Functionality: The propeller Vortex Lattice Method QCM developed at HSVA is tailored to predict the cavitation induced pressure fluctuations. It is an in-viscid approach which is modeling all relevant flow features via a complex vortex system. This may be divided into bound vortices and trailing or shed vortices, where the former system is assembling the unknowns (individual vortex strengths to be solved for). In the unsteady case, the method is simulating the moving blades via a time stepping procedure.
Features: In the 2D case, QCM manages to get the right pressure for a plate at a certain angle of attack using just 2 vertices and 2 control points (Lan, 1974). The clue for this behavior is the special arrangement of vortices and control points. For a 2D wing it is the so called ‘cosine-spacing’. For a 3D wing the double cosine spacing turned out to be beneficial, i.e. extending the chord-wise arrangement to the span-wise direction (Fig. 1).
One basic property of QCM is the very genuine approach for setting up the boundary conditions which determine the system of linear equations to be solved. QCM is velocity based, i.e. the boundary condition applied at the lifting surface control points just request, that the sum of onset-velocities and induced velocities should result to zero normal components (‘normal’ to be understood as the direction perpendicular to the lifting surface).
Generally, considering the propeller case, the method is capable to take into account details related to pitch, chord and camber of the blade geometry in a true 3D manner. Solely the blade thickness, which is not too essential in the propeller case, is modeled in a 2D way.
Figure 1: The control point / vortex lattice arrangement of qcm
Experience and recommendations: By using QCM, Nakamura (1985) calculated open water characteristics of various propellers in good agreement with experimental results, and established a method for estimating open-water characteristics of unconventional propellers, e.g. contra-rotating, controllable pitch and tandem propellers. Chao and Streckwall (1989) have compared their calculations with other theoretical methods and measurements, showing also good agreement. It is however also possible to set up a Vortex Lattice Method with other arrangement of singularities and control points, which was demonstrated by Kerwin and Lee (1978) as well as Greeley and Kerwin (1982).
As mentioned above, QCM can be used to compute the propeller performance also for unsteady inflow condition as for instance present behind the hull (Fig. 2). However, we do not provide a procedure, which ‘updates’ a nominal inflow due to the presence of the propeller. This lack of strictness can be justified as follows. Formally a contraction of streamlines may result into a modified wake, which could be called the effective wake distribution and which should be more suitable to assure the right thrust at a given speed and RPM. Fortunately, if the nominal flow at the propeller plane is available and propulsion tests can be referenced which give the thrust coefficient KT at the desired ship speed, it is straight forward to correct the nominal wake implicitly by requesting a KT-matching. To enforce the agreement of given and calculated KT no complex manipulation of the nominal wake is required. It is just necessary to introduce a modified reference speed (usually higher than the ship speed) if the nominal wake is given in the typical normalized form, i.e. ship speed based.
The viscous effect of the propeller blades are considered in QCM via empirical correction taking into account the profiles viscous resistance. This approach may be called a ‘strip method’ as relevant Reynolds numbers are derived for every blade strip showing a control point radius in its center.
More details about the method are given in the report by Streckwall (1997).
Figure 2: In-behind pressure results obtained by qcm
Figure 3: Cavitation results obtained by qcm
Software + Licensing: Covering the fully wetted propeller flow, the effect of cavitation on the blade surface and the influence of the hull, HSVAs QCM is delivered as 2 modules:
- The propeller program qcm (Quasi Continuous Method) solves the unsteady fully wetted propeller flow and calculates the sheet cavitation on the blades. For simplicity, cavitation is treated in a 2D manner, but iteratively i.e. enforcing a match of constant (vapor) pressure below the cavity and simultaneously a streamline parallel to the rigid surface at the end of the cavity. The latter condition may sometimes also referenced as ‘open cavity model’, they are displayed however with a kind of elliptical closure to provide a suitable picture for a cavitation extent plot (Fig. 3). The results describing the cavitation extent and volume are added to the singularity system from the fully wetted solution.
- The program sbfs (Solid Boundary Free Surface) determines, how the hull and the free surface effect the propeller pressure field which is due to the combined action of the singularities from the fully wetted and cavitation solutions.
We supply this program system on an unlimited license base. As indicated in Fig. 4, the system of interacting programs (modules generating lattices and assuring imports are not cited in detail here) is supported by a Graphical User Interface (GUI). A manual describes the propeller/hull program system.
Figure 4: The GUI confirms the submitted wake components when invoking an unsteady qcm analysis
Chao, K. Y. and Streckwall, H. (1989): Berechnung der Propellerumstroemung mit einer Vortex-Lattice Method, Jahrbuch der Schiffbautechnischen Gesellschaft, Band 83, 1989
Greeley, D. S. and Kerwin, J. E. (1982): Numerical Methods for Propeller Design and Analysis in Steady Flows. SNAME Transactions, Vol. 90, 1982
Kerwin, J. E. and Lee, C. S. (1978): Prediction of Steady and Unsteady Marine Propeller Performance by Numerical Lifting-Surface Theory. SNAME Transactions, Vol. 86, 1978
Lan, C. E. (1974): A Quasi-Vertex-Lattice Method in thin Wing Theory, (E), J. of Aircraft, Vol. 11.
Nakamura, N. (1985): Estimation of Propeller Open-Water Characteristics Based on Quasi-Continuous Method. Joun. Of the Soc. Of Nav. Arch. of Japan, Vol. 157, 1985
Streckwall, H. (1997): Description of a Vortex Lattice Method for Propellers in Steady and Non Steady Flow. Hamburgische Schiffbau-Versuchsanstalt GmbH. Nr. 18/97. Hamburg.