, Table 1 illustrates the calculations for one or more Full scale vortex generators utilizing parameters assumed therein:

TABLE-US-00001 Quantity Model Full Scale Length (m) 1.4 294.4 Speed (m/s) 1.3 7.46 Number of VG 15 31 Length of VG (m) 0.028 1.424 Height of VG (m) 0.007 0.356 Surface Area of VG (m.sup.2) 0.000298 0.772 Surface Friction 0.00413 0.01703 Boundary Layer height (m) 0.029 1.475

[0046] FIG. 4-5 illustrate an embodiment of a vortex generator 400 according to aspects of the present invention. Vortex generator (VG) 400 has a shape having a plurality of faces, or surfaces, and is configured to reduce drag by energizing a boundary layer of a medium. In embodiments, VG 400 has one or more design parameters which are determining, and/or optimized, utilizing the data-driven methodology 100 above, for optimal sizing and placement. In embodiments, VG 400 is shaped as a wedge having a plurality of faces, such an upper face 402, a first side face 404, a second side face (not shown), a rear face 502, and a base face 504. In embodiments, VG is symmetric along a longitudinal axis. In embodiments, upper face 402 is curved, or convex, so as to improve energization to the boundary layer.

[0047] Additionally, FIG. 4-5 illustrate one or more parameters optimized by the data-driven methodology 100, such as VG wedge angle A, VG wedge elevation angle B, a tip to base length C, and a base bottom width D. In an exemplary embodiment, the VG wedge angle A, optimized utilizing the data-drive methodology 100, results in an angle of 29.10.2. Additionally, a VG wedge elevation angle B, optimized utilizing the data-drive methodology 100, results in an angle of 17.80.2. Additionally, a tip to base length C, optimized utilizing the data-drive methodology 100, results in a length of 1.424 m. While exemplary embodiments, show specific values, it is understood that the data-driven methodology 100 results in a model with one or more optimized parameters, which are scaled utilizing the equations above.

[0048] FIG. 6-7 illustrates an embodiment of the vortex generation system 600. The vortex generation system 600 includes a hull, or body, 602, and a plurality of vortex generators 604. In embodiments, hull 604 can be axisymmetrical, but is not so limited, as any known hull design can be utilized in the present invention. Briefly, and describe in more detail below, FIG. 6-7 illustrate one or more parameters, or dimensions, of vortex generator system 600 and/or VGs 604. The one or more parameters include, but are not limited to: a VG wedge elevation angle (between arrows of E), a VG length F (also illustrated a reference H in FIG. 7), a VG wedge angle (between arrows of G), a VG wedge base length I, a VG spacing J, a distance from hull midsection K, and a VG height L.

[0049] The plurality of vortex generators 604 each have one or more design parameters such as shape, a VG wedge elevation angle (between arrows of E), a VG length F, a VG wedge angle (between arrows of G), a VG wedge base length I, a VG spacing J, a distance from hull midsection K, and a VG height L, and number of vortex generators necessary, and longitudinal location of the plurality of vortex generators relative to a point of detachment on hull 602, which are determining utilizing the data-driven methodology above, for optimal sizing and placement. In embodiments, the shape of the plurality of vortex generators is a wedge shape, which one or more dimensions of the wedge determined using the data driven methodology above. In embodiments, a data-driven methodology, described hereinafter, can be utilized to determine the most appropriate design parameters for the plurality of vortex generators 604. In embodiments, each of the plurality of vortex generators is place circumferentially around a hull of a vessel, and the placement is at a longitudinal location of the plurality of vortex generators relative to a point of detachment on hull 602 determined by the data-driven methodology above.

[0050] A number of VG required for a vortex generator system on a hull is estimated using a estimation factor. In embodiments, the estimation factor as a ratio of the following general formula:

[00007]$N_{\mathrm{VG}}=\frac{2r}{w_{\mathrm{VG}}},$

where r is the equivalent radius of the hull, and w.sub.VGm is the width of a VG. The ratio giving the estimation factor is given by

[00008]$\frac{N_S}{N_M},$

wherein N.sub.S utilizes r as the radius of the full size hull, and w.sub.VG as the width of the full size VG. Similarly, N.sub.M utilizes r as the radius of the model size hull tested, and w.sub.VG as the width of the model size VG tested.

[0051] The data-driven methodology utilizes GPR to determine relationships between the plurality of design parameters and resulting hydrodynamic drag. Specifically, a series of iterative calculations can be conducted while varying the plurality of design parameters, which results in a GPR model which can be utilized to determine optimal design parameters for the vortex generation system. Advantageously, the GPR model facilitates a nuanced understanding of the complex interplay between design parameters, and effectively addresses the moving detachment point dilemma and aids in the identification of an optimal design configuration that significantly reduced hydrodynamic drag.

[0052] Broadly the methods of the present invention may include one or more computer programs that are executable on a computer system including at least one processor coupled to receive data and instructions from, and to transmit data and instructions to, a data storage system, at least one input device, and at least one output device. Each computer program can be implemented in any suitable manner, including via a high-level procedural or object-oriented programming language and/or via assembly or machine language. Systems of the present disclosure may include, by way of example, both general and special purpose microprocessors which may retrieve instructions and data to and from various types of volatile and/or non-volatile memory. Computer systems operating in conjunction with the embodiments of the present disclosure may include one or more mass storage devices for storing data files, which may include: magnetic disks, such as internal hard disks and removable disks; magneto-optical disks; and optical disks. Storage devices suitable for tangibly embodying computer program instructions and data (also called the non-transitory computer-readable storage media) include all forms of non-volatile memory, including by way of example semiconductor memory devices, such as EPROM, EEPROM, and flash memory devices; magnetic disks such as internal hard disks and removable disks; magneto-optical disks; and CD-ROM disks. Any of the foregoing can be supplemented by, or incorporated in, ASICs (application-specific integrated circuits) and other forms of hardware. The computer systems may include smartphones, tablets, or other similar devices.

[0053] It should be understood, of course, that the foregoing relates to exemplary embodiments of the invention and that modifications may be made without departing from the spirit and scope of the invention as set forth in the following claims.