|October 26th, 2006, 04:36 PM||#1|
FCG-FF-01: Installing Identical Pumps in Parallel - Why You Probably Shouldn't...
I've decided to start a series of informational threads on heat-transfer, thermodynamics/fluid flow and mechanical principles here at TTR. I hope to teach the basics on these subjects, just enough for those that don't have a lot of experience or formal education in these areas to get a better grasp of what you are doing when watercooling. Please don't think of these "lessons" as being all inclusive, I certainly can't cover everything, nor would I have the time. With that being said, please, if you feel that I have made a mistake somewhere (we all make them from time to time, including me), think you may have a better and/or easier way of explaining a particular concept, or that I just left something out that you would like to know more about; email me (firstname.lastname@example.org) I will do my best to accomodate.
For those that choose not to post something that is beneficial to all, I ask that you simply do not include your comments here. These posts are not meant to start a war about what you do or do not believe to be the case. Not every topic will translate perfectly to an ideal watercooling discussion. Some people may hate what I have to say; others may love it. Let's all just try to share our passion for overclocking in a civilized manner.
Lessons Numbering *
For easy searching and topic grouping I will use the following numbering scheme will posting new topics.
1) FCG obviously refers to my 'handle'
2) Codes: FF = Fluid Flow; HT = Thermodynamics/Heat Transfer; MP = Mechanical Principles
3) The code will be followed by a sequencing number for that topic.
*Will be included in the first post of each uniquely coded topic ONLY.
FCG-FF-01: An Introduction to Pumps in Parallel - Why You Probably Shouldn't...
For a closed system operating at steady-state the pump head developed by the pump(s) equals the headloss of the system. During steady-state operation the change in stored energy of the fluid (potential energy, kenetic energy and flow work) for one complete cycle is zero. (This is the same reason why the installed height of components in a closed system will not affect overall system flowrate, just system pressure at different points in the loop.) Therefore Ideal System Load is the same as Real System Load (RSL) which is the same as the system headloss.
This example is geared toward the installation of identical pumps installed in parallel. This isn't intended to imply that this practice cannot be applied to different model pumps, just that I have purposefully choosen this scenario in order to better explain the principles and make the visual aids easier to follow.
For pumps operating in parallel, the pump head at the system operating point is the same for each pump operating in the system. This value is found by drawing a horizontal line from the intersection of the system curve and the pump operating curve (shown in green). Drawing vertical lines from these intersections down to the x-axis will result in individual pump flow rates when two pumps are operated in parallel. Note that both pumps exert the same head or "push." The sum of the flow through the individual pumps (Vp) is the system flow (Vsystem). Since we have two identical pumps, each pump provides exact half of the system flow, so its easy to see that Vsystem = 2Vp.
For 'System Curve K', it is important to understand that adding a second pump in parallel does not double the system flow. We can see this demonstrated graphically in that Vko is located between Vp and Vsystem where Vko is the system flow developed for one pump and Vsystem is from both pumps:
Vko > Vp and Vsystem = 2Vp => Vko > 1/2*Vsystem => adding a second pump did not double the total system flow rate (Vsystem).
For any closed-loop system the system curve can be computed using the following equation:
hL = Ksys * V^2 where Ksys is the total system resistance developed from the summation of individual component resistances. Note: This is NOT a pure mathematical summation when dealing with components in parallel. (Calculations will be shown in a later lesson.) What's important to realize is the system curve is parabolic (parabola-shaped) where y = Ax^2 + Bx + C where B and C are zero. As we can see, higher values of Ksys quickly create more steeply sloped curves!
'System Curve K2' is less restrictive than 'System Curve K' while 'System Curve K1' is more restrictive (and more indicative of the resistrictions seen in watercooling loops with 1/2" ID tubing and highly-resistrictive CPU and GPU waterblocks and multi-pass radiators). *wink, wink*
We can see that 'System Curve K1' leaves little means for flow increases with the addition of parallel pumps whereas the extremely low resistance curve (K2) shows great gains! Which brings us to our first generalization (I say generalization because there are always situations that don't perfectly fit the model for one reason or another):
For highly-resistrictive systems, it is usually better to install pumps in series rather than in parallel for the creation of additional flow.
We'll further explore this generalization when we discuss pumps in series.
Figure FF-01-1 Explained:
The dark black lines represents the head vs. flow curve for one pump and two pumps (of the same model/ratings). This data usually comes from empirical data collection done by the pump designer/manufacturer and can often be found supplied with the pump. The only trick is getting the axis' into units that you can work with.
The red lines represent system curves for low restriction (K2), high restriction (K1) and moderately restricted (K) systems. Understand that adding more components, more tubing, more splits and bends and the like will cause 'K' to increase. This value is also empirically derived once the system is constructed and tested. This value is different for every system.
The intersection of a 'system curve' and a 'pump curve' develop an 'operating point'. Reading the x- and y-values for this point will tell you the pump head pressure developed (equal to the system headloss in a steady-state system) and the flow rate of the system.
Maximum pump head is called 'shutoff head' and is when a pump creates maximum system pressure but no flow. Freeflow is when a pump create maximum flow with no pressure developed (think the discharge of a pump with no components attached).
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