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Toward a real-world "C/W" Correction Factor

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Tecumseh

Member
Joined
Feb 26, 2002
Location
Ohio
Several of us in discussions while BillA was preparing his great
articles here and here wondered what the "worst case" power
dissipation over the WBs would be due to head loss over the
blocks and flow thru them. It is important to know this because
the power dissipation shows up as heat and must be considered
in the total heat the blocks must remove. Note that this heat is
intrinsic to the block at the various flow rates and is NOT the
heat supplied by the die simulator.

While some may be tempted to use Bernoulli Equations to
calculate this factor, this cannot be done because these
equations are only valid for streamlines i.e. non-turbulent
flow. It is not possible for Bill's equipment to measure the
temp change due to this effect, but as you will see, it does
become a serious factor especially a high flow.

While we all pretty much agreed on the "worst case" power
dissipation, I wanted to know more. The following graphs
come out of that study. They are based on Bill's measurments
on the WBs in his front page articles. After reviewing these
plots, it is hoped that we might discuss how this may be used
as a "correction factor" for doing what has been called the
hack known as C/W e have all come to know and love. :D
All-fullrange.png


Here is a closeup of the range encounted by most OCers:
All-closeup.png
 
I should point out that this was a point pursued with some vigor by LegumaN,
which I spiked in the articles by simply saying "not considered"

there is however (naturally) a bit more to it

without question the heat dissipated within the wb due to the pressure drop and due to friction can be said to add to its 'heat load'
BUT
just where is that load being applied ?

to the bp ?
nooo, not quite
as it is a consequence of the pressure drop and internal friction this heat load can be considered to be applied to all of the internal surfaces of the wb
- and by convection transferred to the coolant as it passes through the wb
(and if no convection is involved then this whole issue is REALLY MOOT as this is a load seen by the radiator, or chiller, and not by the wb at all)

as the bp is at a somewhat higher temp than the rest of the waterbox, the bp will be rather less involved in this 'secondary' transfer
(given that the transfer efficiency will be greatest where the temp differential is greatest, the top waterbox surface actually)

there is another 'problem' as well:
'we' measure the hack "C/W" as the temp difference between the coolant inlet temp and the die
-> so that which occurs to the coolant after the inlet (in this case its picking up some additional heat due to the pressure drop and friction) is not visible, because it is not measured

it would be / is possible to measure this total coolant temp rise (and in fact I do, but do not 'report it), and the mean of the inlet and outlet calculated and used to determine the "C/W"
-> but this is not how it is, or has been, done

and there is an additional difficulty as well:
the temp differential between the inlet and the outlet is VERY small under some conditions
- below really the accurate representation capability of even a temperature indicating system with 0.01°C resolution
(not to even get into the uncertainty / accuracy issue - which makes it worse by far)

so I submit that:
- if it is a 'function' minimally affecting the performance of the wb (which is what is being characterized), and
- it is a VERY small value (wrt the bp), and
- if we have no accurate measurement method, and
- if such will require a change in the manner in which wb "C/W"s are determined
(and then be possible also 'only' by me)

I conclude that while this is a fun theoretical exercise and worth pursuing as such,
-> we should ignore, as a practical matter, the 'effects' of a pressure drop and frictional heating within the wb

did I miss anything, eh ?

be cool
 
Well, I am sure the "good enough" guys will ignore this
dissipation factor. :)

So we now know, for these blocks, how much power is
dissipated due to flow thru the blocks. What's the big deal?
With the current method of measuring C/W this effect is
quite invisible. Measuring the input temp vs the
die temp may not be the best method. Using the mean
of input and output may not be accurate either. Closer,
perhaps is the LMTD, but this is also a problem because
the basic assumptions for its derivation are violated.

Where is the heat load applied? Clearly we must consider the
WB to be a "black box" where the heat is dumped into the
water. This heat is in the water otherwise would not
see head loss. This heat is evolved thruout the time the water
is in the block, but we do have the net power dissipated IN
the block by virtue of the your readings. Since it is IN the water
the same way that heat from the die gets in the water if you
were to characterize the WB other than the convertional C/W
this would have to be considered. Since a WB is a black box
it cannot "tell" if heat is coming from the die or intrinsic dissipation.

What am I missing?
 
I too think we're quite beyond 'good enough', as are for that matter even "C/W"s - but I'll leave that be

looking at the pressure drop only, quite agree that its 'in the water', and so may be said - to the extent of the coolant's temp rise due to this - to raise the effective temp of the 'inlet temp' by some amount
- to get really picky this would also depend on the specific wp configuration; an inlet nozzle directly over the die area would be impacted less by the temp rise due to the pressure drop

and conversely, the (quite undefined but, ahem, rather small) heating due friction would also be somewhat dependent on the wb's configuration

so in summation these effects could be said to affect the coolant's temp rather than any 'heating' as such seen by the wb
correct ?

if so, then the questions are:
(given also that we are unable to quantify such by measurement due to the small resultant temp change)
- can this heat be determined by calculation ?
- how should it be addressed in the determination of "C/W" ?
-> and is the increased complexity 'worth' the increase in accuracy ?

IF we 'pronounce' a new way of calculating the "C/W", that no one (else) has the means of collecting the data with which to do so,
is this of benefit to the WCing community ?
- why are we measuring this hack "C/W" anyway ?

I like a good wrangle,
but am concerned that we are 'picking the pepper out of the fly sh*t'

simplicity, and even simplification, can have certain benefits

Tecumseh
taking the 'effective' coolant temp change in the way you prefer,
what is the impact on the calculated "C/W"s ?

be cool
 
so in summation these effects could be said to affect the coolant's temp
rather than any 'heating' as such seen by the wb

To the extent these effects raise the coolant temp, and ignoring
secondary heat loss, that's where it ends up, then the transfer
from the die heater is diminished by virtue of the diminished
delta T. At high flow rates 4 or 5 watts additional while trying
to cool the 70 watt die becomes significant if you consider
5 to 7 percent significant. :) At low normal flow rates this
can't be any big deal.

Does this matter? That's why the thread is called "Toward....."
At normal flows, these plots show that we are pretty safe in
ignoring intrinsic heating. At high flows, maybe not.

Does knowing the intrinsic power dissipation provide any useful
clues to the nature of a block? I have some ideas, but would
like to hear what others think.

To grossly exagerate, some blocks are making their own hot
water. This could be considered a handicap. :) Perhaps this
is more important to the WB designer.

I need to do more thinking. :)
 
"then the transfer from the die heater is diminished by virtue of the diminished delta T. At high flow rates 4 or 5 watts additional while trying to cool the 70 watt die becomes significant if you consider 5 to 7 percent significant. At low normal flow rates this
can't be any big deal."

5W @ 3gpm ~ 0.01°C increase in the coolant temp of 25.0°C
while 5W may be significant in terms of the applied heat load (with which I would certainaly agree),
the effect on the coolant temp is quite slight in the extreme
(that is the worst case and I can barely hope to measure it)

I'll chew on it some more

be cool
 
Take a look at Bill's Chart 2 from his report.
wbCWcomp.gif

Look Specifically at the curves for the Cooltech WB75 and
the LiquidCC Surge. Notice how the curves cross at 4 lpm.
Now look at the Power Dissipation vs Flow curves above.
These two blocks have almost identical head-loss curves
and so dissipate internally the same amount of power over
the entire flow range.

What we are seeing is the effect of turbulence kicking in at
about 4 lpm. At flows below 4 lpm the LiquidCC Surge has a
lower C/W, but at flows greater than 4 lpm the Cooltech WB75
becomes a lot better than the Surge.

What this shows is that with identical head-loss (power dissipation),
the power is "partitioned" more for useful
turbulence in the WB75 at greater than 4 lpm. The WB75
is a spiral design. The Surge is a 3-fold labyrinth.

There you go. Blocks with identical head-loss and flow demonstrating
the onset of "useful" turbulence.
 
"What this shows is that with identical head-loss (power dissipation),
the power is "partitioned" more for useful turbulence in the WB75 at greater than 4 lpm."
. . . .
"Blocks with identical head-loss and flow demonstrating the onset of "useful" turbulence."

can you rephrase ?
not following this well at all

be cool
 
Sorry, I didn't define that...oops.

What does head loss come from? Friction and turbulence?
The head-loss of these two blocks is the same, yet they
do not perfom the same. The non-linearity in their curves
for C/W most likely comes from the difference in turbulence.
Because the head-loss is the same, they both dissipate the
same power at each flow level. This power is distributed or
partitioned differently in each block. Think of it like a budget or
a pie. The block that has the most turbulence over the hottest
area of the die wins because that gives the best heat transfer
from the die. A block that wastes its budget causing turbulence
and friction where it's colder is just generating head-loss.
So "useful" turbulence is turbulence over the hot area of the die.

That help?
 
blind men describing an elephant . . . ?

it can be cast in a much more simple fashion

the WB75 is a center inlet, the Surge is not
the central inlet 'design type' benefits much more from increased flow
blah blah blah

WB%2074%20layout.jpg


and notice just how screwed up that inlet is
(with that big slug of metal on top of the die, phew)
but then when the flow gets up there, swirling around that 'island' . . . .
starts working a bit better

now I agree that too can be called 'turbulence'
- and here we return to that mini and macro characterization I made some time back

be cool
 
I would think better block efficiency would explain the differences rather the anything else. I think without having a full finite element thermal model you are all guessing.

A modified Bernoulli Equations would predict pressure drop but developing the k values would be hard. K valves are easy the obtain for standard fittings but outside that you need to develop them yourself.

I would have though that the pressure drop through the block would end up as heat absorbed by the water (only a very small amout absorbed by the wall). This temp increase of the water would have a minor effect on heat transfer (and I mean minor/you could not measure it). It would finally be removed by the radiator.
 
agreement here; (whole lotta guessin' goin' on)

a heat 'load' within the coolant, and more importantly not being conducted through the bp, does not seem too significant wrt characterizing wb's performance

the resistance coefficient, K, is worth a few words
paraphrasing from Crane #410:

the 3 components of the pressure loss due to a wb are:
1) the pressure drop within the wb itself,
2) the pressure drop in the upstream piping in excess of that which would normally occur were there no wb (small effect), and
3) the pressure drop in the downstream piping in excess of that which would normally occur were there no wb (may have a comparatively large effect).

what I measure is #1 only,

wbloss%20vs%20flowSI.gif


and within the wb the pressure losses are due to
A) wall friction due to roughness, diameter, velocity, density, and viscosity,
B) changes in direction of the flow path,
C) obstructions in the flow path, and
D) changes in the cross section or shape of the flow path.

Velocity is obtained at the expense of static head, and the decrease in static head due to velocity is

hl = v² / 2g

which is defined as the "velocity head"

Flow through a wb also causes a reduction in the static head, which may be expressed in terms of the velocity head. The resistance coefficient K in the equation

hl = K (v² / 2g)

therefore, is defined as the number of velocity heads lost due to the wb.

In most valves and fittings the friction losses are considered to be small wrt the other losses, so K is considered as being independent of friction factor or Reynolds number.
-> this is not the case with wbs

the utility of the resistance coefficient, K, is to relate a specific component configuration to different sizes and by means of such to characterize the component's pressure loss in terms of 'equivalent (size pipe) length' (using the Darcy equation)
K is a constant only if the wbs are geometrically similar.
-> this is also not the case with wbs

I suspect it is much simpler to use measured head loss (pressure drop) values for wbs, as such is what in any case is used as the basis for deriving the K values

an interesting side note to this inquiry was the revelation (to me) that the head loss data plotted on log paper will yield straight lines
- but I suspect such would only add to the confusion

be cool
 
When I said k values I should have said a lot of k values(this would actually also mean friction factor for straight sections). The resistant coeeficient only holds for one given fitting at a given size (I have tables of these valves I use all the time for standard size fittings). And a given system will have multiple values, one for each fitting.

There is data around to convert square channels to equivilent round pipe but at the low heads we are talking about its accuracy would have to be questioned.

Sorry for the confusion.
 
BillA said:

(whole lotta guessin' goin' on)

an interesting side note to this inquiry was the revelation (to me) that the head loss data plotted on log paper will yield straight lines
- but I suspect such would only add to the confusion

be cool

Some more guesswork:-
Guess.jpg


Guesses based on Flomerics and Waterloo calculators for T/W .Used "the two r (and hence two h) sums" method referred to in my second post here http://forums.procooling.com/vbb/showthread.php?s=&threadid=4960&perpage=25&pagenumber=1

"Pressure Drop at Nozzle" guesses based on PD in 14" long tubes - 14" length of 6mm ID tube gave same value as Billa got for 6mm nozzle( http://forums.overclockers.com.au/showthread.php?s=&threadid=58005 ) . Used this calculator [url]http://www.aps.anl.gov/asd/me/FilmPressureDrop.html[/url]

Going to the pub.
 
BillA said:

an interesting side note to this inquiry was the revelation (to me) that the head loss data plotted on log paper will yield straight lines
- but I suspect such would only add to the confusion

be cool

I am not sure why this should be a come as a revelation. It comes
directly out of the integration of the logistics equation for the
flow thru an orifice. Or more simply, the pressure drop or head
loss of an orifice (or nozzle) is propotional to the square root
of the flow thru it. Our buddy Bernoulli gave us that. If you
look at this on a semi-log plot, it is, indeed, linear. The slope can
be determined by least-squares calculations. It might be more
intersting to look at deviations from linearity in your data, but
it might not show much. Now it might be a stretch to think of
a WB as an orifice, but the same physics applies.
 
I decided to plot the square root of the head-loss vs. the flow
rate over the whole data set and got this:
SqrtHLvFR.png


The only significant deviation from linearity is that for the 462-UH with
the 0.39 inch ID barbs...The blue line. Here is a closeup:
SqrtHLvFL-closeup.png

Notice the curves for this block and the WB75 at about 1.9 lpm.
At higher flow rates there is no deviation from linearity.
 
quite interesting (lies, damned lies, and statistics)
off the top of my head I would say 'bum readings'

the 'truth' may be a bit more difficult
at low flowrates the differential pressure resolution of 0.01psi is not sufficient for the level of discrimination we are seeking
- plus, if it is a borderline reading (just flickering - or just not flickering to get the up-tick) the apparent inaccuracy becomes even more exaggerated

clearly I need to take 'extra care'
not quite sure how to be even more fanatical than I am (already obsessive-compulsive)

nice work Tecumseh
a favor, those that deviate - recalc one tick up; I'm curious
thanks

be cool

EDIT: revise request to "recalc one tick up, or down, as appropriate"
 
Last edited:
Is this what you want, Bill? It looks like the first data point
for each block is in question because the rest of the points
are pretty much in a straight line.


Deviate.png
 
Last edited:
no, you have to go back to the psi values in the Excel file
the WB75 for example:
as read, in psi, was 0.05
one increment up would be 0.06, the SQRT of which in mH2O is 0.205

the big anamoly with the -UH is probably due to my use of an (attempted) interpolated value of 0.015psi
would have been better to leave it at 0.01

my point is the same, we are pushing the accuracy envelope

but this is a good 'relative accuracy check', I shall use it in the future

be cool
 
Ok, Bill,
Here is a new plot showing the square root of the head-loss
vs. the flow rate. For "sensitivity analysis" the error bars are
equivalent to +/- 0.01 PSI. ( sqrt(.01) = 0.1)

If you took multiple readings and averaged for each data point
in the same way, clearly your instrument cannot handle the
low flow rates as well. Note that the red regression line was
calculated w/o the first point and is VERY tight. This is a
testament your instruments and the care you take in making
the readings. Now is this close to what you want? :D
Regression.png
 
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