Flow and pressure requirements for the PXL cooler
Updated 5/2/12
According to the cooling study[1] we require an air flow velocity between the PST and the outer PXL ladders of 10 m/s with the ability to throttle back to 7 m/s.
In this document we estimate flow and pressure requirements for the PXL cooling air blower based on our cooling tests using a mockup of the PXL mechanical structure.
The cooling test system consisted of a dust collector blower sucking on the mockup of the PXL system connected with 10 ft of 6 inch flexible duct as shown Figure 1. A schematic diagram of the flow setup is shown in Figure 2. The flow rate was controlled by restricting the 3 inch tubes feeding air into the system. The air velocity was measured with a probe between the outer ladders and the plastic tube. The pressure and flow requirements for a blower are estimated as a function of this velocity parameter. It is assumed that the flow scales as this air velocity and that the pressure drop between the input and output of the PXL assembly scales as the air velocity squared. The flow in these tests was estimated in 3 ways. In one method the flow estimate was made by measuring the DT between input and output and computing flow from the air heat capacity and the known heat input power. In the second method air velocity in the annulus times the area of the annulus between the outer PXL ladders and the outer plastic cylinder provided the estimate. A third flow measurement was done using a velocity probe to measure multiple points across the 6 inch duct and integrating over the area.
The pressure was not measured, but an estimate of the pressure drop in the mockup PXL system is derived from measurements of the unrestricted flow through the system. The pressure drop in the mockup system is the pump pressure minus the pressure drop in the connecting 10 ft long 6 inch Æ duct. The pump pressure is determined from the manufactures pressure vs volume curves (see RD-211 red line, Figure 3). It is apparent from these curves that the internal pump pressure loss scales as the flow squared with a zero flow pressure of 9 inches of water and a maximum flow of 1200 CFPM. The pressure loss in the connecting duct was obtained from a web calculator[2] assuming that the 10ft long 6 inch duct had two 90 deg turns. Again the loss scales as the flow squared. The details of the arithmetic are contained in a separate document[3]. The results from this determination are shown as case 3 in Table 1. The pressures and the volumes for the nominal planned flow appears in the table as case 2 and the possible reduced flow option is shown as case 1. The values for case 1 and 2 are scaled from case 3 with the flow scaling as the velocity and the pressure scaling as flow or velocity squared.
Figure 1 PXL mockup used in cooling tests
Figure 2 Schematic view of PXL mockup used in the cooling tests
Figure 3 Pressure flow curves for the pump used in the PXL mockup thermal tests. The red curve for RD-211 provides the pressure drop. For example the unrestricted flow rate of 700 CFPM gives a pressure drop of 6 inches of water across the mockup system plus flexible duct. Note, the internal resistive pump pressure drop in these plots scale as Flow squared.
case / annulus air speed / Flow from DT / Flow from annulus velocity / Flow from integrated duct velocity(mph) / Flow (CFPM) / Pressure (in wc) / Flow (CFPM) / Pressure (in wc) / Flow (CFPM) / Pressure (in wc)
1 / 16 / 250 / 1.8 / 270 / 1.7 / 360 / 1.2
2 / 23 / 360 / 3.7 / 390 / 3.5 / 510 / 2.5
3 / 31 / 500 / 6.8 / 540 / 6.5 / 700 / 4.7
or with alternate units:
case / annulus air speed / Flow from DT / Flow from annulus velocity / Flow from integrated duct velocity(m/s) / Flow (m3/s) / Pressure (kPa) / Flow (m3/s) / Pressure (kPa) / Flow (m3/s) / Pressure (kPa)
1 / 7 / .12 / .44 / .13 / .42 / .17 / .3
2 / 10 / .17 / .91 / .19 / .87 / .24 / .63
3 / 14 / .24 / 1.7 / .25 / 1.6 / .33 / 1.2
Table 1 Estimated flows and pressure drops during cooling tests with the mockup PXL system for 3 different annulus flow velocities. The nominal flow velocity that is planned for operation of the PXL detector (case 2) is 10 m/s with the option of operating the system at a reduced velocity of 7 m/s. Case 3 is the unrestricted flow measured in the tests and on which the other pressures are based. For these tests the flow was estimated 3 different ways. The first method of determining flow, the DT method is probably the most accurate, but to be conservative the larger flow value of 510 CFPM can be used to be safe. These are the flows through the mockup. The real detector has slightly different dimensions which requires a scale up that is discussed further below.
The spread in values for the three flow determinations gives a feeling for the uncertainties. The DT method is expected to be an over estimate of the flow since all the ducting and the mockup test structure are at room temperature. Any conduction from the heated air to these structures reduces the measured DT resulting in an over estimate of the flow rate. The flow estimate from the annular velocity measurement is also likely too high as the velocity near the walls will be less than the center measured air velocity. The third flow estimate based on the integrated velocity over the cross-section of the 6 inch Æ duct gives the largest flow value, but the measured velocities over the cross section were not axially symmetric suggesting a complicated flow with possible local turbulence leading to measurements of velocities that were not necessarily parallel to the duct axis. To be conservative in setting specifications for the cooler requirements we choose the larger mockup value of 510 CFPM, but it is likely that the correct mockup flow is closer to 360 CFPM, the flow determined using DT. The real detector has a slightly larger annulus area which scales the requirement up in flow by a factor of 1.13. The requirement for the cooling blower is then 580 but that can be restricted to a lower value, namely maximum flow of 410 CFPM with capability of restricting to 280 CFPM, the lower estimate for the reduced flow option.
Estimate of duct pressure loses and flows in STAR installation
The duct pressure drops for a 6 inch duct from the north platform to the PXL detector is obtained using the web calculator[4] for the various sections. This duct pressure drop is what must be overcome by the cooler in addition to the drop in the PXL detector. The pressure drop for the various sections is calculated for a flow of 500 CFPM. The pressure for other flow values scales from these numbers as flow squared. The duct system consists of a 6 inch duct that branches into a y with two 3 inch ducts. The contributions from the different elements of the ducting system are listed in Table 2. The mockup tests used two open straight input tubes that give a pressure drop that will not exist when the duct system is connected. This correction is included in the duct loss tabulation. There is also a correction for the PIT diameter of 9.25 in vs 9 in for the mockup. This is an annulus area increase by a factor of 1.13.
pressure (inch wc) / Duct element.41 / flexible wire covered round 6 inch duct 20 ft long with 5 elbows, at 500 CFPM
1.3 / 4.2 inch diameter (half the area of a 6 inch diameter) taper to 3 inch diameter, at 250 CFPM
.35 / 3 inch diameter flexible wire covered duct 8 ft long, at 250 CFPM
-.81*.8 / 3 inch straight input correction for the mockup detector estimate, at 250 CFPM
1.24 / Total pressure drop of the duct system with 500 CMPM
Table 2 Pressure drop for elements of the duct system connecting the cooler with the PXL. The pressure drop was computed with a web app for a flow of 500 CFPM
case / annulus air speed / Flow from DT / Flow from annulus velocity / Flow from integrated duct velocity(mph) / Flow (CFPM) / Pressure (in wc) / Flow (CFPM) / Pressure (in wc) / Flow (CFPM) / Pressure (in wc)
1 / 16 / 280 / .46 / 310 / .53 / 400 / .91
2 / 23 / 410 / .95 / 440 / 1.1 / 580 / 1.9
Table 3 Pressure drop in the duct system for the various estimates of PXL flow.
case / annulus air speed / Flow from DT / Flow from annulus velocity / Flow from integrated duct velocity(mph) / Flow (CFPM) / Pressure (in wc) / Flow (CFPM) / Pressure (in wc) / Flow (CFPM) / Pressure (in wc)
1 / 16 / 280 / 2.7 / 310 / 2.6 / 400 / 2.4
2 / 23 / 410 / 5.6 / 440 / 5.5 / 580 / 5.1
Table 4 Total pressure, duct loss plus required PXL pressure, listed with flow for different options and estimates. The nominal desired flow is case 2 where the flow estimate varies from 410 to 580 CFPM and the total pressure drop varies from 5.1 to 5.6 inches of water. Case 1 gives the results for the reduced flow option.
Conclusion and Summary
The requirements for the cooling system are summarized in Table 4. At the nominal air speed (case 2) the estimate for the total pressure to overcome duct loss and losses in the PXL detector is 5.1 to 5.6 inches of water and the required flow is between 410 to 580 CFPM. The duct pressure drop was calculated using a web app. We do not know the accuracy of the web app, so this should be checked. The duct loss numbers may be fine, but we do not have experience using these tools.
It is desirable to be able to restrict the flow to case 1 levels should it be necessary to operate at these reduced flow values. It is also desirable to have some over pressure capability to compensate for errors in the above pressure estimates. It is unlikely that the flow requirement will exceed the 580 CFPM appearing in the table, as we have reason to believe that this is an over estimate of the flow.
[1] http://www-rnc.lbl.gov/~wieman/Cooling_tests_Nov2009_.doc
[2] http://www.freecalc.com/ductloss.htm
[3] http://www-rnc.lbl.gov/~wieman/flow%20and%20pressure%20spec%20for%20PXL%20cooler.html
http://www-rnc.lbl.gov/~wieman/flow%20and%20pressure%20spec%20for%20PXL%20cooler.xmcd
[4] http://www.freecalc.com/ductloss.htm