CONSIDERATION OF FLOWS AND PRESSURES IN THE HYDROGEN MANIFOLDS OF THE NPDGAMMA HYDROGEN TARGET SYSTEM

Revision 0.00 Prepared: H. Nann, Indiana University, October 2011 Checked : Z. Tang, Indiana University, October Approved: S. Penttila, ORNL, October 11, 2011 1.0 Scope

We briefly consider the hydrogen flows and pressures in the hydrogen supply and gas-handling manifolds, where hydrogen gas (H2) flow is controlled by regulators, flow-control valves, restrictive flow orifice devices, and pressure limiting relief valves. We will show that proposed flow restrictors and relief valves protect the piping and the manifolds for pressures above the defined operating pressures. The function of the restrictive flow orifice devices is to passively limit flows nominally to 20 SLPM (standard liter per minute) out from the manifolds or below. The maximum hydrogen flow rate into the target vessel can be only about 20 SLPM defined by cooling capacity of the cryo-coolers. The hydrogen gas is flowing in the supply and gas-handling manifolds and connecting lines only during the target filling process that takes less than two days. The estimate for the nominal frequency of the filling is once per two months. During the times when the target is operational, the manifolds and lines are filled with helium gas. 2.0 Piping and flow diagram

Appendix 1 shows the full piping and flow diagram of the NPDGamma LH2 target system (FUND13NPDG24F8U8713A001.pdf). In the calculations we have used the Bates Internal Report # 90-02 [1], the Crane Technical Paper No. 410 [2], sources found in the literature especially for consideration of restrictive flows in orifices, and information from the manufacturers.

3.0 Hydrogen supply manifold; drawing FUND13NPDG24P8713A005

Before the start of filling the LH2 target vessel, three H2 cylinders will be connected to the supply manifold. During the target filling only one H2 cylinder per time is opened to the manifold. When the cylinder is empty, the next cylinder will be opened. If some reason the cylinder needs to be replaced during the target filling operation, the replacement will be performed according to “Operating

Procedures for the NPDGamma Liquid Hydrogen Target at the BL 13; Change of Empty Hydrogen Gas Cylinder” in the presence of a target expert. The regulators PR101, PR102, PR103 and flow restrictors FR101, FR102, FR103 are connected to the supply manifold with flexible pressure lines. During the cylinder change the regulator will be disconnected from the cylinder. After the regulator is reconnected to the new cylinder the remade regulator joint will be tested for leaks with soap bubbles, according to the procedure “Change of Empty Hydrogen Gas Cylinder”. The function of the flow restrictors FR101, FR102, FR103 is to control H2-flow rate out from the cylinder in a case of a regulator failure to the level that the combined flow capacity of the relief valve RV101 and the vent piping after the relief valve can handle the flow rate from the cylinder at the cylinder pressure of 2200 psi without that the pressure in the manifold exceeds significantly the operating pressure of the manifold piping.

FR101, FR102, FR103 are sintered porous flow restrictors manufactured by Mott Corporation: model 5140-1/4-SS-5000 SCCM H2 @ 10 psig. For their flow restrictors Mott Corp. provides flow rate information for hydrogen; for the 5140-1/4-SS-5000 SCCM H2 @ 10 psig model the volumetric flow at 2200 psig is 1100 SLPM, see figure 1. The relief pressure of RV101 is set to 100 psid. Because of the large initial pressure of 2200 psi in cylinder, the flow through the flow restrictive device is in choked flow condition (a sonic flow condition). The flow through a flow restricting device is considered to be choked already at a low value of the ratio of the upstream pressure to the downstream pressure; for instance, for hydrogen the threshold ratio is 1.9. In every incident scenario we discuss in this document flows through the flow restrictors are choked. 3.1. Failure of pressure regulator PR101 (or PR102 or PR103)

First, we consider a scenario where one of the cylinder regulators fails when the cylinder pressure is 2200 psi. We will show that the combined conductance of the RV101 and the relief piping after RV101, through which gas flows to the outside of the cylinder building (Gas Cylinder Bldg. 107100800M8U8711A098), is large enough to handle the flow rate of the flow restrictor. Figure 2 shows the piping/flow diagram of the supply manifold. When the cylinder pressure is 2200 psi, the volumetric flow through the flow restrictor is 1100 SLPM.

Next, we need to check that the flow capacity of RV101 is large enough to handle 1100 SLPM when the pressure in the manifold will stay nominally at 100 psi range. RV101 is model SS-4CA-VCR-150 SS poppet check valve from Swagelok with adjustable cracking pressure. It has a flow coefficient of CV= 0.47. Figure 3 shows the air flow rate through RV101 as a function of inlet pressure given by Swagelok. At 100 psi inlet pressure the flow rate is 700 SLPM for air. The corresponding flow rate for hydrogen is 2450 SLPM, which is significantly smaller than 1100 SLPM from FR101, RV101 has enough capacity to handle the flow rate

from the Mott’s flow restrictor 5140-1/4-SS-5000 SCCM H2 at 2200 psi cylinder pressure.

Fig. 1. Flow rate of the Mott porous flow restrictor as a function of input pressure. The date is from Swagelok. NEEDS TO BE UPDATED to 5000-ccm plot. We are

waiting for the new plot from the Mott Corp. However, it will be just an off set to this graph, at 5000 ccm the pressure difference is 10 psi.

Next, we need to check that the 2-m long ¼” OD vent line from RV101 to the outside of the cylinder storage building can handle the flow rate without increasing the pressure in the manifold significantly over the operating pressure. The vent stack line restricts the flow rate, if the flow is in sonic regime. It can be shown that the flow is in the sonic especially at the end of the pipe. If the upstream-downstream pressure difference of the pipe is sufficiently high, the exit velocity will reach the velocity of sound, and the flow is sonic. We have estimated using Ref. [2] that for a 60-psi pressure drop, the flow in the vent line becomes sonic. For a flow rate of 1100 SLPM, the inlet pressure of RV101 is 140 psia, the pressure drop across RV101 is 50 psia, the upstream pressure of the vent line is 90 psia and the vent line exits to atmospheric pressure. We can conclude that the ¼” OD and 2 m long vent line can handle the 1100 SLPM volumetric flow rate or 1.5 g/s mass flow rate from flow restrictor FR101 (FR102 or FR103), at the beginning of the discharge the pressure in the manifold increases to 140 psia.

Fig. 2. H2 supply manifold; a snapshot from FUND13NPDG24F8U8713A001.pdf.

3.2 Emptying rate of the hydrogen cylinder through flow restrictor

To calculate the effective flow coefficient × the orifice surface area term, CA for the porous flow restrictor from Mott Corp we use equation

€

˙ m = CA kρP 2k +1⎛

⎝ ⎜

⎞

⎠ ⎟

(k+1) /(k−1), (1)

where

€

˙ m [ ]= kg/s, C is discharge coefficient, [A] = m2 is effective discharge cross-sectional area, k = cp/cv ratio of specific heats, [ρ] = kg/m3 is real gas density at P and T, [P] = Pa is absolute upstream gas pressure. Using equation (1) for the flow restrictor 5140-1/4-SS-5000 SCCM H2 @ 10 psig we get CA = 1.62 × 10-7 m2. Next, with this flow coefficient-area value we estimate the rate at which the cylinder leaks if the flex line, for instance, after the flow restrictor FR101 breaks. For realistic flow rate out from the cylinder through the flow restrictor into the cylinder storage building we use the Bird, Stewart, and Lightfoot source-term [5]

€

t = f (1−k) / 2 −1( ) × 2k −1

×VCA

×gkP0ρ0

2k +1⎛

⎝ ⎜

⎞

⎠ ⎟ (k+1) /(k−1)⎡

⎣ ⎢ ⎢

⎤

⎦ ⎥ ⎥

−1/2

. (2)

where t = time in seconds f = fraction of initial gas weight remaining in cylinder at time t k = cp/cv for hydrogen = 1.41 V = volume of the cylinder in ft3 = 1.55 ft3

C = coefficient of discharge A = cross sectional area of the effective orifice in ft2 g = gravitational acceleration = 32.17 ft/s2 P0 = initial gas pressure in the source vessel in lb/ft2 = 316800 lb/ft2 = 2200 psi ρ0 = initial gas density in the cylinder in lb/ft3 at 2200 psi: ρ0=0.748 lb/ft3.

Figure 4 shows the calculated mass flow rate out from the cylinder as a function of time through the Mott 5140-1/4-SS-5000 SCCM H2 @ 10 psig flow restrictor. Figure 5 shows the evolution of the cylinder pressure during the discharge. It will take 4.2 min to pressure in the cylinder to reduce to half.

3.3 Normal operation of the H2 supply manifold

In a normal operation mode the pressure in the supply manifold can go up to 100 psig limited by RV101. The gas pressure out from the manifold is defined

by PR104 followed by FR104, see figure 6. PR104 reduces the initial 100-psig to 80 psig maximum. The function of FR104 is to limit the flow rate out from the supply manifold into the Target Building during an accident scenario where the ~100 ft long ¼” line between the supply manifold and the gas handling manifold is broken. FR104 is a Mott model 5140-1/4-SS-2500 SCCM H2 @ 10 psig flow restrictor. At 80 psig pressure in the supply manifold after PR104 the maximum flow out from the FR104 would be about 25 SLPM corresponding to 0.035 g/s mass flow rate. With this very small flow rate the flow is subsonic and the pressure loss across the 100 ft long line is only 0.1 psi. So, the 80 psig supply pressure is available in the gas handling manifold for the target filling.

Fig. 3. Flow rate as a function of inlet pressure for RV101 when gas is air.

Figure 4. Evolution of the mass flow rate through Mott 5140-1/4-SS-5000 SCCM H2 @ 10 psig flow restrictor from the H2 cylinder.

Figure 5. Cylinder pressure as a function of time when leak is through Mott 5140-1/4-SS-5000 SCCM H2 @ 10 psig flow restrictor.

4. The gas-handling manifold

Figure 6 shows the flow diagram of the gas-handling manifold. The gas from the supply manifold flows along the ¼” OD line to the gas-handling manifold. The maximum pressure in the gas handling manifold could be 80 psi to push the gas into the target through the flow control valve FCV100 and flow restrictor FR100, which is also a Mott 5140-1/4-SS-2500 SCCM H2 @ 10 psig. The maximum hydrogen condensing rate could be 20 SLPM. The maximum operating pressure in the gas-handling manifold is limited to 100 psig by the RV102 and RV103 with 100 psid set pressures.

Figure 6. Gas handling manifold; a snapshot from FUND13NPDG24F8U8713A001.pdf. References: [1] W.M. Schmitt and C.F. Williamson, Boil-off rates of cryogenic targets

subject to catastrophic vacuum failure, Bates Internal Report 90-02 (1990). [2] Flow of Fluids through Valves, Fittings, and Pipe, CRANE Technical Paper

No. 410 (1988). [3] Roger D. Shrouf and Shane R. Page, Gas Flow Characterization of

Restrictive Flow Orifice Devices, Sandia Report SAND97-1670, UC-607 (1997).

[4] Mott Corporation, http://www.mottcorp.com/corp/corp.cfm. [5] Bird, R.B., Stewart, W.E., and Lightfoot, E.N., Transport Phenomena,

John Wiley&Sons, New York, New York, USA, 1960.

APPENDIX