Proceedings of the Sixth International Conference on Numerical Ship Hydrodynamics (1994) / Chapter Skim
Currently Skimming:
Session 13- Lifting-Surface Flow: Unsteady Viscous Methods
Session 13- Lifting-Surface Flow: Unsteady Viscous Methods
Pages 683-738
The Chapter Skim interface presents what we've algorithmically identified as the most significant single chunk of text within every page in the chapter.
Select key terms on the right to highlight them within pages of the chapter.
From page 685... ...
Much research has been devoid to analytical and approximate numerical methods for predicting these forces and there has been considerable success with these approaches. However, with the recent dramatic increases in the speed of computers and the advent of parallel computers, direct numerical simulations of unsteady flows through marine propulsors are becoming increasino feasible.
|
From page 686... ...
In the limit where the pseudo-time step size is infinite, this method is nearly the same as the Newton iteration scheme of Athavale & Merkle t83. The TAP method provides an incompressible flow solution which is a very good approximation of a low Mach number flow.
|
From page 687... ...
Due to the variation in the degree of parallelism during Me course of the forward and backward sweeps, Me maximum achievable parallel efficiency decreases as the number of processors increases. The present approach is by no means the optimal one, but it does produce good results on a moderate number of processors and was easy to implement Parallel Timing Results Figure 2 shows the parallel speed-up obtained win different numbers of processors for an implementation of an ~prox~te LU factorization, similar to that discussed here.
|
From page 688... ...
The various symbols denote runs with differing grids or boundary conditions. Figure 3 shows some parallel timing results obtained with the present code.
|
From page 689... ...
A time step size of AtV/c=0.025 was used in all of the presented results. Figure 6.
|
From page 690... ...
The value of He phase was also checked against the theoretical value for several of the ins estigated cases, and was similarly [Lund to be in good agreement Flapping Foil Detailed measurements of the flowfield about a foil experiencing unsteady time harmonic gusts have recentl~ been performed at the Marine Hydrodynamics Laboratory at MIT t15, 16,j, and have been the subject of an ONR sponsored work shop at which comparisons between the experimental results and numerical simulations were presented [173. The gusts were created by placing two small "flapping', foils in the water tunnel upstream of a larger stationery foil about which the measurements were made.
|
From page 691... ...
We note that the inflow boundary of this grid is quite close to the leading edge of the stationery foil, in order to keep the flapping foils outside of the computational domain. _ _ _ Figure 10.
|
From page 692... ...
is considered. We observe, however, that Me unsteady velocity field introduced by the flapping foils differs substantially from that of such a transverse gust.
|
From page 693... ...
is the initial position of the vortex center. Id, 1 A The boundary velocities were perturbed consistent with the potential flow about such a vortex in the absence of the foil, and the nominal position of the vortex was convected, at each time step, with the uniform frees~eam.
|
From page 694... ...
P Delpero, T~vestiganon of Flows around a Two Dimensional Hydrofoil Subject to a High Reduced Frequency Gust Loading, SM thesis, Massachusetts Institute of Technology, Department of Ocean Engineering, February 1992.
|
From page 695... ...
The strength of the vortex is computed from the measured steady velocity field. · Three unsteady vortices, each representing one of the two moving foils or the unsteady lift component on the fixed foil.
|
From page 696... ...
Computing the Wake Induced Velocity Eq. A-4 is evaluated numerically over a finite extent of the wake.
|
From page 697... ...
where we will take the real part of Eq.
|
From page 699... ...
The solutions give similar overall agreement with the data for both steady and unsteady flow, which demonstrates that such problems can be handled with a variety of formulations, although the boundary data, cpu time, and storage requirements are different. The physics are complex with analogy to Stokes layers and explicated through analysis of the axial pressure gradient, which exhibits upstream and downstream traveling waves over the foil and in the near wake and in the intermediate wake, respectively, due to nonlinearities induced by the convective acceleration and steady/unsteady interactions.
|
From page 700... ...
The situation is similar for oscillating external flows where model problems such as flat-plate boundary layers (i.e., Stokes-layer overshoots, phase angles, and streaming) both for laminar and turbulent flow [101 and foils embedded in transverse gusts t11]
|
From page 701... ...
utilized in [19,201 was developed with the capability of unsteady-flow calculations, only very limited such calculations had previously been performed. In the following, an overview is given of the equations and coordinate system, turbulence model, discretization and velocity-pressure coupling, solution domains and boundary conditions, and grid generation.
|
From page 702... ...
The coupling of the velocity and pressure fields in an efficient time-accurate fashion required changing from a SIMPLER algorithm, which requires global iterations for time accuracy, to a split-operator approach based on the PISO algorithm. The first step is to implicitly solve the momentum equations given the pressure field from the previous time step using (181.
|
From page 703... ...
The interpolation coefficients and holes and hole boundaries were determined a priori for each time step. Figure 4 shows global and detailed views of the overlaid grid system.
|
From page 704... ...
The flappers oscillated with an amplitude of 6° and a frequency of 16 Hz. The corresponding Re based on the foil chord length and reference velocity 20.94 ft/sec is 3.78x106 and the reduced frequency is k = 3.6 Velocity and surface-pressure measurements were made using a two-component laser Doppler velocimeter and miniature pressure transducers, respectively.
|
From page 705... ...
Lastly, for each domain, transition was fixed by forcing the eddy viscosity upstream of the boundary-layer trip to zero. Time-step sensitivity studies were conducted for sd which showed that approximately 50 time steps/period provided a time-step independent solution.
|
From page 706... ...
However, the level of agreement for the solutions without and with the pressure-gradient modifications appears to be a general assessment of the current capabilities of isotropic turbulence models since it is consistent with the overall results reported in the literature. Unsteady Flow Figure 5 includes Id and cd first-harmonic amplitude (U', Vie and phase (by, lo,)
|
From page 707... ...
Figure 16 shows the perturbation axial pressure-gradient contours at the same time steps as figure 15. Comparison of the figures indicates the direct correspondence between the flow pattern and axial pressure gradient, i.e., the flow directions are consistent with the regions of favorable and adverse gradients.
|
From page 708... ...
The physics are complex with analogy to Stokes layers and are explicated through analysis of the axial pressure gradient, which exhibits upstream and downstream traveling waves over the foil and in the near wake and in the intermediate wake, respectively, due to nonlinearities induced by the convective acceleration and steady/unsteady interactions. The nature of the unsteady displacement thickness suggests viscous-inviscid interaction as a possible mechanism for the axial pressure-gradient response.
|
From page 709... ...
13. Katz, Y., Nishri, B., and Wygnanski, I., "The Delay of Turbulent Boundary Layer Separation by Oscillatory Active Control," AIAA 2nd Shear Flow Conference (AIAA 89-0975)
|
From page 710... ...
39. Choi, J.E., "Role of Free-Surface Boundary Conditions and Nonlinearities in Wave Boundary Layer and Wake Interaction," Ph.D Thesis, The University of Iowa, December 1993.
|
From page 711... ...
Flapping-foil experiment geometry and solution domain boundaries.
|
From page 712... ...
il\ o ll oOl`I _ o-W ~ )
|
From page 713... ...
0.03 0.02 0.01 0.00 0.o3r 0.02 0.01 0.00, 0.04 0.08 ul 0.03 0.02 i ~1 0.01- '~ 0.00 lJ 1.25 u.uso 0.000 v.~ - v ~ 0.025 ~0.000' r 0.025 0.000 x/C" 0.389 x/C" 0.611 )
|
From page 714... ...
pressure side Figure 11. Unsteady surface-pressure distribution: first and second harmonics.
|
From page 716... ...
tune = 0T -()
|
From page 717... ...
time = OT _ time= 1/ST C_ time = 4/ST ma__ _._ Figure 16. Perturbation axial pressure-~adient contours: td~p/~,~soluiion.
|
From page 718... ...
360 180 n -lsa -36C 360 180 o -180 -360 y 360 180 o -180 -360 O U U.5 1.U 1.5 0.O U.5 1.U 1.5 xlL y _ _ _ y u1 PX]
|
From page 719... ...
In principle, if the boundary conditions are correct, the small domain solution should be most accurate as it eliminates any uncertainty or inaccuracy associated with outer regions. However, since available experimental data are sparsely distributed, the boundary conditions for the small domain calculation are supplemented by using the tunnel domain calculation.
|
From page 721... ...
Experimental data was taken in the flowfield near the stationary foil as well as on ~ foil itself. The numerical computations were pelfo~ed on the entire experimental domain, including the flapping foils, through the use of a two~iimensional muldblock unsteady incompressible Navier-Stokes algorithm based on artificial compressibility.
|
From page 722... ...
A steady state solution is first obtained and then motion of the flapping foils is initiated by boundary conforming dynamic grids that move in pitch with the flapping foils at a reduced frequency of 3.62 based on the half-chord of the stationary foil. The grid extends approximately two stationary foil chord lengths upstream of the leading edge of the stationary foil and five stationary chord lengths downstream of the trailing edge of the stationary foil.
|
From page 723... ...
(2) in two dimemianal computational space m~ay be written as eQ + 6,fE~4 Ev)
|
From page 724... ...
Although originally developed for compressible flow, this approximate Riemann solver can also be implemented in artificial compressibility formulations for incompressible flow (additional details may be farad in Reference (1011. AI1 essential ingredient af Roe's solver is the construction of a matrix A (hi, qR)
|
From page 725... ...
(13) dlat the eigenvalues and left and r~ght eigenvectors of ~e Roe matr~x must be known in order to perform thc numerical flux calci~lation.
|
From page 726... ...
Recall that the original intent was to devel~ the eigensystem of the flux Jac~ian matrices A and B Having generated the eigensystem ~ x, the eigensystem of the flux Jacobians can be obtained as follows.
|
From page 727... ...
This formulation is used for bow steady state and unsteady solutions. The iterative nature of Newton's method will insure the compatibility of the computed pressure field and the divergence-free velocity field for unsteady calculations.
|
From page 728... ...
It can be seen that the numerical flux at a cell face, say i + 1/2, will be a function of Me mews at i + 1/2 and the dependent variables on either side of the cell face. The same statement applies to the viscous flux vector if ~ cross-denvative terms are not included In its evaluation.
|
From page 729... ...
= b (45) where now z(°' ~ O but is the solution from the previous time step.
|
From page 730... ...
~ Experimental Ices ~1 ~1 ~ Dynamic Grid Botnda" Figure 3. Experimental Locations and Dynamic Grid Boundaries The efficiency of reconstructing a new and at each time step to track the movement of He flapping foils is the primary concern for a dyIlamic grid.
|
From page 731... ...
The boundary layer on He stationary foil (both He suction and pressure sides) was tripped at a distance 0£0.105 chord length from the leading edge, while the boundary layer on the flapping foils and tumlel walls was treated as completely Tent.
|
From page 732... ...
The stadcpressures were measured at different locations than the velocities. The upstream static pressures were measumd at 0.266 chord length in front of the leading edge of the stadona~y foil, while the downstream static pressures were measure at 0.156 chord length behind the trailing edge of the sta80na~y foil.
|
From page 733... ...
A minimum nondimensional time step of 8.7xlO~ was used, which corresponds to 1000 time steps per period of motion for the flapping foils. The Jacobian matrix was updated every cycle and three Newton iterations were performed at each time step.
|
From page 734... ...
The amplitudes al the unsteady surface pressure distribution compare favorably for bow the suction and pressure side, while the overall trend of the phase is captured. Figure 11 contains mean velocity profiles from the suction and pressure side.
|
From page 735... ...
Mem Velocity Profiles OQ2 0.01 on 0 4~3n nil 0.42 -^~ 0.02 0.01o n' on 0.63 Q.2 0.01 20-60 735 .....
|
From page 736... ...
Unsteady Velocity Profiles First Harmonic CONCLUSIONS A tw~dimensional muldblock unsteady incompressible Navier-Stokes algorithm based on ar~cial compressibility has been presented. The unsteady solution was obtained using a dynamic grid that was regeneratM at each time step in order to mimic tiLe motion of the flapping foils.
|
From page 737... ...
10. Taylor, LO., "Unsteady Three-Dimensional Incompressible Algorithm Based on Artificial Compressibility," PhD Dissertation, Mississippi State University, May 1991.
|
From page 738... ...
27. Beak, D.M., '`Three-Dimensional Euler Equations Solutions on Dynamic Blocked Grids," PhD Dissertation, Mississippi State University, August 1986.
|
Key Terms
This material may be derived from roughly machine-read images, and so is provided only to facilitate research.
More
information on Chapter Skim is available.