Resistance and Propulsion

Transcription

1 MASTERS DEGREE IN NAVAL ARCHITECTURE AND PROPULSION Resistance and Propulsion Calculation of the Potential Flow around a Ship with a panel method Program DAWSON0 1

2 Resistance and Propulsion Calculation of the Potential Flow around a Ship with a Panel Method Programa DAWSON0 1. Objectives The proposed practical assignment aims at exposing the students of the Resistance and Propulsion course to the different aspects of the numerical calculation of the flow around a ship. To this end the students have access to the computer code DAWSON0 that includes a panel method for the calculation of the steady, incompressible, irrotational and inviscid flow around ships without free surface boundary conditions (double body). Although the mathematical model incorporated in DAWSON0 is the simplest one that could be adopted to address ship flows, the available code gives the opportunity to perform Code and Solution Verification exercises. Furthermore, the surface pressure distribution and the external flow field obtained in inviscid flow conditions provide sufficient information to discuss qualitatively the properties of the wave system and wake flow of the real viscous (wavy) flow. Predictions of the viscous flow around the same ship are also provided. Therefore, three different tasks are proposed for this work: 1. Perform a Code Verification exercise, i.e. select a geometry that has a known exact solution (as for example a sphere) and demonstrate that the discretization error tends to zero with grid refinement. Furthermore, determine the asymptotic order of grid convergence. 2. Calculate the flow around a ship and estimate the numerical uncertainty of the solution (Solution Verification) for relevant flow quantities. 16 geometrical similar grids are provided to the students. 3. Based on the potential flow field around the (double body) ship and the viscous flow solutions, discuss qualitatively the wave system and the wake flow of the real viscous flow around the ship with free surface boundary conditions. 2. Panel Method: Program DAWSON0 Program DAWSON0 includes a panel method based on linear combinations of singularity distributions, which guarantees that the normal velocity component at the collocation point of each panel is zero (boundary condition). The method adopted uses the sources/sinks formulation proposed by Hess and Smith [1]. The main features of the numerical method are: 1. Flat panels. 2

3 2. Sources/sinks distributions of constant strength in each panel. 3. Collocation point (location where boundary conditions are satisfied) at the panel centroid. 4. Influence coefficients matrix determined analytically for the near-field and with multi-pole expansions for the intermediate and far fields. 5. Iterative solver in the solution of the system of linear equations. 6. Velocity vector and pressure coefficient (Bernoulli s equation) calculated at the collocation points. 7. Extra locations may be defined to determine velocity and pressure. However, distance to the body surface should be larger than the closest panels. The present application of the program explores (using the method of images) the existence of two symmetry planes: the symmetry plane of the ship (body) and the still water plane. This means that only half of the immersed part of the ship needs to be discretized. In the coordinate system of DAWSON0, x is the longitudinal direction, y is the vertical direction and z is the transverse (horizontal) direction. The implementation of the method of images assumes that the symmetry plane of the ship is located at z=0 and that the still water plane is at y=0. 3. Input and output files of DAWSON0 DAWSON0 requires three input files: a simple formatted file with one line identifying the name of the second input file; a formatted file with the control parameters of the calculation and the surface structured grid that defines the geometric discretization; a formatted file with the coordinates of the external locations where the velocity and the pressure coefficient are calculated. It must be emphasized that the panels for the geometric discretization are constructed from points defined along cross-sections or longitudinal sections of the ship (body), which must include the same number of control points for each line. Furthermore, the order of the input points (bow to stern or bottom to top versus stern to bow or top to bottom) must ensure that the normal to each panel points outwards. This means that the rotation between the four vertices of each panel must be anticlockwise. Therefore, one must be careful with the introduction of the surface grid that defines the ship geometry. On the other hand, the external locations are also defined in a structured grid but with no special orientation. The output of DAWSON0 includes three files in TECPLOT format: a file with the coordinates of the vertices of the panels; a file with the coordinates, velocity components and pressure coefficient at the collocation points; a file with the velocity components and pressure coefficient at the required external locations. 3.1 Input files dawson0.in file 3

4 is: This is an ASCII formatted file that includes a single line. A typical example 'MODEL' 'xxxx' This means that the code will open the file geomxxxx.dat to read the main calculation options and the surface grid that defines the ship (body) geomxxxx.dat file This file is also an ASCII formatted file that contains the following information: Line 1: KOP1 Line 2: KOPP Line 3: NCL,NCOL,MAXCON Line 4: NCL Do J=1,NCL NCONT Do I=1,NCONT XP(I,J),YP(I,J),ZP(I,J) End do End do The meaning of the variables is the following: Input Variable Type Description KOP1 Text Header KOPP Text Header NCL Integer Number of contours NCOL Integer Number of collocation points (NCL-1)*(NCONT-1) MAXCON Integer Maximum number of points of the NCL contours MAXCON=NCONT NCONT Integer Number of points for each contour XP(I,J),YP(I,J),ZP(I,J) Real Dimensionless coordinates for panel definition. XP longitudinal; YP vertical and ZP horizontal Offptsxxxx.dat file This file contains the coordinates of external locations where the solution is to be computed. It is an ASCII file with the following information: Line 1: NOF NFIELD 4

5 Line 2: NPLANE,NY,NZ do K=1,NPLANE do J=1,NY do I=1,NZ XF(I,J,K),YF(I,J,K), ZF(I,J,K) The meaning of the variables is the following: Input Variable Type Descrição NFIELD Integer Total number of exterior locations. NFIELD=NPLANE NY NZ If NFIELD=0, no action is taken NPLANE Integer Number of planes with extrenal grids NY Integer Number of points in J direction. NZ Integer Number of points in K direction. XF(I,J,K),YF(I,J;K),ZF(I,J,K) Real Dimensionless coordinates of locations to compute velocity and pressure field 3.2 Output files All output files are written in TECPLOT format to facilitate plotting Painelxxxx.dat file This file includes the geometric discretization Velpresxxxx.dat file This file includes the coordinates and the velocity vector and pressure coefficient at the control points Velcampoxxxx.dat file This file includes the velocity components and the pressure coefficient at the selected external location. References [1] Hess, J., Smith, A.M.O., Calculation of Nonlifting Potential Flow About Arbitrary Three-Dimensional Bodies, Journal of Ship Research, September 1964, pp [2] Katz, J., Plotkin, A., Low-Speed Aerodynamics, McGraw-Hill,