Pressure distribution on a hull in a slanted flow ...

Indeed, as most do, to 'explain' their theory better.

But the point is/was, that Munk moment is associated with the reaction/behaviour of a fully submerged body to an inline flow.
The separation of flow of fluid at the fore body and after body creates the pitch up moment, which if said body has insufficient restoring force, destabilises the body...think sub's and swaths.

A yacht, is not a fully submerged body.

 

I agree. Airplanes with keels make the best boats.

 

I don't know whether this video might help our original enquirer but it might justify a bit of his time to evaluate the possibilities .

 

Munk moment is an inviscid phenomena, not resulting from separation. There can also be a moment due to separation.

MIT Open Course notes: chrome-extension://efaidnbmnnnibpcajpcglclefindmkaj/https://ocw.mit.edu/courses/2-154-m...004/a13938a09eb13e7d8be464545141aaab_lec8.pdf

8.2 Munk Moment
Any shape other than a sphere generates a moment when inclined in an inviscid flow. d’Alembert’s paradox predicts zero net force, but not necessarily a zero moment. This Munk moment arises for a simple reason, the asymmetric location of the stagnation points, where pressure is highest on the front of the body (decelerating flow) and lowest on the back (accelerating flow). The Munk moment is always destabilizing, in the sense that it acts to turn the vehicle perpendicular to the flow. Consider a symmetric body with added mass components Axx along the vehicle (slender) xaxis (forward), and Azz along the vehicle’s z-axis z (up). We will limit the present discussion to the vertical plane, but similar arguments can be used to describe the horizontal plane. Let ∂ represent the angle of attack, taken to be positive with the nose up – this equates to a negative pitch angle δ in vehicle coordinates, if it is moving horizontally.
(See equations in link.)
The added mass terms Azz and Axx can be estimated from analytical expressions (available only for regular shapes such as ellipsoids), from numerical calculation, or from slender body approximation (to follow).

8.3 Separation Moment
In a viscous fluid, flow over a streamlined body is similar to that of potential flow, with the exceptions of the boundary layer, and a small region near the trailing end. In this latter area, a helical vortex may form and convect downstream. Since vortices correlate with low pressure, the effect of such a vortex is stabilizing, but it also induces drag. The formation of the vortex depends on the angle of attack, and it may cover a larger area (increasing the stabilizing moment and drag) for a larger angle of attack. ....​

 

The usual expressions for calculating Munk Moment of regular shapes are for fully submerged flow. The same phenomena exists for bodies which are not fully submerged, but with the added effects of free surface wave generation.

 

Do you have references for such?

 

PNA 1988, Vol III, Section 9.4 Page 238 has a discussion of the differences due to free surface effects.

What is your reference for:

The applicability of the solution for a submerged ellipsoid as shown in Lamb 1945 is a different question than whether the same phenomena with with the added effects of free surface wave generation exist for bodies which are not fully submerged. The latter is what my comment which you quoted was about, not the former.

 

So a yacht, is not a fully submerged body, the vast majority of the time on a good day.

I see your point.

 

Correct.
Since in PNA the authors are attempting to use the Munk moment (and a bastardisation of the theory) to generate hydrodynamic coefficients, for predicting/estimating the control of a vessel.

 

My opinion is that you are both correct within the limits of the direction you approach it from. I still remember the days where this problem would have been solved by sources and sinks and a mirror surface (circa 1984 when I graduated), so it was applicable as the body was effectively "fully submerged". Even recently when I retired (2018) there wasn't a "good solution" to the whole problem of viscous flow pressures on the body surfaces at (or near) the air-water interface under random waves and orientation. Hell, the best we could do was to use model derived coefficients. As I said at the beginning, you could force AeroHydro to do it for a fixed angle in planer water, or conversely you could use WAMIT to give you a moment due to the waves from any angle but no way on. This and the TBL are the next peaks in the mountain range we must overcome.

 

CFD with free surface effects and a 6-dof model could be considered as a good solution?

"This Munk moment arises for a simple reason, the asymmetric location of the stagnation points, where pressure is highest on the front of the body (decelerating flow) and lowest on the back (accelerating flow)." Same appliess even if the body at the interface of air & water, like a sailboat hull?

 

CFD? It all depends. Generally, codes that consider the general pressure over the body due to the flow are calibrated by specific, geometrically simple, theory and model testing...most confined to large Reynolds numbers. So the codes that can do this spit out answers that can be anything from so-so to absolutely horrible when correlated to real-world data on 'general' shapes. CFD is more like Ouroboros than Athena...it devours what it knows rather than springing forth fully ready. Additionally, when dealing with the free surface, there are no codes I know of that deal stochastic waves and body flow at the same time. This would require output in the frequency domain, not a single "answer". So running a "CFD with free surface effects and a 6-dof model" would give you a single pixel in a megapixel picture of response that would be good for that single instance only. You would then need to take all that data and chuck it into stochastic methods to derive confidence values.

I think the point the Ad Hoc was making is that the Munk moment is totally due to the flow, and derivative pressures, about the body. Any wave flow and pressures on the body are going to disrupt this, resulting in a transformed pressure distribution and therefore not a true correlation to the Munk moment.

 

Thanks for that video. For those who haven't seen it - it shows the use of the CFDOF workbench as an interface between CAD and CFD - and it makes setting up a simulation, including meshing, pre- and postprocessing MUCH easier.

I tested it on a simple setup – relatively coarse mesh, generic V-hull, symmetric setup (no angle of attack), and fixed position (no degrees of freedom of movement) – on an old laptop ... after 2 weeks, I aborted the simulation.

To work seriously with CFD, you need really powerful hardware, something like AMD Epyc with 128 cores. A powerful GPU won't help - while there is a GPU fork of Openfoam (RapidCFD), it's based on version 2.3, and Openfoam is at version 7, so many models are not compatible without changing.

The huge advantage of this method is still the computation time - a few hundred unknown source strengths and control points compared to several million 3D cells, each with at least 6 surfaces... despite all the difficulties with frictional flow and turbulence, depending on the problem I still find potential flow methods to be relevant.

Unfortunately, I haven't made much progress in my attempt to replicate the above-cited method of simulating surface waves using potential methods. My math and programming skills are a bit rusty.

 

What is your main interest in terms of asymmetrical hull pressures due to yaw or drift? Is it steady motion, looking at resistance/optimization? estimating motion derivatives? seakeeping? structures? curiosity? Are you more interested in planing or non-planing hulls?

There appear to be a variety of (more and less mature) approaches out there - I might have gone down a bit of a rabbit hole - but the specifics are definitely widely varied depending on the application. I agree the speed of potential-flow methods needs to be in the toolbox even with the impressive capabilities of viscous solvers now.

(Edit to add) Yes, OpenFoam is quite hungry in terms of resources; increasingly there is an implicit assumption that for anything commercial beyond rough problem setup models you are willing to go to cloud-scale these days. However, folks like SimScale (and others) have web-based cloud interfaces and not-terrible a-la-carte pricing after free trial periods.