Update added on 2015.05.17; check out the near the end of this post.
* * * * * * * * * * * * * * *
More on the project ideas:
In my last post [^], I had given a description of 3 different ideas for student projects. I would be interested in guiding all these projects in the near future, once I get a suitable job.
If you had gone through my earlier post about my current research interests [^], you would have sure noticed how the project idea no. 2 and 3 relate to my current research in computational modeling of the ceramic injection moulding (CIM) process.
These ideas are basically meant to provide reliable experimental bench-marks for validating separate aspects of the software that I will be writing. (I am still considering and reconsidering the issue of whether to write the software starting from the scratch, or only adapt/extend OpenFOAM.)
The project idea no. 3 (viz., paste-filling in cavity) completely keeps out the aspects of heat transfer and phase transformations, and instead selectively focuses on the aspect of mould-filling using a non-Newtonian material. Thus, if the momentum equations are handled right, predictions about the progress in the filling and the instantaneous shapes of the front at different times would be accurate. If not, the software would have to address only the momentum equations, but with better models/parameter values for the wall friction, viscosity, and surface tension.
In contrast, the project idea no. 2 (viz., melting of wax by a source) tries to selectively focus on the heat transfer and phase transformation aspects, but without significantly involving any momentum transport. (It is anticipated that the symmetry of the configuration means that convection within the molten wax would not be of much significance. However, this part, too, will have to be carefully looked into, at a later stage.)
The CIM process itself involves a liquid-to-solid phase transformation. In contrast, what the idea no. 2 models is the opposite phase transformation, viz., from solid-to-liquid. However, it does have a travelling interface. If the software handles the energy equation, the phase-transformations, and the motion of the liquid-solid interface right, then the speed of the interface should get predicted accurately. If not, the software development work would have to selectively focus only on this part.
Thus, the two project ideas split up the CIM process into two different parts. The reason is the complexity of such problems—the accurate predictions of the instantaneous positions of the moving boundary.
I was only partly successful while comutationally modeling the melting snowman (which I did during my PhD research). The software I wrote had qualitatively predicted the evolution of the shape right, but the speed of the evolution was quantitatively off the mark. I therefore knew that I had to further simplify even just this much part: of transient heat transfer, phase transformation and moving interface, but without any momentum exchanges involved in it. The project idea no. 2 tries to do precisely that: simplify just the heat-related part even further.
In the case of the melting snowman, the outer boundary happens to be the singular location where all the action happens: heat enters, phase-transformation occurs, and then, importantly, the resulting liquid gets drained away, traveling under gravity over the outer surface, and in the process exposing a new surface for the heat to enter, and also moving back the phase-transformation interface. The process thus has a kind of a loop built into it, and so, despite the apparent simplicity, from a modeling viewpoint, it actually is quite complex. Something went wrong with the timings at which the successive processes took place in the simulation. But I could not reliably locate precisely where; I didn’t have any experimental data to be able to do so. My experimentation was too simple; I could not get funds for instrumented data logging, and therefore, I had to remain content with just photographically capturing the outer profiles at successive instants; continuous monitoring of temperatures at various points within the volume of the snowman was not possible.
The current project idea tries to rectify the situation. It reduces the complexity a bit further, by completely doing away with the draining part—the molten wax remains in the jar.
However, in the process, I now realized, the experimental part has become perhaps a bit too simple for a project at the ME level. Some more work could be thrown in. So, here are two possibilities:
1. Also model solidification of wax (instead of only its melting). The liquid-to-solid is anyway the direction of the phase transformation in the actual CIM process.
The simplest model to try would be just to take an instrumented jar, pour some molten wax in it, and let it solidify. If the predictions for the solidification front—its shape and size at various times—are accurate enough, then well and good.
Realize that the project idea no. 2 (viz., wax-melting using a rod for heat input) remains absolutely essential, because experimental errors involved in determining the geometry of the phase transformation front are minimal in it: the boundary of the front has a very simple geometry (ideally, circular on the top surface), and its biggest section remains at the top surface, and therefore easily visible, throughout the process. For both these reasons, its motion would be very accurately measurable. In contrast, in solidification studies, the shape of the solidification front would remain more complicated. Further, since the front would lie interior to the block, it would not be as easy to measure ina continuous nondestructive manner.
2. Another idea is related to bench-marking and testing. I will later on post this part (may be with a little additions and editing) on iMechanica and CFD-related fora, so as to solicit some informal comments about it. Let me note down a preliminary description here, in the next section.
* * * * * * * * * * * * * * *
A new software benchmark-cum-shopfloor test:
In CFD, the utility of suitable bench-marks is well-established. Think of some typical cases: flow through a converging-diverging channel, flow at a corner or at a T-joint, lid-driven flow with formation of vortices at the corners, flow past an obstacle or over a step and the resultant vortex shedding, the Ahmed body, the Rayleigh-Taylor instability, the dam-break simulation, the falling droplet, etc. These have proved very helpful in validating CFD techniques and software codes/packages—at least for comparing different packages against each other. The idea I propose is in a similar vein.
The proposed experiment is very simple to perform, and yet, it is expected to be very useful. At least I am convinced about its utility enough that I have decided to write a short journal paper on it, just for proposing this test—I mean just for putting forth only the idea of the test, without performing any experimentation/simulation involving it.
Here is the idea.
Take a small solid object, say, a ball-bearing ball made of alloy steel, or a small machined cube of copper, or a small cone of brass. (The surface roughness would need to be specified.)
Hold the object at a suitably high temperature for a sufficiently long of time that it develops a steady temperature throughout its section. Or, assuming that it initially has been at the room temperature for a sufficiently long time, now place it inside a furnace (or over a hot-plate) of a well-controlled constant temperature for a specified period of time. Basically, the idea is that we come to specify the entire temperature profile of the object.
Take a block of wax of a specified grade i.e. material properties. (Shape and size is to be given some thought, and the issue is to be finalied after some preliminary experiments.) Drill a small hole of a specified shape and size at the center of its top surface. The size of the hole should slightly exceed that of the heated small object.
Place the block snugly fitting inside a well-insulated enclosure (of specified dimensions and material/properties). Or, may be, just place it on a ceramic tile on the laboratory table. (This in fact should work better.)
Rapidly take the small object out of the furnace (or from the hot plate) and gently place it in the hole drilled in the block of wax.
Initially, the hot object will give off its heat to the air above and to the portions of the wax block surrounding it, and so, the wax will melt locally. The object being heavy will displace the molten wax underneath, and thus it will slide deeper into the block. The molten wax will rise from the side-ways. The object will soon get completely covered with a layer of the so-molten wax now convected also onto its top surface. Simultaneously, the column of the molten wax above the object will begin to solidify from the top, by giving off its heat to the air as well as to the surrounding unmolten portions of the block. Also, the heat of the object will continue to get transferred to the wax, and so, its own temperature will go on dropping down, even as it slides down. All these processes will continue until a time when the temperature of the object goes below the melting point of the wax, and so, unable any more to melt the wax, it will come to a stand-still. All of the molten wax wouldn’t have solidified by this time, and so, so we have to wait a little longer for this to happen.
Then (i.e., after waiting for sufficient time), carefully cut through the block, and measure the shape of the region of the wax affected by the heat—in particular, the depth of penetration.
The software should be able to accurately predict the extent of the heat-affected zone, esp. its depth, say as measured by the penetration depth of the object.
This experiment is very simple to perform—it involves no instrumentation. Yet it yields a very specific measure, viz., the extent of the heat affected zone, and most particularly, the depth of the penetration.
However, the process involved in the test is expected to pose a sufficiently difficult case for any CFD software to handle. There is transient heat transfer in two different phases, two successive phase transformations (solid-to-liquid, and then, also liquid-to-solid), convection of liquid wax, buyoancy effects for both the molten wax and the hot object, and motion of the solid-liquid interface. Yet, the overall geometry remains simple enough.
In CFD, people have been studying things such as rising of bubbles and rising/falling of droplets of a second-phase fluid. The process here is somewhat similar.
It is anticipated that during the experimentation, the test should also show good repeatability, provided the wax is homogeneous, and different blocks carry the same material properties.
For processes such as the CIM, the proposed test should be of definite help in two completely different ways: not just as a benchmark for validating software, but also in industrial practice, as a convenient shop-floor test for characterizing the feedstock (i.e. for the routine process quality-control purposes).
For the latter purpose, the feedstock would have to be pressed into the form of a block. This may be achieved via simple cold-pressing, say by filling the feedstock in a container of a square base and then simply placing a specified weight on its top for a specified period of time. These aspects need to be looked into and finalized after some preliminary experimentation.
* * * * * * * * * * * * * * *
Update added on 2015.05.17:
This update concerns the software benchmark. A couple of points occurred to me after publishing the post.
1. Note the difference of this test from the hot penetration test of bitumen, or the hot hardness test of metals.
In the proposed test here, the hot object gets completely immersed within the wax block. We are interested not only in melting, but also in the relative motion between the hot and cold objects even as cooling takes place simultaneously. Further, we are also interested in solidification. Finally, unlike those two tests, we are not interested in measurements of forces.
(Indeed, when I thought of this idea, the hot hardness/penetration tests were not even in my peripheral awareness; I was just trying to have as simple a test suitable for processing like CIM, as might be possible.)
2. On the second thoughts, completely doing away with instrumentation may not be such a good idea.
Going by my experience of simulating the melting snowman (as well as my browsing of the transient simulations, and their experimental validations), I think that if this test is to be used as an experimental benchmark for software validation (rather than just as a quick quality-control test on the shopfloor), then it should also specify measuring the precise positions of the hot object at different times, and not just the final depth of penetration it reaches.
In other words, the software should be able to predict the times required to reach the intermediate positions, too, accutately. The intermediate times would come out right only if the software handles the entire process right.
Coming to timings, we should not ask only for the final time when the object comes to a rest. After all, it is possible that the computational technique is such that it errs on the intermediate timings, but it does so in such a way that these errors get cancelled out, and so, the total time taken for the object to come to a rest still is predicted right. Such computational techniques will still not be reliable for modeling the actual CIM processing. So, the time-position profile is of primary importance.
Since the wax (and feedstock in general) is not transparent, for experimental measurements of positions, we cannot use light, and so, a simple technique like video shooting wouldn’t work.
However, since the hot object anyway would be metallic (read: electrically conducting), it would always be possible to sense its internal positions using electromagnetic induction. From my experience of the eddy current NDT, I think, it wouldn’t necessarily have to be an LVDT, and the sensing coil wouldn’t have to necessarily enclose the entire block of wax. If my feel is right (though this will have to be determined after a bit of a trial), a simple “one-way” coil placed on one side of the wax block, should also turn out to be sensitive and accurate enough. Of course, the issue of a differential vs. a direct solenoid is something that needs to be looked into separately.
Now, inductive sensing does make the test much more complicated—you have to firsst calibrate the output of the sensing coil. However, realize, the time-position measurements would be performed only in a laboratory, not under the routine production environments. So, it should be OK. …
… Research is always multi-disciplinary. Indeed, knowledge itself cannot be compartmentalized—regardless of what many influential academicians from the Savitribai Phule University of Pune evidently think. (Though, it was not to show them down that I wrote this post/update. I was mainly concerned only with the research, here.)
* * * * * * * * * * * * * * *
A Song I Like:
(Marathi) “manmohana juLatil naa, taaraa punhaa”
Music: Kedar Pandit
Singer: Ketaki Mategaonkar
[There are two versions of this song, both by the same music director, the same singer, the same melody, and in fact, both also come in the same album! One is in the usual Marathi “bhavgeet” style, whereas the other one is in the “jazz” style. (Not quite jazz all the way through, but it does use some Western instruments someway along that genre.) Surprisingly, the melody fits both the styles so well! I honestly cannot decide which one I like better, though perhaps it’s an indication of my age that I am at times inclined ever so slightly towards the “bhavgeet” version. Or may be, it’s because of Kedar Pandit’s restrained but competent “tablaa” which comes only in that version. (I didn’t know anything about him, but the Wiki tells me that he accompanies Pandit Jasraj on all concerts.) Ketaki is young, and does have limitations to her voice, but the songs here have come out very well. May be with a little help coming in from all those track-editing and pitch-correcting software they all use these days. I don’t know really, but that could easily be the case. But it also is a fact that this kind of a melody would suit her well. And, in any case, the final outcome has come out pretty neat. That counts. … I was driving in the Pune city when I first heard the jazz version on radio, and wished I were driving through a lonely rural patch, instead. So, noted down the words, and looked up the ‘net later on. … Give both the versions a try, even if you don’t know Marathi.]