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Validation of a new method for flow in cryogenic systems Andreas Janzen1,*, Steffen Grohmann1,2, Heinz Schön2, Michael Stamm2 1 Institute for Technical Thermodynamics and Refrigeration (ITTK) 2 Institute for Technical Physics (ITEP) * Email: [email protected], Tel.: +49-721-608-42328

The Cal²-Flow measurement principle Principle Measurement Data evaluation Minimization Caloric measuring principle Combined evaluation of energy T M M Q4 balance and energy transport TA Q3 Q d oa M=A Q2 l 1 c(T-T)pF'' F ' In situ calibration during operation t ea 2 Q1 h 3 4 ng 2 si 1 2 3 4 Complete compensation of ea 1 3 4 u<1%M cr '' 3 4 systematic measuring uncertainties In TF 2 1 1 M=B ' TF' T-TAF Advantages Rcp ln T-TAF'' No additional pressure drop Q Q Systematic ∆ errors Negligible heat input ∆Tm Tm 4 Q=kA∆ Tm = Fluid increase of just a R 3 '' ' few mK T-TFF ' '' 2 R ∆ M TF TA TF T=m ' Uncertainties < 1% w.r.t. the actual T-TAF 1 ln '' flow rate T-TAF Q

Experimental validation at room temperature Reference method First experimental results

0.5 0.5 Comparison ṀSNG = 0.394 g/s 0.4 Ideal case േ 5%

ṀB,raw uṀ = 0.37% 0.4 0.3 PTS

ṀPTS = 0.391 g/s 0.2 (Result) 0.3

Mass flow rate / g/s 0.1 ṀPTS Mass flow rate PTS / g/s ṀA,raw 0.0 0.2 Sonic nozzle gallery (SNG) with 4 calibrated nozzles 0 102030405060 0.2 0.3 0.4 0.5 Heat load / mW Mass flow rate SNG / g/s

Flow range: 0.04 g/s ≤ ṀSNG ≤ 0.5 g/s Uncertainty of the reference method: u 0.33% Reference Prototype Offset ṀSNG ṀSNG / g/s ṀPTS / g/s g/s 0.300 േ 0.17% 0.290 േ 0.95% - 0.010 Prototype sensor (PTS) 0.394 േ 0.15% 0.391 േ 0.37% - 0.003 0.467 േ 0.10% 0.452 േ 0.36% - 0.015 TA Q TF' TF′′ Successful validation of the Cal²-Flow measurement principle Small heat loads: Q = 10 …40 mW Designed for room temperature experiments Fluid temperature increase: TF'' - TF' = 30 …180 mK Tube diameter: 4 mm, total length: 250 mm Design improvement to eliminate remaining offset Temperature measurement with 3 PT100 sensors (class A) mounted Mean fluid on copper blocks Heater performance Integrated heating element Ongoing development of cryogenic sensor and electronics

Literature Grohmann, S. (2014): A new method for flow measurement in cryogenic systems. Cryogenics, vol. 60, March–April 2014, pp. 9-18.

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