GTA
All Springer/NP/PCP Air Gun Discussion General => Air Gun Gate => Topic started by: rgb1 on March 01, 2018, 08:48:05 AM
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Using CFD, we can calculate and analyze the flow around a pellet in order to better understand the nature of drag. To broaden the approach we’ll look at several pellets, each with a different nose shape. The examples selected are: Crosman Premier Heavy, PDG pointed (mfg in Argentina, imported by Predator International and marketed by Air Gun Depot) and RWS Super-Mag. These three are similar in overall size and weight and representative of the general class of nose shape: round, pointed and flat. In the pics they will be designated as R, P and F respectively. Download them here......
http://104.131.46.156/nextcloud/index.php/s/uPRExQe7ehVv7nL (http://104.131.46.156/nextcloud/index.php/s/uPRExQe7ehVv7nL)
The bulk of information being presented is graphic and I suspect most readers will be unfamiliar with it's form. While there's a lot to digest, take your time working through it......perhaps go through it several times. And please ask questions.
Mathematical models were created using pels that have been pushed through a bore so as to have engraving and a slight amount of flare extrusion. An accurate and detailed representation is essential for good results
Flight conditions are 770 f/s and 560 rev/s. This is typical of what we would see with a muzzle velocity of 875 f/s from a 1:18 twist barrel after traveling downrange 10-25 yd. The pel has lost substantial momentum though still spinning rapidly. Just as important for our analysis, the flow field is subsonic.
The calculator used is openFoam…a well-developed piece of open source software, available to anyone for the asking. The solution I’ve chosen is steady state (RANS) and includes the effects of viscosity and turbulence. Runs require 6-8 hours for convergence, data visualization is with ParaView.
Let’s start by looking at several pics…R_1, P_1 and F_1. With a streamline generator placed at some distance ahead of our pel the general nature of things can be assessed. At three calibers sideways from the body very little influence is observed, even with the flat nose example. The pointed pel has no rifling marks on the head…this batch happens to be undersized.
By moving the generator closer and increasing the line density, we can see more detail around the nose (series 2 pics). There are no stagnation zones that project forward, even with the wad cutter. Flow separation occurs slightly ahead of maximum diameter, just as expected (shown more clearly on pressure graphs).
In series 3 pics, we can see circulation in the waist cavity. The round nose example is the only one that demonstrates flow reattachment at approximately 2/3 of the flare. The other two don’t even come close. And finally in series 4, we see what happens in the wake..……again, lots of circulation.
Next, let’s look at pressures…this is where we can begin to see how our pel is influenced. Pic series 5 shows relative pressure on the pel surface and nearby flow field. Here, relative means with respect to the free stream ambient valve, 14.7 psi. The idea of negative pressure may seem strange at first but it’s a key aerodynamic concept. As with streamlines, the sphere of influence is several calibers or less.
Series 6 is a graph of how relative pressure is distributed over the pel surface. The white line is the intersection with a meridional cutting plane along which values are extracted. Included is a partial pel profile for reference. In each example, relative pressure in the waist area is negative everywhere……and this will lead to interesting circumstances. Base pressures have recovered to less than 1 psi difference in spite of the fact that flow reattachment did not occur.
In order to quantify how pressure creates drag, we must consider only the stream wise component. Therefore, in the next series of pics (7), Prel_x is the variable. Any red or red tinted surface contributes to the production of drag while blue surfaces decrease it. The waist of each pel (as does the nose on CPH ) has both and consequently some cancellation takes place.
By integrating this pressure component over the pel surface, we can obtain drag force. Moreover, if we apply the process to a particular area, we can determine its contribution. For purposes of demonstration, let’s divide the pel into four parts:
Nose, which includes the rifling grooves
Shoulder, extends from behind the rifling grooves to the minimum waist diameter
Flare, minimum waist diameter to an including the rifling grooves
Base
Integration results for each component are shown in table_1, where the top number is drag force (grams) and the lower is percentage of total force. For further comparison and as a check on overall accuracy, Cd values are included. The top number is cfd calculated, the bottom is derived from velocity loss using two chronographs (raw data available).
Ron
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Excellent data, Ron.... I knew this was coming (thanks for the preview and opportunity to input).... but I had no idea how comprehensive it would be.... GREAT JOB.... The correlation between calculated Cd and measured is outstanding....
I would like to comment on a couple of things that stood out to me.... The most remarkable was the large percentage of area on the last half of the nose of the round-nosed design that actually has NEGATIVE drag.... where the blue area in R_7 is actually "pulling the pellet forward" against the rest of the drag forces.... There is only a tiny area with a similar effect on the flat and pointed designs.... The other thing is the summary table, where you can see that the drag of a pointed pellet is roughly 50% higher than a round-nose.... and a wadcutter is nearly double.... Also in the summary table, the grams of drag from each part of the pellet (nose, shoulder, flare and base) is extremely interesting.... I assume the "shoulder" is the inward sloping surface directly behind the head?....
I notice that the contribution to drag from the shoulder of the RN design is about half that of the flat and pointed pellets.... Do you think that is because of the sharply concave shape, right behind the head, compared to the more gentle taper of the others?.... Also, does that feature pull the vortices in the waist forward, or make them smaller, enhancing reattachment of the flow on the RN design at the back of the flare?....
Bob
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Bob, I appreciate the compliments....thank you.
What happens in the shoulder area is partly a function
of nose shape. Though separation occurs with all three, it’s
much less pronounced with a rounded nose. Look at series
6 pics and notice how low the pressure drops just before
the maximum diameter and also the value to which it
recovers. Crosman is much better than the other two.
And, as you suggest, the sharply concave surface also helps.
Regarding the vortices question…..they are smaller because
the flow DID reattach and they simply occupy the resulting
space that’s available.
Ron
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Great stuff! Interesting. It got me thinking... as the pellet picks up scoring from the rifling, that spin stabilizes the flight but does it maybe also help trip the flow over to turbulent?
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Even if the flow was laminar over the nose, it would trip to turbulent at the start of the shoulder, with or without rifling marks at that point....
Bob
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Bob, yes for sure. Right after I posted I realized there is detachment anyway behind the head, then reattachment on the skirt as the figures show. Maybe there are some interesting profiles to explore in non-diabolo shapes? I'm new to ag, so just trying to learn.