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Eliminating flow-induced microphonics in a superfluid helium cryogenic system
Cryogenics 104 (2019) 102984
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Eliminating flow-induced microphonics in a superfluid helium cryogenic system Dhananjay K. Ravikumara,
⁎,1
T
, Yatming R. Thanc, Jon P. Longtinb
a
Plasma Science and Fusion Center, Massachusetts Institute of Technology, Cambridge, MA, United States Department of Mechanical Engineering, Stony Brook University, Stony Brook, NY 11790, United States c Collider – Accelerator Department, Brookhaven National Laboratory, Upton, NY 11973, United States b
A R T I C LE I N FO
A B S T R A C T
Keywords: Superfluid helium Superconducting radio frequency (SRF) cavity Microphonics Cryogenic system design
Superconducting radio frequency cavities are the devices of choice when it comes to accelerating charged particle beams in modern particle accelerators. They are held in a bath of liquid helium, to maintain their operating temperature at 2.0 K. The dimensions of these cavities are controlled within microns to facilitate operation at design conditions. During operation however, these cavities experience microphonic disturbances i.e., small mechanical deformations, that cause an undesired response in the electrical performance of the cavity. This paper proposes solutions to mitigate microphonics caused by fluid flow, particularly by the fill line into the helium bath in a 2.0 K cryogenic system. Three different systems designs are proposed, two of which dramatically reduce vapor generation and thereby its contribution to microphonics. The third design is found to completely suppress vapor generation and is explored in further detail.
2010 MSC: 80A-20
1. Introduction Modern particle colliders are colossal machines that energize and steer counter-rotating beams of charged particles to collide head-on. The Relativistic Heavy Ion Collider (RHIC) at Brookhaven National Lab (BNL) is one such facility, capable of colliding gold ions together and, until recently, spin-polarized proton beams too. Electric and magnetic fields are used to accelerate and steer the beam along the collider’s 4 km circumference. The devices that maintain the required electric fields to accelerate such beams are metallic structures called Radio Frequency (RF) cavities. Oscillating magnetic fields inside RF cavities create electric currents in the cavity walls. Joule heating from these currents causes energy loss and is dissipated as heat. The proposed upgrade of the existing RHIC facility into an electron-ion collider (EIC) [1], calls for high-gradient and high-field RF cavities, which require the use of superconducting radio frequency (SRF) cavities. The SRF cavities are made from niobium and become superconducting below 9.16 K. Helium is the only cryogen that can be used in conventional large scale systems to achieve such temperatures. Even when the material is in the superconducting state there is still a small finite energy dissipation due to residual surface impedance of the niobium when interacting with an RF field. This resistance, called the BCS resistance, drops with temperature.
To offer an operating margin and suppress BCS resistance, these cavities are typically operated at or below 4.5 K. SRF cavity assemblies consist of the cavities themselves, housed in a helium vessel which is, in turn, surrounded by a vacuum chamber with pressures of ≈10−6 Torr. Cavities are precisely held in their designed shape in order to maintain the specific frequency at which they are designed to operate. It is common to have a mechanical and piezoelectric tuner arrangement [9] to compensate for a shift in operating frequency caused by minute deformations. During routine operation, effects of mechanical disturbances from the environment are felt by the cavity, causing it to detune. This phenomenon, called microphonics detuning can be the cause of significant degradation in the machine’s performance [3–5,7].Microphonic disturbances originate from various sources. This study is concerned primarily with disturbances caused by the flow of helium in the cryogenic system, herein referred to as ‘flow induced’ microphonics. This scope of this study is restricted in particular, to the flow of helium into the cavity bath. Other possible source of acoustic energy such as those from flow, driven by compressor or vacuum pump suction used to pump on the helium bath, out of the system does not have any measurable impact on microphonics. This has been observed while testing other cavities here at BNL and is corroborated by [8].
⁎
Corresponding author. E-mail address: [email protected] (D.K. Ravikumar). 1 This is the author’s current active affiliation. All work for this manuscript was performed during the author’s previous appointments at Brookhaven National Laboratory and Stony Brook University. https://doi.org/10.1016/j.cryogenics.2019.102984 Received 9 April 2019; Received in revised form 7 October 2019; Accepted 9 October 2019 Available online 31 October 2019 0011-2275/ © 2019 Elsevier Ltd. All rights reserved.
Cryogenics 104 (2019) 102984
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At Helium-I temperatures near 4.5 K, the pool boiling regime can be nucleate or film boiling, depending on the surface heat fluxes on the cavity into the helium bath. Pressure fluctuations caused by the violent bubble expansion and collapse is transferred to the cavity and is a dominant source of microphonics. Other popular choices for operating temperatures lie in the Helium - II regime, at or below 2.0 K. Owing to the superfluid state’s vastly superior transport properties [2], most cases of routine operation of SRF cavities do not produce a heat flux high enough to form bubbles. Although heat movement through helium at 2 K is silent there is still significant microphonics felt by the cavities. This can be attributed to pressure disturbances above the liquid bath, either from the incoming flow of helium or the discharge of the helium vapor. At 2 K, SRF cavities are cooled in a bath of helium - II, that is continuously evaporating. Helium leaving the bath is replenished at the same rate as the evaporation to maintain steady-state operation. In most cases, the source of this He supply stream is at a higher pressure and temperature. Typically, refrigeration recovery from the low-pressure vapor is done with a heat exchanger. This lowers the enthalpy of the incoming warmer higher pressure liquid helium. At some point before it enters the cavity bath, flow passes through a throttling device and leaves at saturation pressure, Psat that corresponds to bath temperature. In current system designs, the inlet stream’s enthalpy is still relatively high leading to significant vapor generation upon expansion through the throttling device, resulting in a two-phase slug flow. Slugs of liquid helium are interspersed between packets of helium vapor, causing microphonic disturbances in an otherwise quiet 2 K system. Lowering the vapor generation will help mitigate microphonic effects. While this can be done by reducing enthalpy [10] or by separating the volumes through a heat exchanger [6], this study provides an alternate approach where even a relatively high enthalpy stream can be delivered with no vapor being generated. The follow sections detail several different system designs and the motivation behind them. Following this, an analysis is presented comparing the features of each design with a particular emphasis on vapor generation. The goal of the study, is to minimize the vapor mass fraction x for the He flow into the cavity bath volume. Also included is a short consideration of how these designs can be used in tandem for special cases.
Fig. 1. Schematic of current 2 K systems.
state system, one can solve for the mass throughput for the system once the design conditions for the system are specified
ṁ 1 = ṁ 5 =
Qcavity + Q valve + QleakHX h5 − h1
(1)
Here ‘h’ is the enthalpy, Qcavity is the dynamic heat load contributed by the SRF cavity, Q valve is the static heat load due to the valve and QleakHX is the static heat leak through the heat exchanger. If a smaller part of the system is used such as the cavity bath, the expression can be written as:
Qin + ṁ 3 h3 = ṁ 4 h4
(2)
Realizing that ṁ 3 = ṁ 4 = ṁ must be equal for steady-state operation, Eq. (2) can be rewritten as
ṁ =
Qin h4 − h3
(3)
Here h4 is the saturated vapor enthalpy at 2 K, and h3 = h2 since expansion through the valve is isenthalpic, for the case where there is no heat leak through the valve. During the expansion process, vapor is generated and in this case the mass fraction of vapor, x, is 18.25% as obtained from HePak[12], a helium property database, at a pressure of 3129.3 Pa. This corresponds to vapor temperature of 2 K and an enthalpy of h3 = 5914.6 J/kg, for the chosen operating temperature at point 2 of 2.6 K. If the valve contributes a heat leakage of 1 W, this enthalpy now rises to 6552.4 J/kg. The difference between the inlet and exit enthalpies is around 20000 J/kg, which is available to cool the SRF cavity at 2 K.
2. Methods Before discussing proposed system configurations, the most current system configuration, shown in Fig. 1 is reviewed. Warm streams/sections are red in color and cold regions are blue. For the purpose of this study, it is assumed that helium will be drawn from a supply at 4.5 K and 3 bar, which sets the boundary condition for process point 1, where it enters a heat exchanger (HX). At point 2, the enthalpy of the stream is lowered as a consequence of its energy exchange with the low pressure cold stream passing through points 4 and 5 in the HX. The heat exchanger is selected as the control volume of interest. In its current form the problem is not fully constrained. Both points 5 and 2 are not known and a design point is assumed for the heat exchanger in order to complete the model. Once the complete process model is set up with design data, the results are checked for second law violations to ensure that the assumptions are valid. There are two contributions to the total heat load, Qin , for this system. First is a static load that arises due to components that provide a direct thermal link between the cold region and the ambient such as power couplers, waveguides, and, valves. The second is a dynamic load that appears as a consequence of routine operation of the SRF cavity. A combined total heat load of 30 W can be assumed but the model can be normalized for the purpose of this study. Once exact heat loads are calculated which depends on the RF system requirements and broader cryomodule design, this change can be effected with ease in the process model. Knowing the value of Qin , the mass flow rate required for steady state operation can be calculated. Applying the first law to this steady
2.1. A dual-bath-single-temperature system The first proposed design is a dual-bath-single-temperature (DBST) configuration, shown in Fig. 2 [11]. This configuration proposes operating two separate liquid helium baths, both at 2 K. The SRF cavity is placed in the bath enclosed within process points 6 and 7. The separate bath (3-4-5) allows for pure liquid to be drawn from point 5 and fed to the SRF cavity bath. Flow is driven by the pressure head that exists because of the height of the liquid He II column in the reservoir. Between points 5 and 6, He flow is regulated by means of a valve that is thermally coupled to with the ambient and thus represents a source of additional heat that must be taken into account when calculating the enthalpy at point 6. Calculating the enthalpy at 5 requires special attention. Its position at the bottom of the liquid reservoir results in an increased pressure, 2
Cryogenics 104 (2019) 102984
D.K. Ravikumar, et al.
Fig. 2. Schematic of a dual-bath-single-temperature system. Fig. 3. Schematic of a dual-bath-dual-temperature system.
creating a corresponding increase in enthalpy. This can be treated as an isothermal compression process, with gravity providing the compression. The saturation pressure Psat of He at 2 K is 3129.3 Pa. Thus, at the bottom of a 10 cm-deep helium II reservoir, the combined pressure is 3272 Pa. The enthalpy corresponding to a temperature of 2 K and pressure at point 5 is now 1643.2 J/kg as opposed to 1642.4 J/kg for liquid close to the surface of the reservoir. For zero heat leak into the reservoir 3-4-5, the energy balance equation is:
ṁ 3 = ṁ 5
(h5 − h4 ) (h3 − h4 )
motivation behind holding the reservoir at 1.9 K is that a third heat exchanger can be used in the colder bath to further lower the enthalpy of the incoming stream of helium into the cavity bath. Upon leaving this heat exchanger, the flow branches into two streams, one to replenish the cavity bath and the other to replenish the reservoir. Control valves are required to control the flow into both baths. The performance of each heat exchanger sets the conditions at points 3 and 4. The mass flow for the system as a whole, ṁ 1 is simply the sum of ṁ 4 and ṁ 6 . Flow required for the cavity bath, ṁ 6 is obtained from
(4)
ṁ 6 can be calculated from a similar energy balance for the cavity bath; ṁ 6 =
ṁ 6 =
Qcavity h 7 − h6
Qcavity h 7 − h6
(6)
A first-law analysis for the control volume 3-4-5 at steady state and with zero heat leak yields:
(5)
This configuration can be setup with or without a valve between points 5 and 6. Without a valve, the supply reservoir has to be located such that the liquid level and the cross connecting line comes to level equilibrium with the cavity bath, and thus will have no vapor generation. If a valve is used, some vapor generation is expected owing to the heat leakage through the valve. In this case, the enthalpy rises from 1643.2 J/kg to 2320.7 J/kg, if the valve contributes 1 W. For a typical heat leak range depending on the size of the system, the vapor fraction can be significant. Microphonics generated in the reservoir space due to the incoming stream would propagate via the reservoir volume, the fill line and valve into the cavity bath. Some attenuation is expected since the transmitted mechanical energy from above the reservoir will spread throughout the liquid reservoir inventory, only a fraction of which will continue through the fill line into the cavity bath. The remaining energy is transmitted via the vapor exit line that shares the return with vapor exit from the cavity bath.
ṁ 4 = ṁ 6
(h4 − h3) (h5 − h3)
(7)
In order for the DBDT configuration to supply liquid at a sufficiently low enthalpy not to generate vapor into both cavity and reservoir baths, the pressurized liquid must be cooled below the saturation enthalpy of the respective baths. Because of the finite temperature approach of the heat exchanger and non zero heat leakage through the fill valve, the required subcooling bath temperature has to be sufficiently lowered to offset these factors. In fact the pressurized supply stream enthalpy will never be able to reach the reservoir/subcooler bath enthalpy and will still generate vapor for a top fill configuration into the subcooler bath. There are three parameters that dictate operating pressure/temperature of the subcooling bath: Valve heat leak, pressure of the subcooled stream, and temperature approach of the subcooler heat exchanger. The DBDT configuration just as the first DBST, communicates any microhponics generated in the reservoir/subcooling bath via the vapor exit line to the cavity bath volume. The DBDT has an advantage over the DBST system because it generates significantly smaller vapor fraction, provided that the temperature is sufficiently low. Both the DBST and DBDT system configurations discussed have been drawn up with the notion of lowering the enthalpy of the incoming stream, which is one way of reducing vapor generation.
2.2. A dual-bath-dual-temperature system Another proposed configuration is the dual-bath-dual-temperature (DBDT) system, show in Fig. 3 [11]. In the DBDT system, the reservoir and the bath are held at different temperatures. Although this represents a small change, it requires significant reconfiguration to the adjoining systems. Psat for 1.9 K is 2299.3 Pa. The inlet enthalpy to the cavity bath is 2020.9 J/kg, if the valve between points 4 and 6 contributes 1 W of heat. If the cavity bath and the reservoir are to be connected to the same return line, a flow restriction in line 7–8 is required to hold the 2 K cavity bath at a higher pressure. The two different temperature stages now allow for two heat exchanger stages. The first, where the cold stream is sourced from the 2.0 K bath and the second, where the cold stream is sourced from the 1.9 K reservoir. The
2.3. A quiet helium source The third system, called the Quiet Helium Source (QHS), is shown in Fig. 4 [11]. This system consists of a single bath where the SRF cavity will be housed. Liquid helium is held at a temperature of 2.0 K. Also present is a heat exchanger to lower the enthalpy of the incoming helium stream. The QHS works on the principle that controlling the 3
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Fig. 5. Trends in liquid head required as the approach (Δ T) changes.
superior performance, the system is analyzed in further detail below. To start, the difference in temperatures ΔT between the supply helium leaving the heat exchanger and the helium in the bath, called the ‘approach’ is assumed. If the exit temperature increases, it is important to track how the required height of the liquid column responds. In the ideal case, the valve that controls the flow between the heat exchanger and the bath will have no heat leakage. The liquid head required to exceed saturation pressure is shown in Fig. 5. For the current application in an SRF cavity cryostat, a liquid head greater than a meter may not be practical. Data beyond this range is provided for the sake of completeness to cover the range of temperatures beyond 2.0 K where helium remains a superfluid. In practice a finite amount of heat will leak through valves and any other components that might interface with the ambient. If properly engineered, the heat leak from these contributions can be reduced to a watt or less. The plot in Fig. 6 has been generated for different values of heat leak. For convenience, the mass flow rate and heat contribution from the valve are collapsed into a single parameter as the change in enthalpy, Δ h. For each value of the change in enthalpy, variations in the height of the liquid column are tracked for different pressures. As is seen in the figure, for a supply pressure of 3 bar, the lowest liquid head required to suppress vapor generation is about 5 m. Typically, SRF cavity cryomodules measure no more than 1.5 m in the vertical direction. To stay within a reasonable range of 1 m for the liquid head requirement, the inlet stream enthalpy should be less than 2500 J/kg. From Fig. 5, the inlet stream pressure upstream of the inlet valve, point 4, needs to be below 1.5 bar. The approach, Δ T needs to be even lower. For a helium supply fixed at 4.5 K and 3 bar, and for a given performance of the refrigeration recovery heat exchanger, the pressure downstream of point 2 can be lowered. An interesting effect of such a pressure decrease is that helium experiences a rise in temperature due to the Joule-Thomson effect. Such a rise in temperature, coupled with the changing specific heat of the incoming helium dramatically improves the performance of the subcooler heat exchanger, thus producing a lower exit enthalpy. As a consequence of this lower enthalpy stream, the liquid head required to suppress vapor generation is reduced by an order of magnitude. Minimum head requirements from a parametric study are summarized in Table 2. This study is carried out given a performance of the refrigeration recovery heat exchanger (point 2), which sets the lowest allowable pressure for points 3 and 4, that would allow for the best level of subcooling. The pressure at process point 3 cannot be lowered freely. It is bounded by the constraint, to keep the system quiet, that the pressure must be high enough to suppress any vapor being generated between process points 3 and 4.
Fig. 4. Schematic of a quiet helium source (QHS) system.
pressure above a liquid surface can control vapor fraction of the incoming stream. If the pressure is greater than the saturation pressure at that point, then no vapor is generated. The incoming stream of higher-enthalpy helium can thus be released into the bath without any vapor generation. This can be achieved if the height of the liquid column above the helium inlet is properly calibrated such that the pressure at its bottom is higher than Psat for the incoming stream. A throttling valve is required after the subcooler to control the flow of the liquid helium into the bath. As in the other cases, the inclusion of this valve and it’s heat leakage of 1 W means the enthalpy at point 5 is 4000 J/kg. The simplicity of this design means it can be implemented with relative ease in conjunction with either a DBST or a DBDT system. There is a legitimate concern however, that the presence of multiple valves can cause pressure instabilities due to thermoacoustic instabilities. For situations where this is an overwhelming concern, a phase separator operating between 1.2 and 1.5 bar can be added upstream of point 1. The first valve, between 1 and 2 can thus be eliminated. This will ensure that only subcooled liquid is drawn through the rest of the system until the fill valve into the 2 K bath.
3. Results and discussion Process models have been devised using data from HePak, a property data package for helium. For each of these systems, helium is supplied at 3 bar and 4.5 K. The enthalpy and quality are shown in Table 1. As is evident from Table 1, the QHS system completely eliminates flow induced microphonics by not generating any vapor. It is worth noting that the exit enthalpy for the QHS system is high since it corresponds to a supply pressure of 3 bar. Since the QHS system offers Table 1 Change in performance parameters for different system configurations. System configuration
Exit enthalpy (J/kg)
x (%)
Current DBST DBDT QHS
6552.45 2320.70 2020.87 4000.56
20 7 2 0
4
Cryogenics 104 (2019) 102984
D.K. Ravikumar, et al.
Fig. 6. Variation in liquid head for different values of pressure and heat leak through the control valve.
head requirements by 1.9%. All of these studies point toward the conclusion that the QHS is a very practical design.
The subcooler HX approach, Δ T on the horizontal axis in Fig. 6 represents the difference in temperature between the bath at 2 K and the temperature at which supply helium leaves the heat exchanger. For this study, the approach is varied from 10 mK to 200 mK. It can be seen that the rise in head is very sensitive to changes in enthalpy of the supply stream. Thus, for situations where the liquid head is a constraint, the heat exchanger should be sized to deliver an approach of 50 mK or lower. In addition, the valve heat leakage into the supply helium stream should be kept less than 0.5 W. For cases where both the liquid head and the heat exchanger sizes are constrained, the QHS can be deployed in tandem with either the DBST or a DBDT system described earlier. This would facilitate a much lower supply enthalpy while ensuring no vapor is generated when helium enters the bath. For example, in the DBST case (Fig. 2), this would mean that the QHS would be located between points 6 and 7. Point 7 would then lie at the bottom of the SRF cavity bath. In addition, sensitivity studies, particularly the effects of uncertainties in property data, due to pressure control limitations and from heat exchanger performance on the required liquid head were calculated for the design case of 25 mK approach for the subcooler exit temperature (Appendix A). The liquid head required for a 25 mK approach is 1.19 m. It is found that for a 10% variation in the overall heat transfer coefficient ‘U’, there is a 1% change in the liquid head. For control issues in pressure with a over a margin of 25 mbar, the liquid head rises by 1.2%. In the third case where the upstream HX performance is inadequate, a 0.7 K rise in the exit temperature caused only a 5 mK rise in the subcooler’s exit temperature. This in turn raises the liquid
4. Conclusions Different system configurations have been proposed to reduce or eliminate flow-induced microphonics in 2 K cryogenic systems. A thermodynamic process model has been established for each of these designs, and is used to calculate how much vapor is generated for each configuration. The QHS design appears to completely suppress vapor generation and thus outperforms the other two designs. Parametric studies have been performed to explore trends in key design parameters for this configuration, notable to obtain a practical system size, the operating pressure in the subcooler stream upstream of the supply valve to the cavity bath needs to be less than 1 bar. It is noted that the liquid head required for the QHS to work effectively is very sensitive to the enthalpy and pressure at which helium is supplied. For special cases that are further constrained, the QHS system can be used as a modification to the DBST or DBDT systems. The studies summarized in this paper are conceptual solutions to this problem. Practical concerns surrounding implementations in a real cryogenic system are yet to be explored. Potential limitations to the solutions proposed include thermoacoustic oscillations (TAOs) through valve stems that may generate vapor and thereby induce vibrations. Actual achievable performance limit of the subcooler heat exchanger which will also reduce the available enthalpy margin and may thus generate vapor. It is also necessary to be mindful of the placement of
Table 2 Point 2
Point 3
Point 4
Point 5
Point6
T2 K
P2 kPa
h2 J/kg
T3 K
P3 kPa
h3 J/kg
T4 K
P4 kPa
h4 J/kg
T5 K
P5 kPa
h5 J/kg
2 K bath min head reqd (m)
3.6 3.4 3.2 3.0 2.6 2.3 2.3
300 300 300 300 300 300 300
8376.8 7786.3 7249.9 6766.1 5915.3 5287.5 5287.5
3.89 3.75 3.62 3.49 3.24 3.03 2.81
72.6 62.7 54.0 46.4 33.8 25.2 120.0
8376.8 7786.4 7249.9 6766.1 5915.3 5287.5 5287.5
2.01 2.01 2.01 2.01 2.01 2.01 2.01
72.6 62.7 54.0 46.4 33.8 25.2 120.0
2181.3 2112.1 2051.1 1998.0 1909.8 1849.8 2511.9
2.089 2.079 2.070 2.062 2.047 2.037 2.132
4.021 3.912 3.817 3.731 3.587 3.487 4.588
2181.3 2112.1 2051.1 1998.0 1909.8 1849.8 2511.9
0.624 0.548 0.481 0.421 0.32 0.25 1.00
5
Cryogenics 104 (2019) 102984
D.K. Ravikumar, et al.
valves owing to flow instabilities and control issues that can arise. These concerns define the scope for future studies to investigate such issues on a case-by-case basis.
how sensitive the exit enthalpy is in relation to the changes in the supply pressure. Our current sensors are accurate to 1% of their design range, which is 20 mbar. With a control window of 5 mbar, the 25 mbar change in pressure results in a rise of 17.5 J/kg in the enthalpy. This rise in enthalpy corresponds to a rise in the liquid head required to suppress vapor by 1.4 cm, which is a 1.2% change. It is thus concluded that errors in controlling the pressure do not result in a significant negative impact on the process.
Acknowledgments The study has been supported by Brookhaven Science Associates, LLC under contract No. DE-SC0012704 with the U.S. Department of Energy.
A.3. Variations due to inadequacies in the upstream HX Appendix A. Error and uncertainty analysis Lastly, the case where the upstream heat exchanger does not perform as expected is analyzed. For this case, the exit temperature of the upstream heat exchanger was changed. The rise in the exit temperature from the subcooler was then calculated for a fixed ‘UA’. When the exit from the upstream heat exchanger is 2.8 K, the subcooler is engineered for an exit temperature of 2.025 K. Raising the exit temperature from 2.8 K to 3.5 K saw the exit temperature from the subcooler rise by 50 mK, raising the liquid head requirements by 2.3 cm or 1.9%. Thus, a significantly worse performance of the upstream heat exchanger doesn’t have a proportionate impact on the stream leaving the subcooler.
An error and uncertainty analysis has been performed for various parameters that affect the exit enthalpy of the subcooler stream and thus the required design liquid head for the QHS process to perform. For example, a design case where the subcooler is designed for a stream pressure of 1.45 bar and an exit temperature approach of 25 mK. This corresponds to an exit temperature (Texit ) of 2.025 K and a required liquid head of 1.19 m. Around 2 K, the saturated enthalpy change versus boiling point pressure change is approximately dHsat / DPsat = 580 J/Kg/ KPa, corresponding to a liquid head requirement of 0.0017 m per J/kg change in enthalpy of the inlet stream into the bath. Uncertainty in obtaining the subcooler’s design exit temperature and controlling the supply pressure would lead to an uncertainty in the subcooler exit stream’s enthalpy. The Cp of the subcooler exit stream is nominally 5700 J/kg-K. With a 5 mK rise, the stream enthalpy changes by 34 J/kg, leading to a liquid head change of 2 cm. Uncertainty in pressure of the 1.45 bar inlet stream, with a dH/dP = 7 J/kg/kPa, leads to less than 1 cm/kPa in liquid head requirement.
References [1] Accardi A, et al. Electron ion collider: the next QCD frontier. arxiv:1212.1701v3. [2] Van Sciver SW. Helium cryogenics. 2nd ed. NewYork: Springer New York; 2012. [3] Ge M, et al. Measurements and analysis of cavity microhponics and frequency control in the cornellERL mail LINAC prototype cryomodule. In: Proceedings of LINAC 2016, East Lansing, MI, USA. [4] Grimm TL, et al. Measurement and control of microphonics in high loaded-Q superconducting RF cavities. In: Proceedings of LINAC 2004, Lübeck, Germany. [5] McGee MW, et al. Investigation of thermal acoustic effects on SRF cavities within CM1 at Fermilab. arxiv. [6] Huang Y, et al. Cryogenic systems for proof of the principle experiment of coherent electron cooling at RHIC. AIP Conf Proc 2014;1573:1325. [7] Kugeler O, et al. Measurement and compensation of microphonics in CW-operated tesla-type cavities. In: Proceedings of ERL07, Daresbury, UK. [8] Kugeler O, et al. Microphonics measurements in a CW-driven tesla-type cavities. In: Proceedings of EPAC06, Edinburgh, Scotland. [9] Padamsee H. RF superconductivity. Dramstadt, Germany: Wiley publishing; 2009. [10] Knudsen P. Testing and analysis of an exergetically efficient 4 K to 2 K helium heat exchanger PhD Dissertation Mechanical Engineering, Old Dominion University; 2016. [11] Ravikumar D. Thermal studies on cryogenic components for the electron – ion collider at Brookhaven National Laboratory PhD Dissertation Mechanical Engineering, Stony Brook University; 2018. [12] Arp V, McCarthy, RD. HEPAK – NIST technical Note 1334; 1989.
A.1. Uncertainty in the transport properties The first of these is the uncertainty in the transport properties. Once the heat exchanger design point performance or the ‘UA’ is fixed, the effect of the variation of U on the exit temperature is calculated. Here, ‘U’ is the overall heat transfer coefficient and ‘A’ is the area of the heat exchanger. On performing such an analysis, it is found that a 10% decrease in ‘U’ corresponds to a 4.4 mK rise in the exit temperature. The head required to suppress vapor for such a case rises by 2.0 cm, or 1.7%. Thus, the exit temperatures are not very sensitive to a change in U, caused by uncertainty in transport property data. A.2. Sensitivity due to pressure control issues Another subject of interest in this series of studies is determining
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Cryogenics journal homepage: www.elsevier.com/locate/cryogenics
Eliminating flow-induced microphonics in a superfluid helium cryogenic system Dhananjay K. Ravikumara,
⁎,1
T
, Yatming R. Thanc, Jon P. Longtinb
a
Plasma Science and Fusion Center, Massachusetts Institute of Technology, Cambridge, MA, United States Department of Mechanical Engineering, Stony Brook University, Stony Brook, NY 11790, United States c Collider – Accelerator Department, Brookhaven National Laboratory, Upton, NY 11973, United States b
A R T I C LE I N FO
A B S T R A C T
Keywords: Superfluid helium Superconducting radio frequency (SRF) cavity Microphonics Cryogenic system design
Superconducting radio frequency cavities are the devices of choice when it comes to accelerating charged particle beams in modern particle accelerators. They are held in a bath of liquid helium, to maintain their operating temperature at 2.0 K. The dimensions of these cavities are controlled within microns to facilitate operation at design conditions. During operation however, these cavities experience microphonic disturbances i.e., small mechanical deformations, that cause an undesired response in the electrical performance of the cavity. This paper proposes solutions to mitigate microphonics caused by fluid flow, particularly by the fill line into the helium bath in a 2.0 K cryogenic system. Three different systems designs are proposed, two of which dramatically reduce vapor generation and thereby its contribution to microphonics. The third design is found to completely suppress vapor generation and is explored in further detail.
2010 MSC: 80A-20
1. Introduction Modern particle colliders are colossal machines that energize and steer counter-rotating beams of charged particles to collide head-on. The Relativistic Heavy Ion Collider (RHIC) at Brookhaven National Lab (BNL) is one such facility, capable of colliding gold ions together and, until recently, spin-polarized proton beams too. Electric and magnetic fields are used to accelerate and steer the beam along the collider’s 4 km circumference. The devices that maintain the required electric fields to accelerate such beams are metallic structures called Radio Frequency (RF) cavities. Oscillating magnetic fields inside RF cavities create electric currents in the cavity walls. Joule heating from these currents causes energy loss and is dissipated as heat. The proposed upgrade of the existing RHIC facility into an electron-ion collider (EIC) [1], calls for high-gradient and high-field RF cavities, which require the use of superconducting radio frequency (SRF) cavities. The SRF cavities are made from niobium and become superconducting below 9.16 K. Helium is the only cryogen that can be used in conventional large scale systems to achieve such temperatures. Even when the material is in the superconducting state there is still a small finite energy dissipation due to residual surface impedance of the niobium when interacting with an RF field. This resistance, called the BCS resistance, drops with temperature.
To offer an operating margin and suppress BCS resistance, these cavities are typically operated at or below 4.5 K. SRF cavity assemblies consist of the cavities themselves, housed in a helium vessel which is, in turn, surrounded by a vacuum chamber with pressures of ≈10−6 Torr. Cavities are precisely held in their designed shape in order to maintain the specific frequency at which they are designed to operate. It is common to have a mechanical and piezoelectric tuner arrangement [9] to compensate for a shift in operating frequency caused by minute deformations. During routine operation, effects of mechanical disturbances from the environment are felt by the cavity, causing it to detune. This phenomenon, called microphonics detuning can be the cause of significant degradation in the machine’s performance [3–5,7].Microphonic disturbances originate from various sources. This study is concerned primarily with disturbances caused by the flow of helium in the cryogenic system, herein referred to as ‘flow induced’ microphonics. This scope of this study is restricted in particular, to the flow of helium into the cavity bath. Other possible source of acoustic energy such as those from flow, driven by compressor or vacuum pump suction used to pump on the helium bath, out of the system does not have any measurable impact on microphonics. This has been observed while testing other cavities here at BNL and is corroborated by [8].
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Corresponding author. E-mail address: [email protected] (D.K. Ravikumar). 1 This is the author’s current active affiliation. All work for this manuscript was performed during the author’s previous appointments at Brookhaven National Laboratory and Stony Brook University. https://doi.org/10.1016/j.cryogenics.2019.102984 Received 9 April 2019; Received in revised form 7 October 2019; Accepted 9 October 2019 Available online 31 October 2019 0011-2275/ © 2019 Elsevier Ltd. All rights reserved.
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At Helium-I temperatures near 4.5 K, the pool boiling regime can be nucleate or film boiling, depending on the surface heat fluxes on the cavity into the helium bath. Pressure fluctuations caused by the violent bubble expansion and collapse is transferred to the cavity and is a dominant source of microphonics. Other popular choices for operating temperatures lie in the Helium - II regime, at or below 2.0 K. Owing to the superfluid state’s vastly superior transport properties [2], most cases of routine operation of SRF cavities do not produce a heat flux high enough to form bubbles. Although heat movement through helium at 2 K is silent there is still significant microphonics felt by the cavities. This can be attributed to pressure disturbances above the liquid bath, either from the incoming flow of helium or the discharge of the helium vapor. At 2 K, SRF cavities are cooled in a bath of helium - II, that is continuously evaporating. Helium leaving the bath is replenished at the same rate as the evaporation to maintain steady-state operation. In most cases, the source of this He supply stream is at a higher pressure and temperature. Typically, refrigeration recovery from the low-pressure vapor is done with a heat exchanger. This lowers the enthalpy of the incoming warmer higher pressure liquid helium. At some point before it enters the cavity bath, flow passes through a throttling device and leaves at saturation pressure, Psat that corresponds to bath temperature. In current system designs, the inlet stream’s enthalpy is still relatively high leading to significant vapor generation upon expansion through the throttling device, resulting in a two-phase slug flow. Slugs of liquid helium are interspersed between packets of helium vapor, causing microphonic disturbances in an otherwise quiet 2 K system. Lowering the vapor generation will help mitigate microphonic effects. While this can be done by reducing enthalpy [10] or by separating the volumes through a heat exchanger [6], this study provides an alternate approach where even a relatively high enthalpy stream can be delivered with no vapor being generated. The follow sections detail several different system designs and the motivation behind them. Following this, an analysis is presented comparing the features of each design with a particular emphasis on vapor generation. The goal of the study, is to minimize the vapor mass fraction x for the He flow into the cavity bath volume. Also included is a short consideration of how these designs can be used in tandem for special cases.
Fig. 1. Schematic of current 2 K systems.
state system, one can solve for the mass throughput for the system once the design conditions for the system are specified
ṁ 1 = ṁ 5 =
Qcavity + Q valve + QleakHX h5 − h1
(1)
Here ‘h’ is the enthalpy, Qcavity is the dynamic heat load contributed by the SRF cavity, Q valve is the static heat load due to the valve and QleakHX is the static heat leak through the heat exchanger. If a smaller part of the system is used such as the cavity bath, the expression can be written as:
Qin + ṁ 3 h3 = ṁ 4 h4
(2)
Realizing that ṁ 3 = ṁ 4 = ṁ must be equal for steady-state operation, Eq. (2) can be rewritten as
ṁ =
Qin h4 − h3
(3)
Here h4 is the saturated vapor enthalpy at 2 K, and h3 = h2 since expansion through the valve is isenthalpic, for the case where there is no heat leak through the valve. During the expansion process, vapor is generated and in this case the mass fraction of vapor, x, is 18.25% as obtained from HePak[12], a helium property database, at a pressure of 3129.3 Pa. This corresponds to vapor temperature of 2 K and an enthalpy of h3 = 5914.6 J/kg, for the chosen operating temperature at point 2 of 2.6 K. If the valve contributes a heat leakage of 1 W, this enthalpy now rises to 6552.4 J/kg. The difference between the inlet and exit enthalpies is around 20000 J/kg, which is available to cool the SRF cavity at 2 K.
2. Methods Before discussing proposed system configurations, the most current system configuration, shown in Fig. 1 is reviewed. Warm streams/sections are red in color and cold regions are blue. For the purpose of this study, it is assumed that helium will be drawn from a supply at 4.5 K and 3 bar, which sets the boundary condition for process point 1, where it enters a heat exchanger (HX). At point 2, the enthalpy of the stream is lowered as a consequence of its energy exchange with the low pressure cold stream passing through points 4 and 5 in the HX. The heat exchanger is selected as the control volume of interest. In its current form the problem is not fully constrained. Both points 5 and 2 are not known and a design point is assumed for the heat exchanger in order to complete the model. Once the complete process model is set up with design data, the results are checked for second law violations to ensure that the assumptions are valid. There are two contributions to the total heat load, Qin , for this system. First is a static load that arises due to components that provide a direct thermal link between the cold region and the ambient such as power couplers, waveguides, and, valves. The second is a dynamic load that appears as a consequence of routine operation of the SRF cavity. A combined total heat load of 30 W can be assumed but the model can be normalized for the purpose of this study. Once exact heat loads are calculated which depends on the RF system requirements and broader cryomodule design, this change can be effected with ease in the process model. Knowing the value of Qin , the mass flow rate required for steady state operation can be calculated. Applying the first law to this steady
2.1. A dual-bath-single-temperature system The first proposed design is a dual-bath-single-temperature (DBST) configuration, shown in Fig. 2 [11]. This configuration proposes operating two separate liquid helium baths, both at 2 K. The SRF cavity is placed in the bath enclosed within process points 6 and 7. The separate bath (3-4-5) allows for pure liquid to be drawn from point 5 and fed to the SRF cavity bath. Flow is driven by the pressure head that exists because of the height of the liquid He II column in the reservoir. Between points 5 and 6, He flow is regulated by means of a valve that is thermally coupled to with the ambient and thus represents a source of additional heat that must be taken into account when calculating the enthalpy at point 6. Calculating the enthalpy at 5 requires special attention. Its position at the bottom of the liquid reservoir results in an increased pressure, 2
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Fig. 2. Schematic of a dual-bath-single-temperature system. Fig. 3. Schematic of a dual-bath-dual-temperature system.
creating a corresponding increase in enthalpy. This can be treated as an isothermal compression process, with gravity providing the compression. The saturation pressure Psat of He at 2 K is 3129.3 Pa. Thus, at the bottom of a 10 cm-deep helium II reservoir, the combined pressure is 3272 Pa. The enthalpy corresponding to a temperature of 2 K and pressure at point 5 is now 1643.2 J/kg as opposed to 1642.4 J/kg for liquid close to the surface of the reservoir. For zero heat leak into the reservoir 3-4-5, the energy balance equation is:
ṁ 3 = ṁ 5
(h5 − h4 ) (h3 − h4 )
motivation behind holding the reservoir at 1.9 K is that a third heat exchanger can be used in the colder bath to further lower the enthalpy of the incoming stream of helium into the cavity bath. Upon leaving this heat exchanger, the flow branches into two streams, one to replenish the cavity bath and the other to replenish the reservoir. Control valves are required to control the flow into both baths. The performance of each heat exchanger sets the conditions at points 3 and 4. The mass flow for the system as a whole, ṁ 1 is simply the sum of ṁ 4 and ṁ 6 . Flow required for the cavity bath, ṁ 6 is obtained from
(4)
ṁ 6 can be calculated from a similar energy balance for the cavity bath; ṁ 6 =
ṁ 6 =
Qcavity h 7 − h6
Qcavity h 7 − h6
(6)
A first-law analysis for the control volume 3-4-5 at steady state and with zero heat leak yields:
(5)
This configuration can be setup with or without a valve between points 5 and 6. Without a valve, the supply reservoir has to be located such that the liquid level and the cross connecting line comes to level equilibrium with the cavity bath, and thus will have no vapor generation. If a valve is used, some vapor generation is expected owing to the heat leakage through the valve. In this case, the enthalpy rises from 1643.2 J/kg to 2320.7 J/kg, if the valve contributes 1 W. For a typical heat leak range depending on the size of the system, the vapor fraction can be significant. Microphonics generated in the reservoir space due to the incoming stream would propagate via the reservoir volume, the fill line and valve into the cavity bath. Some attenuation is expected since the transmitted mechanical energy from above the reservoir will spread throughout the liquid reservoir inventory, only a fraction of which will continue through the fill line into the cavity bath. The remaining energy is transmitted via the vapor exit line that shares the return with vapor exit from the cavity bath.
ṁ 4 = ṁ 6
(h4 − h3) (h5 − h3)
(7)
In order for the DBDT configuration to supply liquid at a sufficiently low enthalpy not to generate vapor into both cavity and reservoir baths, the pressurized liquid must be cooled below the saturation enthalpy of the respective baths. Because of the finite temperature approach of the heat exchanger and non zero heat leakage through the fill valve, the required subcooling bath temperature has to be sufficiently lowered to offset these factors. In fact the pressurized supply stream enthalpy will never be able to reach the reservoir/subcooler bath enthalpy and will still generate vapor for a top fill configuration into the subcooler bath. There are three parameters that dictate operating pressure/temperature of the subcooling bath: Valve heat leak, pressure of the subcooled stream, and temperature approach of the subcooler heat exchanger. The DBDT configuration just as the first DBST, communicates any microhponics generated in the reservoir/subcooling bath via the vapor exit line to the cavity bath volume. The DBDT has an advantage over the DBST system because it generates significantly smaller vapor fraction, provided that the temperature is sufficiently low. Both the DBST and DBDT system configurations discussed have been drawn up with the notion of lowering the enthalpy of the incoming stream, which is one way of reducing vapor generation.
2.2. A dual-bath-dual-temperature system Another proposed configuration is the dual-bath-dual-temperature (DBDT) system, show in Fig. 3 [11]. In the DBDT system, the reservoir and the bath are held at different temperatures. Although this represents a small change, it requires significant reconfiguration to the adjoining systems. Psat for 1.9 K is 2299.3 Pa. The inlet enthalpy to the cavity bath is 2020.9 J/kg, if the valve between points 4 and 6 contributes 1 W of heat. If the cavity bath and the reservoir are to be connected to the same return line, a flow restriction in line 7–8 is required to hold the 2 K cavity bath at a higher pressure. The two different temperature stages now allow for two heat exchanger stages. The first, where the cold stream is sourced from the 2.0 K bath and the second, where the cold stream is sourced from the 1.9 K reservoir. The
2.3. A quiet helium source The third system, called the Quiet Helium Source (QHS), is shown in Fig. 4 [11]. This system consists of a single bath where the SRF cavity will be housed. Liquid helium is held at a temperature of 2.0 K. Also present is a heat exchanger to lower the enthalpy of the incoming helium stream. The QHS works on the principle that controlling the 3
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Fig. 5. Trends in liquid head required as the approach (Δ T) changes.
superior performance, the system is analyzed in further detail below. To start, the difference in temperatures ΔT between the supply helium leaving the heat exchanger and the helium in the bath, called the ‘approach’ is assumed. If the exit temperature increases, it is important to track how the required height of the liquid column responds. In the ideal case, the valve that controls the flow between the heat exchanger and the bath will have no heat leakage. The liquid head required to exceed saturation pressure is shown in Fig. 5. For the current application in an SRF cavity cryostat, a liquid head greater than a meter may not be practical. Data beyond this range is provided for the sake of completeness to cover the range of temperatures beyond 2.0 K where helium remains a superfluid. In practice a finite amount of heat will leak through valves and any other components that might interface with the ambient. If properly engineered, the heat leak from these contributions can be reduced to a watt or less. The plot in Fig. 6 has been generated for different values of heat leak. For convenience, the mass flow rate and heat contribution from the valve are collapsed into a single parameter as the change in enthalpy, Δ h. For each value of the change in enthalpy, variations in the height of the liquid column are tracked for different pressures. As is seen in the figure, for a supply pressure of 3 bar, the lowest liquid head required to suppress vapor generation is about 5 m. Typically, SRF cavity cryomodules measure no more than 1.5 m in the vertical direction. To stay within a reasonable range of 1 m for the liquid head requirement, the inlet stream enthalpy should be less than 2500 J/kg. From Fig. 5, the inlet stream pressure upstream of the inlet valve, point 4, needs to be below 1.5 bar. The approach, Δ T needs to be even lower. For a helium supply fixed at 4.5 K and 3 bar, and for a given performance of the refrigeration recovery heat exchanger, the pressure downstream of point 2 can be lowered. An interesting effect of such a pressure decrease is that helium experiences a rise in temperature due to the Joule-Thomson effect. Such a rise in temperature, coupled with the changing specific heat of the incoming helium dramatically improves the performance of the subcooler heat exchanger, thus producing a lower exit enthalpy. As a consequence of this lower enthalpy stream, the liquid head required to suppress vapor generation is reduced by an order of magnitude. Minimum head requirements from a parametric study are summarized in Table 2. This study is carried out given a performance of the refrigeration recovery heat exchanger (point 2), which sets the lowest allowable pressure for points 3 and 4, that would allow for the best level of subcooling. The pressure at process point 3 cannot be lowered freely. It is bounded by the constraint, to keep the system quiet, that the pressure must be high enough to suppress any vapor being generated between process points 3 and 4.
Fig. 4. Schematic of a quiet helium source (QHS) system.
pressure above a liquid surface can control vapor fraction of the incoming stream. If the pressure is greater than the saturation pressure at that point, then no vapor is generated. The incoming stream of higher-enthalpy helium can thus be released into the bath without any vapor generation. This can be achieved if the height of the liquid column above the helium inlet is properly calibrated such that the pressure at its bottom is higher than Psat for the incoming stream. A throttling valve is required after the subcooler to control the flow of the liquid helium into the bath. As in the other cases, the inclusion of this valve and it’s heat leakage of 1 W means the enthalpy at point 5 is 4000 J/kg. The simplicity of this design means it can be implemented with relative ease in conjunction with either a DBST or a DBDT system. There is a legitimate concern however, that the presence of multiple valves can cause pressure instabilities due to thermoacoustic instabilities. For situations where this is an overwhelming concern, a phase separator operating between 1.2 and 1.5 bar can be added upstream of point 1. The first valve, between 1 and 2 can thus be eliminated. This will ensure that only subcooled liquid is drawn through the rest of the system until the fill valve into the 2 K bath.
3. Results and discussion Process models have been devised using data from HePak, a property data package for helium. For each of these systems, helium is supplied at 3 bar and 4.5 K. The enthalpy and quality are shown in Table 1. As is evident from Table 1, the QHS system completely eliminates flow induced microphonics by not generating any vapor. It is worth noting that the exit enthalpy for the QHS system is high since it corresponds to a supply pressure of 3 bar. Since the QHS system offers Table 1 Change in performance parameters for different system configurations. System configuration
Exit enthalpy (J/kg)
x (%)
Current DBST DBDT QHS
6552.45 2320.70 2020.87 4000.56
20 7 2 0
4
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Fig. 6. Variation in liquid head for different values of pressure and heat leak through the control valve.
head requirements by 1.9%. All of these studies point toward the conclusion that the QHS is a very practical design.
The subcooler HX approach, Δ T on the horizontal axis in Fig. 6 represents the difference in temperature between the bath at 2 K and the temperature at which supply helium leaves the heat exchanger. For this study, the approach is varied from 10 mK to 200 mK. It can be seen that the rise in head is very sensitive to changes in enthalpy of the supply stream. Thus, for situations where the liquid head is a constraint, the heat exchanger should be sized to deliver an approach of 50 mK or lower. In addition, the valve heat leakage into the supply helium stream should be kept less than 0.5 W. For cases where both the liquid head and the heat exchanger sizes are constrained, the QHS can be deployed in tandem with either the DBST or a DBDT system described earlier. This would facilitate a much lower supply enthalpy while ensuring no vapor is generated when helium enters the bath. For example, in the DBST case (Fig. 2), this would mean that the QHS would be located between points 6 and 7. Point 7 would then lie at the bottom of the SRF cavity bath. In addition, sensitivity studies, particularly the effects of uncertainties in property data, due to pressure control limitations and from heat exchanger performance on the required liquid head were calculated for the design case of 25 mK approach for the subcooler exit temperature (Appendix A). The liquid head required for a 25 mK approach is 1.19 m. It is found that for a 10% variation in the overall heat transfer coefficient ‘U’, there is a 1% change in the liquid head. For control issues in pressure with a over a margin of 25 mbar, the liquid head rises by 1.2%. In the third case where the upstream HX performance is inadequate, a 0.7 K rise in the exit temperature caused only a 5 mK rise in the subcooler’s exit temperature. This in turn raises the liquid
4. Conclusions Different system configurations have been proposed to reduce or eliminate flow-induced microphonics in 2 K cryogenic systems. A thermodynamic process model has been established for each of these designs, and is used to calculate how much vapor is generated for each configuration. The QHS design appears to completely suppress vapor generation and thus outperforms the other two designs. Parametric studies have been performed to explore trends in key design parameters for this configuration, notable to obtain a practical system size, the operating pressure in the subcooler stream upstream of the supply valve to the cavity bath needs to be less than 1 bar. It is noted that the liquid head required for the QHS to work effectively is very sensitive to the enthalpy and pressure at which helium is supplied. For special cases that are further constrained, the QHS system can be used as a modification to the DBST or DBDT systems. The studies summarized in this paper are conceptual solutions to this problem. Practical concerns surrounding implementations in a real cryogenic system are yet to be explored. Potential limitations to the solutions proposed include thermoacoustic oscillations (TAOs) through valve stems that may generate vapor and thereby induce vibrations. Actual achievable performance limit of the subcooler heat exchanger which will also reduce the available enthalpy margin and may thus generate vapor. It is also necessary to be mindful of the placement of
Table 2 Point 2
Point 3
Point 4
Point 5
Point6
T2 K
P2 kPa
h2 J/kg
T3 K
P3 kPa
h3 J/kg
T4 K
P4 kPa
h4 J/kg
T5 K
P5 kPa
h5 J/kg
2 K bath min head reqd (m)
3.6 3.4 3.2 3.0 2.6 2.3 2.3
300 300 300 300 300 300 300
8376.8 7786.3 7249.9 6766.1 5915.3 5287.5 5287.5
3.89 3.75 3.62 3.49 3.24 3.03 2.81
72.6 62.7 54.0 46.4 33.8 25.2 120.0
8376.8 7786.4 7249.9 6766.1 5915.3 5287.5 5287.5
2.01 2.01 2.01 2.01 2.01 2.01 2.01
72.6 62.7 54.0 46.4 33.8 25.2 120.0
2181.3 2112.1 2051.1 1998.0 1909.8 1849.8 2511.9
2.089 2.079 2.070 2.062 2.047 2.037 2.132
4.021 3.912 3.817 3.731 3.587 3.487 4.588
2181.3 2112.1 2051.1 1998.0 1909.8 1849.8 2511.9
0.624 0.548 0.481 0.421 0.32 0.25 1.00
5
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valves owing to flow instabilities and control issues that can arise. These concerns define the scope for future studies to investigate such issues on a case-by-case basis.
how sensitive the exit enthalpy is in relation to the changes in the supply pressure. Our current sensors are accurate to 1% of their design range, which is 20 mbar. With a control window of 5 mbar, the 25 mbar change in pressure results in a rise of 17.5 J/kg in the enthalpy. This rise in enthalpy corresponds to a rise in the liquid head required to suppress vapor by 1.4 cm, which is a 1.2% change. It is thus concluded that errors in controlling the pressure do not result in a significant negative impact on the process.
Acknowledgments The study has been supported by Brookhaven Science Associates, LLC under contract No. DE-SC0012704 with the U.S. Department of Energy.
A.3. Variations due to inadequacies in the upstream HX Appendix A. Error and uncertainty analysis Lastly, the case where the upstream heat exchanger does not perform as expected is analyzed. For this case, the exit temperature of the upstream heat exchanger was changed. The rise in the exit temperature from the subcooler was then calculated for a fixed ‘UA’. When the exit from the upstream heat exchanger is 2.8 K, the subcooler is engineered for an exit temperature of 2.025 K. Raising the exit temperature from 2.8 K to 3.5 K saw the exit temperature from the subcooler rise by 50 mK, raising the liquid head requirements by 2.3 cm or 1.9%. Thus, a significantly worse performance of the upstream heat exchanger doesn’t have a proportionate impact on the stream leaving the subcooler.
An error and uncertainty analysis has been performed for various parameters that affect the exit enthalpy of the subcooler stream and thus the required design liquid head for the QHS process to perform. For example, a design case where the subcooler is designed for a stream pressure of 1.45 bar and an exit temperature approach of 25 mK. This corresponds to an exit temperature (Texit ) of 2.025 K and a required liquid head of 1.19 m. Around 2 K, the saturated enthalpy change versus boiling point pressure change is approximately dHsat / DPsat = 580 J/Kg/ KPa, corresponding to a liquid head requirement of 0.0017 m per J/kg change in enthalpy of the inlet stream into the bath. Uncertainty in obtaining the subcooler’s design exit temperature and controlling the supply pressure would lead to an uncertainty in the subcooler exit stream’s enthalpy. The Cp of the subcooler exit stream is nominally 5700 J/kg-K. With a 5 mK rise, the stream enthalpy changes by 34 J/kg, leading to a liquid head change of 2 cm. Uncertainty in pressure of the 1.45 bar inlet stream, with a dH/dP = 7 J/kg/kPa, leads to less than 1 cm/kPa in liquid head requirement.
References [1] Accardi A, et al. Electron ion collider: the next QCD frontier. arxiv:1212.1701v3. [2] Van Sciver SW. Helium cryogenics. 2nd ed. NewYork: Springer New York; 2012. [3] Ge M, et al. Measurements and analysis of cavity microhponics and frequency control in the cornellERL mail LINAC prototype cryomodule. In: Proceedings of LINAC 2016, East Lansing, MI, USA. [4] Grimm TL, et al. Measurement and control of microphonics in high loaded-Q superconducting RF cavities. In: Proceedings of LINAC 2004, Lübeck, Germany. [5] McGee MW, et al. Investigation of thermal acoustic effects on SRF cavities within CM1 at Fermilab. arxiv. [6] Huang Y, et al. Cryogenic systems for proof of the principle experiment of coherent electron cooling at RHIC. AIP Conf Proc 2014;1573:1325. [7] Kugeler O, et al. Measurement and compensation of microphonics in CW-operated tesla-type cavities. In: Proceedings of ERL07, Daresbury, UK. [8] Kugeler O, et al. Microphonics measurements in a CW-driven tesla-type cavities. In: Proceedings of EPAC06, Edinburgh, Scotland. [9] Padamsee H. RF superconductivity. Dramstadt, Germany: Wiley publishing; 2009. [10] Knudsen P. Testing and analysis of an exergetically efficient 4 K to 2 K helium heat exchanger PhD Dissertation Mechanical Engineering, Old Dominion University; 2016. [11] Ravikumar D. Thermal studies on cryogenic components for the electron – ion collider at Brookhaven National Laboratory PhD Dissertation Mechanical Engineering, Stony Brook University; 2018. [12] Arp V, McCarthy, RD. HEPAK – NIST technical Note 1334; 1989.
A.1. Uncertainty in the transport properties The first of these is the uncertainty in the transport properties. Once the heat exchanger design point performance or the ‘UA’ is fixed, the effect of the variation of U on the exit temperature is calculated. Here, ‘U’ is the overall heat transfer coefficient and ‘A’ is the area of the heat exchanger. On performing such an analysis, it is found that a 10% decrease in ‘U’ corresponds to a 4.4 mK rise in the exit temperature. The head required to suppress vapor for such a case rises by 2.0 cm, or 1.7%. Thus, the exit temperatures are not very sensitive to a change in U, caused by uncertainty in transport property data. A.2. Sensitivity due to pressure control issues Another subject of interest in this series of studies is determining
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