Hydrodynamic performance of planing craft with interceptor-flap hybrid combination

Abstract

Different innovative ideas on simple stern fixtures such as stern wedges, flaps, interceptors have evolved over the past few years to improve the hydrodynamic performance of high-speed vessels, including planing crafts. This paper examines the hydrodynamic performance of a planing craft fitted with an interceptor alone and also an interceptor-flap combination at its stern, and the results are compared with the case where the craft uses the interceptor alone. An interceptor-flap combination is the one where an interceptor extends vertically downward at the transom with a flap attached to its end. Different angular orientations of the flap attached to interceptor bottom end and project towards aft are considered in the present study. The effectiveness of the integrated interceptor-flap system on the hydrodynamic performance of the vessel is influenced by the angular orientation of flap to the interceptor. Experiments were carried out on a planing hull with and without interceptor in the towing tank, Department of Ocean Engineering, Indian Institute of Technology Madras. Computational fluid dynamics (CFD) simulations are performed for the planing hull fitted with an integrated interceptor and flap. The investigations look into the aspects of vessel resistance, trim and bottom pressure distribution while it operates in calm water condition and at different speeds. The results show that trim and resistance of the vessel reduce with the use of integrated interceptor-flap at the stern with the flap angle at about 4° to the horizontal and they are less compared with a case where the only interceptor is used.

Appendix A

1.1 Grid, iterative and time-step convergence verification study

The response variables, which are analysed in the simulations are the total resistance coefficient (C_T), pressure resistance coefficient (C_F), wetted surface area (S_W) and running trim (τ). The resistance coefficients are evaluated using the formula:

$$ C_{{\text{T}}} = R_{{\text{T}}} /0.5\rho S_{{\text{W}}} V^{2} , $$

(8)

$$ C_{{\text{F}}} \, = \,R_{{\text{F}}} /0.5\rho S_{{\text{W}}} V^{2} . $$

(9)

The response variable S_W representing the wetted surface is estimated using the distribution of volume fraction of water (α) over the hull surface. The statistical convergence is estimated by calculating the difference of the mean obtained from the time history of the response variable in the asymptotic window with the mean in the last oscillation. The running mean of oscillations is less than 0.85% of the mean value for all response variables across the cases.

The grid convergence studies are performed using three progressively refined grids called Grid-A, B and C which are coarse, fine and finest, respectively, the cell count for each successive refinement increases approximately by a factor of √2; the details are given in Table 3.

Table 14 Grid dependency study for various response variables

The data obtained from grid dependency analysis is given in Table 14; the analysis uses the correction factor method from prescribed by Stern et al. (2001). It is established that the condition for monotonic convergence is achieved since for all the response variables considered, the grid convergence ratio (R_G) is less than one. The grid uncertainty parameter (U_G) shows the grid uncertainity for various variables such as C_T, C_P, trim and S_W in percentage. C_G denotes correction factor and P_G is the order of accuracy for various response variables. The statistical convergence is estimated by calculating the difference of the mean obtained from the time history of the response variable in the asymptotic window with the mean in the last oscillation. The running mean of oscillations is less than 0.8% of the mean value for all response variables across the cases.

Inner iterations are performed for convergence of solution in each time step and the iterative uncertainty is defined based on Stern et al. (2001). Table 15 shows the iterative uncertainty for all the response variables using Grid B at a speed of 25 knots. This study executes the simulations with ten inner iterations.

Table 15 Iterative convergence study for the Grid B at 25 knots speed (U_I values are a percentage of the solution with 10 inner iterations)

To obtain the time step uncertainty this study generates three solutions using the ratio of √2 between succeeding time steps. Table 16 shows the time step convergence analysis. The study performs simulations using corresponding Grid B which show that the convergence ratio (R_G) is less than unity, indicative of monotonic convergence towards the time step. The time step uncertainty for C_T and C_P is less than 0.6% for the mesh.

Table 16 Time step convergence analysis for a time step ratio √2 at a design speed of 25 knots (grid B)

1.2 Validation

The validation of simulations follows the method based on Stern et al. (2001). It estimates the error between simulation results (S) and experimental data (D) namely, the comparison error (E) and the validation uncertainty (U_V) in it. Here uncertainty U_V is the combination of experimental uncertainties (U_D), simulation uncertainties (U_SN) and input uncertainty (U_Input). Simulation error and uncertainty have components from modelling, numerical and input elements. The modelling error is due to assumptions and approximations of the simulation model in representing the physical phenomena. The numerical error is introduced due to numerical computations based on the governing equations and the input error is due to the errors in the simulation input parameters.

$$ E = D - S = \delta_{{\text{D}}} - \left( {\delta_{{{\text{SM}}}} + \delta_{{{\text{SN}}}} + \delta_{{{\text{input}}}} } \right), $$

(10)

$${U}_{\mathrm{V}}^{2}={U}_{\mathrm{SN}}^{2}+{U}_{\mathrm{D}}^{2}+{U}_{\mathrm{input}}^{2}.$$

(11)

The uncertainty in the input data is related to the body geometry, and fluid parameters such as density and viscosity. It is assumed that the input uncertainty is negligible in comparison to other numerical uncertainties.

If │E│ < U_V i.e., the error lies within the validation uncertainty, then validation is achieved for this uncertainty level.

If │E│ > U_V i.e., the error lies outside the validation uncertainty, then validation has not been achieved for this uncertainty level and therefore, there is a need for improving the simulation modelling.

Fig. 21

Comparison between validation uncertainity and error

Figure 21 displays the validation uncertainity and error comparison. It shows that │E│ < U_V i.e., the error lies within the validation uncertainty, then the validation is achieved for this uncertainty level.