4.2, there will be no problems resolving the free surface flow. Neither will there be a problem resolving the viscous full scale flow in a RANS method with the same resolution as presently at model scale. Accurate full scale RANS calculations with a free surface thus seem feasible.

Even more exciting are the prospects for less approximate solutions of the Navier-Stokes equations. Large eddy simulations (LES) should be more exact than RANS, since only the smaller eddies, which are more universal, i.e. less dependant on the boundary conditions, need to be modelled. Ultimately, even direct numerical solutions (DNS) may be feasible. In a recent paper one of the authors (Larsson (23)) estimated the computational effort required for LES and DNS solutions at model and full scale Reynolds numbers. The estimate was based on the assumption that the smallest scale of the flow, the Kolmogorov turbulence scale, should be resolved. Following Wilcox (59) and assuming that the boundary layer thickness could be set equal to half the channel height, experience from channel flow calculations could be utilized The estimate took into account the number of grid points as well as the number of time steps required, but it did not consider the lateral extension of the hull surface. Considering this, the effort for model scale LES will be 104–105 times that of a RANS solution today. For DNS the increase will be 106–107 times. LES is thus likely to be possible before 2010 on super computers. Within another decade model scale LES might be possible on workstations and DNS on super computers. At that stage the accuracy of the CFD predictions will have passed that of the towing tank.

6. Conclusions

In this review the present status of CFD in ship hydrodynamics has been assessed. Ongoing research has been reviewed and the short term benefits of the research has been evaluated. Long term developments relying on increases in computer capacity have been outlined. The main conclusions are:

  1. At present, the most useful CFD results are offered by the potential flow panel methods which are used extensively for the optimization of hull shapes. Optimization of cruiser stern shapes should be avoided, however.

  2. The optimization is normally based on the predicted waves and hull pressure distribution. Wave resistance coefficients may be used as well at higher speed but should not, at present, be trusted at low speeds (below Fn=0.2, say).

  3. RANS methods can predict integrated quantities of the wake reasonably well, while the details cannot be obtained accurately.

  4. The viscous resistance obtained by RANS methods is accurate enough for ranking purposes, provided care is exercised in the generation of the grid, particularly at the hull ends.

  5. The body force approach is common for representing the propeller and many methods are capable of predicting the propeller/hull interaction.

  6. Great efforts are being made to improve the grid generation and one interesting approach is the Chimera technique, which facilitates the inclusion of appendages.

  7. Many free surface RANS methods are now available. The normally predict the hull wave profile quite well, but cannot predict the Kelvin wave pattern due to insufficient resolution. This problem will be removed thanks to the increase in computer power.

  8. Turbulence modelling is the key issue in the prediction of the wake details. Full Reynolds stress models have shown very promising results, but some less demanding methods have been almost as accurate. Simple corrections have shown promise as well, at least for the few cases where they have been applied.

  9. Several methods for predicting the flow around an operating propeller have been presented. In general, quite accurate propeller characteristics are obtained. Two methods have been applied to the propeller operating in the behind condition, with promising results.

  10. Full scale RANS calculations suffer from numerical problems due to very high aspect ratio cells, but some methods are capable of handling the problem. The small viscous length scale calls for a very high resolution close to the hull and this is presently achieved by extreme stretching. This may reduce accuracy, but this is a problem to be resolved by the rapidly increasing computer power. Standard turbulence models seem to be capable of predicting flows at very high Reynolds number.

  11. The rapidly increasing computer power will enable both LES and DNS solutions to be obtained at model scale within the foreseeable future. Most likely, the accuracy will then be higher than in experimental facilities.


(1) HESS, J.L.; SMITH, A.M.O (1962) Calculation of non-lifting potential flow about arbitrary three-dimensional bodies, Douglas Aircraft report No ES 40622

(2) DAWSON, C. (1977) A practical computer method for solving ship wave problems, 2nd Int. Conf. on Numerical Hydrodynamics, Berkeley

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