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Acta Astronautica

Acta Astronautica 86 (2013) 188–200

0094-57

http://d

n Corr

E-m1 Cu

(NASA)

32899,

journal homepage: www.elsevier.com/locate/actaastro

An improved approach for tank purge modeling

Jacob R. Roth 1, Sunil Chintalapati n, Hector M. Gutierrez, Daniel R. Kirk

Mechanical and Aerospace Engineering, 150 West University Boulevard, Florida Institute of Technology, Melbourne, FL 32901, USA

a r t i c l e i n f o

Article history:

Received 28 June 2012

Received in revised form

14 January 2013

Accepted 18 January 2013Available online 31 January 2013

Keywords:

Liquid rocket propulsion

Helium

Tank purging

Computational fluid dynamics (CFD)

65/$ - see front matter & 2013 IAA. Publish

x.doi.org/10.1016/j.actaastro.2013.01.009

esponding author. Tel.: þ1 3214128233; fa

ail address: chintals@fit.edu (S. Chintalapati

rrest address: National Aeronautics and S

Launch Services Program VA-H3, Kenned

USA.

a b s t r a c t

Many launch support processes use helium gas to purge rocket propellant tanks and fill

lines to rid them of hazardous contaminants. As an example, the purge of the Space

Shuttle’s External Tank used approximately 1,100 kg of helium. With the rising cost of

helium, initiatives are underway to examine methods to reduce helium consumption.

Current helium purge processes have not been optimized using physics-based models,

but rather use historical ‘rules of thumb’. To develop a more accurate and useful model of

the tank purge process, computational fluid dynamics simulations of several tank

configurations were completed and used as the basis for the development of an algebraic

model of the purge process. The computationally efficient algebraic model of the purge

process compares well with a detailed transient, three-dimensional computational fluid

dynamics (CFD) simulation as well as with experimental data from two external tank

purges.

& 2013 IAA. Published by Elsevier Ltd. All rights reserved.

1. Introduction and background

PURGING rocket propellant tanks with helium is doneto ensure that contaminant gases or water that maybecome a hazard during flight are removed from the tankprior to filling with propellant. For example, residualnitrogen or water may freeze and solidify when broughtinto contact with cryogenic propellants such as hydrogenor oxygen. Catastrophic damage may occur, if rocketengine’s turbomachinery would ingest solid nitrogen orwater particles. A commonly used purge gas is heliumbecause of its lower boiling point, 4.22 K at 1 atm, thanany liquid propellant [1]. The low boiling point is impor-tant since the introduction of cryogenic liquids will notcause helium to solidify, unlike many of the contami-nants, which a purge is attempting to replace. With thecost of helium continuing to rise, initiatives undertaken

ed by Elsevier Ltd. All right

x: þ1 3216748813.

).

pace Administration

y Space Center, FL

are to attempt to reduce the amount of helium used in atank purge process, while still ensuring complete com-pliance with purging criteria [2].

An example of a process that uses a significant amountof helium is the purge of the Space Shuttle ExternalTank (ET) prior to the introduction of propellants,although what follows will be true for propellant tanksused on the next generation of rockets as well. At theconclusion of the purge process, samples taken wouldanalyze the relative humidity of the gas mixture insideof the tank. If the purge is successful, the gas remainingin the tank will have a relative humidity below acritical threshold thus ensuring that only acceptablelevels of residual water remain inside the tank. Addition-ally, the amount of nitrogen or other contaminant gasesmonitored to ensure that these gases are at acceptablelevels.

The purge flow rate and purge time for the ET are notcurrently based on any detailed models to optimize theprocess, but rather on loose historical ‘rules of thumb’.Additionally, within the literature, there does not appearto be any type of systematic study for providing basicguidelines of purge characteristics of tanks and lines and

s reserved.

Nomenclature

d diameter, (m)D tank outer diameter, (m)DAB binary diffusion coefficient, (m2/s)Fr Froude number; ratio of inertial to gravita-

tional forces, ðU=ffiffiffiffiffigL

pÞ

g gravitational acceleration, (m/s2)G constant of obstruction diameter and velocity

combinationH* tank heightHn

o obstruction location below inletK representative parameterL representative length, (m)Ln

L layer formation locationLn

m layer location during steady motionP parameterQ volumetric flow rate, (m3/s)Pl layer thickness fraction parameterRe Reynolds number, ratio of inertial to viscous

forces, (rUL/m)t no obstruction time constant downstream, (s)tþ time constant addition due to an obstruction,

(s)tL layer formation time constant, (s)tL layer formation time, (s)t time, (s)tm motion initialization time constant, (s)to obstruction impact time constant, (s)tpo obstruction time constant downstream, (s)

THn

L layer formation thicknessTHn

m thickness during steady motionU velocity, (m/s)UI inlet representative velocity, (m/s)Un

L center layer velocity, (D/s)Zn

p depth of penetration

Greek symbols

a thermal diffusivity; (m2/s)b thermal expansion coefficient; (1/K)m dynamic viscosity, (kg/m*s)r density; (kg/m3)u kinematic viscosity, (m2/s)

Subscripts

D due to diffusione exiti inletL layermin minimumND without diffusiono obstruction

Superscripts

* length dimension normalized by D

J.R. Roth et al. / Acta Astronautica 86 (2013) 188–200 189

purging of tanks or lines is currently limited to using oneof two methods:

1.

Advanced modeling, such as computational fluiddynamics (CFD) of purge performed on each tank or line. 2. An overly conservative estimate of purge time and gasreplacement volume based on the experience and datafrom prior tank purges.

Fig. 1. Generic tank geometry mimicking key features of the ET

Any new model used to predict the success of a purgeprocess or employed to minimize the use of heliummust successfully predict the level of relative humidityand contaminant gases left inside of the propellanttank after the purge. In order to develop a physics-basedmodel of the tank purge process a generic tankcreated which is much similar to the ET and displayedin Fig. 1.

The tank mimics features of the ET including theoverall height to diameter ratio, gas inlet and outletgeometries, and anti-vortex baffle system located at thebase of the tank. Unlike the actual ET which has a series ofstiffener rings located along the inside diameter of thetank, the tank used for this study has a smooth inner wall.

The tank purged in the vertical orientation done withhelium introduced at the top inlet through a radialdiffuser. The helium displaces the gas within the tank

and the resulting mixture of gas forces through the outlet.Examining two limiting cases of tank purging allows forapproximate minimum and maximum expected purgingtimes to be determined.

1.

The minimum expected purge time for a cylindricaltank at a constant pressure is; when, the purge gas atthe inlet, enters the tank with no mixing, no moleculardiffusion, and acts as the face of piston, which forcesthe tank gas through the outlet located at the bottomof the tank. The minimum purge time for the geometry

Fig. 2. Contours of nitrogen mole fraction for low (upper) and high (lower) purge flow rates.

J.R. Roth et al. / Acta Astronautica 86 (2013) 188–200190

shown in Fig. 1 and given by Eq. (1) is approximately1,200 s.

tmin ¼p4

HD2

Qið1Þ

2.

An estimate for the maximum purge time occurs whenthe purge gas completely mixes with the tank gas andthe mixture exits through the outlet. To predict thetank time for the perfectly mixed scenario, a numericalcode iteratively solves the governing differential equa-tions for the concentration of gases inside the tank.This model takes into account the inlet flow rate ofpurge gas, the complete mixing of purge and tankgases, changes in pressure inside the tank and finallyexit mass flow rate of the tank gases for a given exitarea. For the geometry shown in Fig. 1 the completelymixed purge time is approximately 10,000 s.

Fig. 2 shows the examples of these two limiting casesmodeled using computational fluid dynamics (CFD), witha tank initially filled with nitrogen and using helium as apurge gas. The top row of pictures shows nitrogen molefraction contours during a low flow rate purge, in whichthe helium forms a ‘piston’ face on top of the nitrogen andpushes the tank gas out of the exit without creating aswirling, mixed flow, i.e. the purge and tank gases remain

separated throughout the purging process. This case tendsto lead to shorter purge times and minimal use of heliumpurge gas. However, purging too slowly allows for mole-cular mixing via diffusion to take place and thus increasesthe actual purge time above a perfectly non-mixed case.

The bottom row of pictures in Fig. 2 shows a purgeusing a much higher flow rate of purge gas. The high flowrate purge gas enters the tank through the radial diffuserand quickly forms vorticies, which mix the two gasestogether within the tank. This mixing is detrimentalbecause it then takes an enormous supply of helium topurge the tank to satisfactory levels. These two illustra-tive cases show that to purge tanks in the least time withthe least use of helium, an optimal flow rate of purge gasis to be determined. A full 3D transient computationalfluid dynamics (CFD) simulation of the purging processincorporating all essential physics using this tank wascompleted and discussed in Section 5.

2. Computational modeling

In order to develop an accurate, quick turnaround-timetank purge process simulation tool, a systematic anddetailed numerical survey was performed in order tobetter understand the underlying physics of purge beha-vior. These studies elucidated key aspects associatedwith the purge process. Simulation performed used

J.R. Roth et al. / Acta Astronautica 86 (2013) 188–200 191

commercial computational fluid dynamics (CFD) codeANSYS FLUENT (version 6.3). Gambit (version 2.4), pre-processor for FLUENT used to create and mesh geome-tries. A large number of simulation were run in two-dimensional configuration while some three-dimensionalsimulation were run to account for obstructions in themodel, such as stiffener rings or baffles located within thetank. The computational model used a double precision-

Fig. 3. Binary Vs. multi-compon

Fig. 4. Purge models of, (left) inlet, (right) purge l

pressure based implicit solver with a species model.Second order discretization used for density, momentum,species components, and energy calculations. Grid densityand time-step size sensitivity study performed to ensurethat the solution was capturing essential spatial andtemporal features associated with the purge process. Agrid resolution study was completed to ensure gridindependence in the solution.

ent diffusion comparison.

ayer encounter with obstruction and outlet.

J.R. Roth et al. / Acta Astronautica 86 (2013) 188–200192

Viscosity and diffusion models examined prior to per-forming the parametric study. A full multi-componentmodel option for diffusion is only available with the laminarviscous model. Two purge simulations performed werewith binary diffusion that only differed by the viscousmodel employed. Results showed 6.3% percent differencebetween the laminar and turbulent models. The laminarflow model selected was because of this level of agreementand because of the low flow speeds involved (ReD of theinlet helium flow was 142). A test concerning the behaviorof binary and multi-component diffusion was performedand the results shown in Fig. 3. In all cases, the inlet gas ishelium. The tank gas for the binary case was pure nitrogen.In the multi-component cases, the tank gas was standard airwith the given humidity levels. Standard air was assumedto contain only nitrogen, oxygen, argon, and the necessaryamount of water vapor for the given humidity level.

The difference in starting density relates to the chosenstarting tank purge gas and is not due in any manner tothe actual purge. From the figure, it is evident that theoverall behavior of all the cases is remarkably similar.Most of the differences simply relate to different startingdensity, so binary diffusion option is preferred to allow forshorter simulation times.

3. Numerical modeling of tank purge processes

For a numerical model of a tank purge, the physicalprocesses taking place can be broken into three sections:

1.

TabOve

C

In

1

2

3

4

5

6

7

8

9

1

1

1

1

1

1

1

O

C

1

1

1

2

2

2

Introduction of the purge gas through an inlet.

2. Formation of a purge layer and interaction with tank

wall obstructions (such as baffles or stiffener rings).

le 1rview of numerical simulations sets.

ase H (m) di (m) D (m) di/D

let simulation set

0.102 0.076 0.152 0.5

0.102 0.038 0.152 0.25

0.203 0.102 0.152 0.667

0.203 0.076 0.152 0.5

0.203 0.076 0.152 0.5

0.203 0.051 0.152 0.333

0.203 0.038 0.152 0.25

0.203 0.015 0.152 0.1

0.203 0.137 0.152 0.9

0 0.136 0.025 0.102 0.25

1 0.136 0.051 0.102 0.5

2 0.102 0.051 0.076 0.667

3 0.102 0.038 0.076 0.5

4 0.102 0.025 0.076 0.333

5 0.102 0.008 0.076 0.1

6 0.102 0.069 0.076 0.9

bstruction and exit simulation set

ase H (m) do or de (m) D (m) do/D or

7 0.152 0.076 0.152 0.9

8 0.152 0.038 0.152 0.7

9 0.152 0.102 0.152 0.5

0 0.305 0.076 0.152 0.9

1 0.305 0.076 0.152 0.7

2 0.305 0.051 0.152 0.5

3.

Exit of the contaminant and purging gas mixturethrough the tank’s outlet.

Each section was independently analyzed using aparametric set of computational fluid dynamics (CFD)simulations to explore different tank geometries andsizes, purge flow rates, purge gas conditions (temperatureand pressure) and initial composition of contaminantgases within the tank. For the inlets in this section, anaxial inlet was used to make the models more genericthan those associated with a specific radial inlet diffuser.Fig. 4 shows the modeling approach for each section ofthe purge.

Table 1 presents a summary of the simulations per-formed. For each case, the helium purge gas inlet velocityis uniform across the inlet diameter, and the heliumtemperature and total pressure are 300 K and 1 atm,respectively. The tank initially is completely full of drynitrogen (no water) and with binary diffusion enabled.

The individual obstruction and outflow simulation setscan merge to form a single simulation set because an exitlocated at the bottom of the tank is analogous to anobstruction. Table 1 also presents a summary of theobstruction and exit simulation cases performed. Thecases performed were using laminar flow models withthe tanks oriented vertically.

3.1. Inlet behavior of purge gas

The behavior of the incoming purge gas may introducelarge levels of mixing with gases contained in the tank.These re-circulating flows rapidly mix the purge gaseswith the tank gases, which make the tank more difficult to

Ui (m/s) Rei Fri

0.152–0.762 95–473 0.141–0.70

0.61–3.048 189–947 0.563–2.816

0.114–0.572 95–474 0.106–0.528

0.076–0.114 47–71 0.070–0.106

0.152–0.76 95–473 0.141–0.703

0.229–1.372 95–568 0.211–1.266

0.305–2.134 95–663 0.281–1.97

0.61–1.524 76–189 0.563–1.407

0.038–0.229 43–256 0.035–0.211

0.203–1.413 42–293 0.230–1.597

0.152–0.762 63–316 0.172–0.862

0.076–0.381 32–158 0.100–0.497

0.076–0.686 24–213 0.100–0.895

0.229–1.372 47–284 0.298–1.791

0.61–1.524 38–95 0.796–1.990

0.038–0.229 21–128 0.050–0.298

de/D UL (m/s) Reo or Ree Fro or Fre

0.0152–0.152 17–170 0.014–0.141

0.0152–0.152 13–133 0.014–0.141

0.0152–0.152 9–95 0.014–0.141

0.0152–0.152 17–170 0.014–0.141

0.0152–0.152 13–133 0.014–0.141

0.0152–0.152 9–95 0.014–0.141

J.R. Roth et al. / Acta Astronautica 86 (2013) 188–200 193

purge, and consequently higher purge gas flow rates donot necessarily lead to faster times for a purge. For thecurrent analysis, it is more accurate to have the inlet gasavoid creating any macroscopic vortex development.This criterion ensures that the purge and tank gasesremain in distinct layers defining a boundary betweenthe purge and tank gases that will be referred to simply asthe layer. It is this layer that acts as a piston face todisplace the existing tank gases with purge gas. For theinlet velocities shown in Table 1, the Reynolds numberbased on inlet diameter ranged from 21 to 947, with theintent of introducing a laminar jet of purge gas into thetank. Using data obtained from the simulations shown inTable 1, modified Reynolds and Froude numbers identi-fied were necessary to characterize the inlet purge gasbehavior.

For jets issuing into a quiescent ambient of the samefluid, the Reynolds number is useful to determine whenturbulent mixing is important. For the purge scenariosexamined in this work, the purge gas is different from thetank gases and a modified Reynolds number was devel-oped. A Reynolds number which uses the density of theinlet gas, the viscosity of the tank gas, and the inletdiameter as the characteristic length is valuable in pre-dicting turbulence for cases where the diameter ratio (di/D)is greater than 0.6. In this case, the modified Reynoldsnumber needs to be less than 350 to prevent strongturbulent mixing. For smaller diameter ratios, this numberwas not that relevant. However, the Reynolds number doesnot account for buoyant interactions between differentpurge and tank gases, and therefore another non-dimensional number is required.

A modifed Froude number, which is the ratio of inertiaof the inlet jet to gravitational force, was useful tocharacterize the results of the inlet simulations. Theappropriate velocity is the average velocity across theinlet plane, which scales based on the diameter ratio (di/D)is given in Eq. (2).

Fri ¼Ui ðdi=DÞffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffigðp=4DÞd2

i

q ð2Þ

This number proved to be effective for determining if agiven purge scenario produces an unacceptable level ofvortex development. The value of Fri has to be less than 1in order to avoid turbulent behavior and is usuallyrestricted to about 0.75. The smaller the value becomes,the more well behaved the jet will be.

Fig. 5. Nitrogen mole fraction con

The buoyancy of the incoming jet relative to the tankgas governs the details associated with the formation ofthe layer. To highlight various aspects of layer formation,Fig. 5, shows mole fraction contour of nitrogen (in red)with a helium jet (in blue) with a Fri near the imposed0.75 limit issuing into a tank filled with nitrogen, whichcorresponds to case 10 in Table 1. The initial penetrationof the laminar jet to some depth into the nitrogen is basedon the momentum of the incoming gas as well as thebuoyancy force opposing the inlet gas motion (Fig. 5a).The maximum penetration depth achieved is when theseforces balance. The inlet gas fills a hemispherical regionwith a radius equal to the penetration depth, which forthe conditions examined in this study is on the order ofthe inlet diameter, di.

The jet core near the inlet plane begins to spread alongthe inlet plane wall (Fig. 5b) for the cases when a lightergas issues into tank with a heavier gas. As the corespreads the volume of the trapped gas increases, therebyincreasing the buoyancy forces and the inlet gas movesback toward the inlet increasing the speed at whichthe core continues to spread. Core spreading continuesuntil the inlet gas impacts the outer wall of the tank(Fig. 5c).

The buoyant gas then behaves in an oscillatory mannersimilar to a mass-damper system. Samples of velocitycenterline profiles in the tank at various times highlightthis behavioral characteristic. Fig. 6 shows profiles of axialvelocity normalized by inlet velocity (U/Ui) versus pene-tration distance into the tank normalized by tank dia-meter. Each line represents a different time in thesimulation and the collection of lines highlights thebehavior of the lighter helium gas with the nitrogen gas.In Fig. 6a, the centerline velocity penetrates smoothly intothe tank with time. In contrast, Fig. 6b exhibits anoscillatory behavior that is characteristic of most buoyantjets as shown in Fig. 5b and c. This is because the volumeflow rate of the helium was large enough to penetraterapidly into the nitrogen in the vertical direction withoutfirst displacing most of the nitrogen in the radial direction.The feedback of the nitrogen pushing back on the heliumjet produces an oscillatory motion, which creates theoscillatory velocity profiles. Despite the highly erraticmotion the system eventually damps enough (as thehelium fills radially) to begin to form a smooth layer asshown in Fig. 5d and e. Simulations performed with radialdiffusers also exhibited these general physical features inlarge tanks.

tours (di/D¼ 0.25), Case 10..

Fig. 6. Centerline velocity profiles from Case 8 and Case 5 from Table 1.

J.R. Roth et al. / Acta Astronautica 86 (2013) 188–200194

A criterion to determine the layer formation location isdetermined from the simulation data set. A layer formswhen the average absolute value of the slope of the 50%nitrogen mole fraction surface is less than 101, but thiscriterion can be adjusted to give more or less conservativeestimates of layer formulation location. Large slope valuesindicate extreme wave action in the layer (Fig. 6b), whilelower values indicate a relatively flat layer (Fig. 6a).The thickness and formation time are functions of thelayer formation location.

3.2. Steady layer behavior of purge/tank gas

A study of the purge flow behavior revealed withappropriate flow rate a piston-face shape layer ultimatelyforms, which then pushes the tank gas through the outlet.Molecular diffusion taking place during layer motion issymmetric and perpendicular across the layer. The layervelocity during this steady region is a function of the inletflow rate and tank diameter. The layer velocity mentionedhere refers only to the velocity of the layer center sincethe velocities of the outer regions depend on their localdiffusion rates as well as the center velocity.

3.3. Outlet behavior of tank gas

Most of the turbulent behavior caused by an outletoccurs downstream of the outlet plane. However, thevortices generated around the circumference of the tankexit can trap a portion of the remaining tank gas.A modified Froude number for the outlet, given in Eq.(3), is to characterize the importance of the vortexentrapment of tank gases.

Fre ¼Un

L ðD=deÞp3=2ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffigðp=4Þde

p ð3Þ

Un

L ¼Ui

D

di

D

� �2

ð4Þ

This parameter correlates with the size of the shearlayer formed at the exit plane of the tank. It is this shear

layer, which provides the mechanism for transporting anytrapped tank gas above the exit plane out of the tank.

3.4. Quantification of layer thickness and diffusion

Section 4. will detail the development of an algebraicmodel of the tank purge process using the results of thecomputational fluid dynamics (CFD) cases developed inSection 3. Before the development of algebraic model, twometrics need to be accessed, which are vital to describe apurge process and they are quantification of layer thick-ness and diffusion. The mole fraction of the inlet gasdetermines the layer thickness, with the 50% mole frac-tion being the center of the layer. Layer thickness rangesinclude 75–25% inlet gas fraction, 85–15% inlet gas frac-tion, and 90–10% inlet gas fraction with the layer beingsymmetric about its center. The layer thickness quantifiedby Pl, is the difference between the two fractions repre-senting the edges of the layer. Using the combinationslisted above, Pl would be equal to 0.5, 0.7, and 0.8, and canrange from any number between 0 and 1, with 0 indicat-ing no layer and 1 implying an infinitely thick layer.

The layer thickness as defined must then be incorpo-rated into an expression of generic diffusion growth.Fick’s law predicts that the growth rate of the diffusionlayer is proportional to the square root of the product oftime and the binary diffusion coefficient. A generalexpression for the layer thickness, TH(t), as a function ofPl and Fick’s law is given in Eq. (5)

THðtÞ ¼ f ðPlÞffiffiffiffiffiffiffiffiffiffiDABt

pð5Þ

Using values of TH(t) from the numerical model, thefunctional form involving Pl with values with constant DAB

and over the same time interval would force all of thecurves with differing Pl onto a single curve. The necessarymultiplication factors were then curve fit with respect toPl in order to obtain the parameter necessary to completethe thickness growth equation. The result is Eq. (6) andthe usage of this equation is throughout the algebraic

J.R. Roth et al. / Acta Astronautica 86 (2013) 188–200 195

model developed in Section IV.

THnðtÞ ¼

3:422

D

� �Pl

ð1�PlÞ0:17433

! ffiffiffiffiffiffiffiffiffiffiDABt

pð6Þ

This equation specifies layer thickness growth due todiffusion as a function of time in units of outer diameters(D) and thickness fraction parameter.

4. Development of reduced order algebraic tank purgemodel

This section uses the results of the computational fluiddynamics (CFD) studies completed in Section III todevelop a simplified algebraic model capable of replicat-ing the tank purging process. Algebraic models developedare for the inlet, layer, and exit flows and then combinedinto a single model.

4.1. Inlet model development

This section details three quantities that are all asso-ciated with the inlet flow: layer formation location, time,and thickness. In order to compute the layer formationlocation, two parameters need to be determined. The firstparameter referred to as the inlet representative velocity,UI, quantifies the oscillatory behavior of the purge gas fora range of inlet conditions (shown in Fig. 6). This para-meter takes into account the various turbulence effectsassociated with different di/D ratios and is a scaledversion of the average inlet velocity. A higher UI indicatesthat the layer forms further into the tank. Eq. (7) is a curvefit of UI computed as a function of Ui and di/D. The detailsof the curve fit process are in [3].

UI ¼Uidi

D

� �2 di

D

� �0:675

þdi

D

� �7:75

þ0:18di

D

� �3:5 1

1�ðdi=DÞ

� �0:405" #�1

ð7Þ

The second parameter needed for the estimation of thelayer formation location is the penetration depth of theinlet gas Zn

p. This parameter determines if a layer forms atthe end of the oscillatory period or if the jet penetratesdeep enough into the tank gases that the oscillationsdampen prior to reaching that location. The equation forZn

p was derived from a balance of inlet pressure againstthe buoyancy force generated due to the volume of the

Fig. 7. Purge layer surfaces (di/D

enclosed buoyant gas. The result of this balance is Eq. (8).

Zn

P ¼1

D

� �riU

2

i

2gðre�riÞ

" #ð8Þ

From the computational fluid dynamics (CFD) simula-tions, when the oscillatory behavior of the inlet purge gasdampens out, the layer formation location is determinedin comparison to computed UI from, Eq. (7) and a curve fitof the relationship gave the layer formation locationindependent of penetration depth. If the depth of thepenetration affects the layer, it adds to the curve fit resultwith a scale factor. This scale factor allows for theconcurrent behavior of oscillations and penetration withthe oscillatory effect relating to the size of the penetrationdepth column using di/D. As a result, Eq. (9) is a piecewiseequation that varies depending on the relationshipbetween Zn

p and the exponential curve fit of layer forma-tion location.

Ln

L ¼Zn

Pþ0:05e8:428UI

ffiffiffiffiffiffiffiffiffiffiffi1� di

D

qZn

P0:05e8:428UI

0:05e8:428UI Zn

P o0:05e8:428UI

8<: ð9Þ

The second quantity in this analysis is layer formationtime based on the normalized fill rate per unit depthdescribed in Eq. (4) and the layer formation location,Ln

L and given by Eq. (10).

tL ¼Ln

L D

Ui ðdi=DÞ2ð10Þ

This expression assumes symmetric mixing whichmeans that while some of the tank gas displacesupstream, a similar amount of inlet gas has moved furtherdownstream and thus the amount of gas required isroughly equal to the amount needed to fill the entirevolume above the layer formation location.

The third quantity is layer formation thickness, whichdepends on macroscopic mixing phenomenon betweenthe inlet purge gas and tank gas as well as the moleculardiffusion between these two gases. The effect of macro-scopic mixing assessed was by examining the computa-tional fluid dynamics (CFD) cases with no diffusion.Relevant variables were examined and a following para-meter was identified, Ln

L ðUn

i DtLðdi=DÞ0:8ðDÞ�0:8Þ, which was

plotted versus the computational fluid dynamics (CFD)layer formation thicknesses for four different Pl values.

¼0.167 and Ui¼0.61 m/s) .

J.R. Roth et al. / Acta Astronautica 86 (2013) 188–200196

The results were curve fit and given in Eq. (11).

THn

L,ND ¼ Ln

L

Un

i DtLðdi=DÞ

D

" #0:83:422

5:75

� �Pl

ð1�PlÞ0:17433

!" #

ð11ÞThis curve fit is a scaled version of the generic thick-

ness curve described in Eq. (6). Fig. 7 shows a side-by-sidecomparison of layer thicknesses with time, without andwith the effects of molecular diffusion. The impact ofmolecular diffusion may be significant, for example, at 3 sthe layer with diffusion is approximately twice as thick asthe no diffusion model.

Qualitatively the general shapes of the layer are thesame without and with diffusion and hence the layerformation locations are essentially identical.

To include the effects of molecular diffusion on layerformation thickness, a layer formation time constant wasascertained from a curve fit of tL versus a time scale thatdepends on the difference between the simulation thicknessand the no-diffusion thickness, and is given in Eq. (12).

tL ¼ tL 1þdi

D

� �4

ð12Þ

Eq. (12) is from the layer formation time from Eq. (10)and using the time constant and the representative curvein Eq. (6) the additional thickness of the layer generatedby diffusion can be accounted for using Eq. (13).

THn

L,D ¼3:422

D

� �Pl

ð1�PlÞ0:17433

" # ffiffiffiffiffiffiffiffiffiffiffiffiDABtL

pð13Þ

Diffusion is an additive process and thus the macro-scopic mixing thickness computed in Eq. (13) would addto the molecular diffusion thickness computed in Eq. (11)to produce the layer formation thickness, shown inEq. (14).

THn

L ¼3

4THn

L,NDþ1

2THn

L,D ð14Þ

Eq. (14) without the constant scale factors on the twoinput thicknesses ignores the concurrent growth due tomixing and diffusion, which can hamper diffusion effectsdepending on the particular geometry during the waveaction. Layer thickness due to molecular diffusion

Fig. 8. Final layer formation thickness accuracy.

depends on current thickness of layer and as such, athicker layer grows slower. This effect is incorporated intoEq. (14) using scale factors computed using a curve fitfrom computational fluid dynamics (CFD) simulation data.Fig. 8 shows the plot of Eq. (14) for four different values ofPl and its accuracy.

The precision in final layer formation thickness dependson accurately identifying the initial thickness. Whenattempting to minimize purge times, this is a conservativecomputation because it over-predicts the size of the mix-ing region in most cases.

4.2. Steady layer model development

This section details the progress of the layer as itmoves through the tank. In most of the purging scenarios,the inner circumference of propellant tanks are lined withobstructions (shown in Fig. 4) such as baffles and stiffenerrings. This section also assesses the impact of theseobstructions on the steady layer development. Two quan-tities fully describe the steady layer as it moves throughthe tank and then an additional two quantities character-ize obstruction effects on the steady layer development.The first sets of quantities are steady layer velocity at thecenterline of the tank (axial direction) and a diffusiontime constant for the beginning of layer motion. Theadditional quantities needed to quantify the effects ofhaving obstruction in a tank is the diameter ratio of theobstruction diameter to the outer diameter and thelocation below the inlet plane of the obstruction Hn

o ,which is in units of outer diameters (D’s).

Steady velocity at the center of the tank is from aconstant pressure and temperature requirement that thevolume flow of the inlet gas be equal to the volumedisplacement of the tank gas. It is this requirement thatleads directly to Eq. (4) which defines the velocity of thecenter of the layer.

The diffusion time constant for the beginning of layermotion gives the amount of time required for a sharpinterface between the inlet purge gas and tank gas tobecome the thickness solved for at the end of layerformation. This allows the thickness to continue to growdue to diffusion from its current state. Rearranging Eq. (6)gives the diffusion time constant (for time, tm), and thethickness value in the new equation would be the layerformation thickness from the preceding sub-section.

Steady layer motion is a combination of the quantitiesdefined above along with the fundamental equations ofmotion. Eq. (15) is the equation for layer location as afunction of time, while, Eq. (16) is the thickness equationas a function of time and solved consecutively or as asystem. Layer location Ln

m, in Eq. (15) is measured in unitsof outer diameters (D’s) from the inlet plane.

Ln

mðtþtLÞ ¼ Ln

LþUn

Lt ð15Þ

THn

mðtþtLÞ ¼3:422

D

� �Pl

ð1�PlÞ0:17433

! ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiDABðtmþtÞ

pð16Þ

In order to compute the effect of a given obstruction,the model assumes that the obstructions are sufficiently

J.R. Roth et al. / Acta Astronautica 86 (2013) 188–200 197

far away from each other such that they do not influenceeach other. This modeling assumption would produceinaccurate results for obstructions, which are closelyspaced inside of a tank. Computational fluid dynamics(CFD) simulations show that the obstruction had no effecton the movement of the center layer, but had a macro-scopic effect on layer thickness. Thus, a thickness timeconstant to account for the added layer thickness due toan obstruction is required. The additional time added bythe obstruction (tþ) was characterized by an obstructiontime constant (to) when the center of the layer impactedthe obstruction, a measured post-obstruction time con-stant (tpo), and the expected time constant (t) at the post-obstruction position if no obstruction had been present.The difference between tpo and t is tþ . For differentvalues of to the ratio of the additional time constant to thetime constant at the obstruction is found to be roughly aconstant. The relationship shown in Eq. (17) is with G

being a constant for each obstruction diameter andvelocity combination.

tþtoffiGðdo,U

n

L Þ ð17Þ

The above relation showed some deviation for largervelocities or larger obstructions, which cause heavy mix-ing prior to the obstruction plane. A modified Froudenumber, Eq. (18), similar to the one used in inlet modeldevelopment was useful to characterize the amount ofmixing that a given obstruction would cause to a layer.

Fro ¼U

n

L ðD=doÞp3=2ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffigðp=4Þdo

p ð18Þ

In order to prevent significant mixing, Fro needs to beless than 0.5 for accurate prediction by this algebraicmodel. This value is from computational fluid dynamics(CFD) simulations, which showed macroscopic turbulenceat the higher Fro values, which would impact the layerbefore the obstruction plane. Plots of the time constantratio values in Eq. (17) versus different obstruction para-meters and a curve fit of those plots identified the

Fig. 9. Obstruction effect with curve fit.

relationship given in Eq. (19).

Po ¼

ffiffiffiffiffiffiffiffiffiffiffido=D

pU

n

L

ð19Þ

Plotting this parameter against the values of Eq. (17)gives a curve of the data. Fig. 9 shows the plotted datapoints as well as the curve fit.

The curve fit has a relatively small error if the value ofPo is greater than 15. This requirement is quantitativelysimilar to Fro being less than 0.5. Both parameter restric-tions prevent heavy mixing and trapped purge gas accu-mulation as well as reduce the error inherent in thiscomputation. Using the curve fit from Fig. 9, an equationfor tþ based on known constants previously measured orcalculated as well as the curve fit constants forms Eq. (20).

tþ ¼ ðtoÞ

ffiffiffiffiffiffiffiffiffiffiffido=D

p29:458ðUn

L Þ

" #�1=0:89

ð20Þ

The additional thickness resulting from the obstruc-tion can remain in this form or altered to an actualthickness value using Eq. (6), which, then adds to thelayer when the layer center is at the location of theobstruction. This introduces a discontinuity at eachobstruction and by adding the additional thickness in afunctional manner around the obstruction rectifies thediscontinuity. The work, however, to define the necessaryfunction was not undertaken in this analysis.

4.3. Outlet model development

The difference between obstruction and outlet geome-tries is the location of data collection, as highlighted inFig. 4. The outlet data collection is at the obstructionplane because of the behavior downstream of the outletis of no consequence to the purge procedure. Fre, which isidentical to Fro, has the same maxing restriction, which isFre needs to be less than 0.5 for the model to be accurate.This is due to the fact that the long-term entrainment oftank gas in the vortex regions surrounding the exit is notmodeled.

Each purge case required two modeling approaches. Inthe first model, the exit diameter of the tank (de) is equalto D. In the second model, the exit diameter (de) is treatedas an obstruction (do) in which the resulting additionalthickness is added prior to the exit plane. The twodifferent model approaches for each purge case wereplotted along with the computational fluid dynamics(CFD) results at the exit plane. Examination of the plotlead to an insight of the total additional obstructionthickness that would add to the layer before it reachesthe exit plane. A sample of these results provided in theleft side of Fig. 10a, which has an outlet diameter ratio of0.5 but a value of 0.576 for Fre. This case is extremeexample as it is on the edge of the acceptable Fre rangeand shows the largest difference in curve shape.

As a note, the motion of center layer accelerates at theoutlet plane. However, to maintain simplicity of thealgebraic model, this center layer motion is not consid-ered. This is a reasonable assumption because if there isno motion then the model will be a conservative estimate

Fig. 10. Sample outlet data and blended solution (do/D¼0.5), a) sample outlet data (UL¼0.06096 m/s), b) outlet blended solution (UL¼0.01524 m/s).

J.R. Roth et al. / Acta Astronautica 86 (2013) 188–200198

of the actual values. To reconcile this center layer changewith the obstruction results, it is prudent to assume thatthe center of the layer accelerates through the obstructionand then slows during the mixing downstream. Thiswould provide for the zero net change in center layerlocation seen in the obstruction data sets.

A quantity was needed to explain the difference incurves between the simulation results and model resultsin Fig. 10a, while making sure it would be an overallconservative estimate. A reasonable quantity developed isfrom the adjusted average of the two simulationapproaches discussed in the earlier paragraph. This aver-age is from the value of Fre and a representative equation,shown in Eq. (21) with K being a representative para-meter.

K ¼KNo,eþFreðKeÞ

1þFreð21Þ

Using Eq. (21), any variable as a function of time isfrom the results of both the model run without an outletand the model run with the full obstruction treatment.The solution from this blend is in Fig. 10b alongside theoriginal model data from which the blended solution iscomputed.

5. Full purge model validation

This section compares the model developed in Section 4against experimental data acquired from the purging of twoET hydrogen tanks at the NASA Kennedy Space Center [4].This section also compares the model and experimentaldata with a detailed transient three-dimensional computa-tional fluid dynamics (CFD) simulation.

A standard helium ET purge occurs after an initialnitrogen gas purge, however, prior to the helium purgethe outlet of the tank is open to the ambient and air canintrude into the ET while inspections occur. Helium purgegas enters the tank through the inlet diffuser and the tankgases exit through the outlet port. This purge lastsapproximately 1 h and uses about 1,100 kg of helium.

The data collected during this purge are used to assess theperformance and accuracy of the models. Measurementsof exiting gas concentration are acquired using a PortableRefrigerant Leak Indication System (PReLIS), which is asingle quadropole mass spectrometer system. A capillarytube located just outside of the outlet port samples thegas concentration at 14 s-intervals [4]. Experimental datafor purges of two different ET purges were acquired onDecember 15, 2007 (ET 125) and on April 8, 2008 (ET 128).At the conclusion of this helium purge the outlet port iscovered with a flange which has a 1 in. diameter hole andadditional purging takes place. The purge continues until a1.5–2.5 psig pressure builds up within the tank, after whichthe helium inflow stops but the 1 in. outlet port remainsopen to ambient for about 10 min to vent. The outlet port isthen closed and the tank is pressurized with helium toabout 8.5 psig.

Measurements from nitrogen concentration from theET 125 and ET 128 purges are shown in Fig. 11. The twopurges were completed on different days with somewhatdifferent set volumetric helium purge flow rates. Initialdata from the measurement suggested a volumetric flowrate (2675 standard cubic feet per minute), a revisedestimate was provided later suggested a volumetric flowrate of 1.35 m3/s (2859 cubic feet per minute), Thepurpose of the data is to show approximately how longit takes to purge the ET with helium and the general shapeof the nitrogen mole fraction at tank exit port as afunction of time. The top plot shows nitrogen molefraction at the exit port of the tank during the first1,800 s (30 min) of the purge process. At around 1,100 sa steep drop-off in nitrogen concentration is observedwhich is when the bulk of the nitrogen has been displacedfrom the tank by the incoming helium gas. The middleplot shows a zoom-in of the nitrogen mole fraction at theexit port between 1,000 and 1,250 s from the initiation ofthe purge. Finally, the third plot shows a zoom-in at thetail-end of the purge process between 1,300 and 1,350 swhich is when the data shows less than half a percent ofnitrogen mole fraction exiting the tank. This last plot is

Fig. 11. Comparison between experimental, computation and analytical model prediction of nitrogen mole fraction at tank exit.

J.R. Roth et al. / Acta Astronautica 86 (2013) 188–200 199

particularly valuable to assess the levels of nitrogencontaminant gas still left within the tank after a majorityof the nitrogen has been displaced.

Fig. 11 shows the comparison of the measured nitro-gen mole fraction versus the model developed in Section4. This model was performed with a volumetric flow rateof helium of 1.18 m3/s (2500 standard cubic feet perminute), which was an approximate historical averageof purge flow rates used on numerous ET purges. As canbe seen from the figure the model prediction of N2 molefraction versus time agrees with the overall trends seen inthe measured data. Furthermore, the model also showsthe rapid depletion of nitrogen from the ET between 1,050and 1,200 s. It is interesting to note that this agrees wellwith the very simple estimate made in Eq. (1) for the no-mixing case. However, the no mixing estimate cannotpredict the details of the shape shown in the figure andsimply predicts an abrupt exhaustion in N2, rather thanthe exponential shape shown in Fig. 11.

Fig. 11 also shows results of detailed transient three-dimensional computational fluid dynamics (CFD) simula-tions using the geometry shown in Fig. 1. Fig. 1 shows thecomputational domain for computational fluid dynamics(CFD) simulation, with a close up of inlet diffuser andoutlet port boundary in the domain. The model uses aninlet volumetric flow rate of 1.18 m3/s, which is the sameas the flow rate used in the model. To examine thesensitivity of the purge process to the volumetric flowrate used, a second simulation was completed using1.416 m3/s (3000 cubic feet per minute).

The results show that the model is accurate for thissystem to within o5% of purge time on either data curve.The algebraic model did not consider the effect of interior

stiffeners and small geometric obstruction within thetank because of their relatively small effect on overallpurge behavior. The inlet diffuser area would map to acircular inlet at the top of the tank. The same methodwould map the exit tube at the bottom the tank. Theoverall length would decrease so that the total volume ofthe cylindrical model is the same as the pill shapedhydrogen tank.

While the overall trend of the purge appears to besimilar, there is still an error of about 5% in differentportions of the purge curve. This maximum 5% error isa resulting miscalculation of up to 90 s on the 30-minutepurge. The errors are particularly noticeable in the inletand exit regions because this is where the concentrationschange the slowest. Fig. 11 highlights this fact by picturein bottom showing the region of the purge where themole fraction of tank gas changes from nitrogen tohelium. The initial change in concentration and the finalchange in concentration from nitrogen to helium is lotslower than overall change in concentration. The model iseffective even with tanks that are much different scalesthan the test cases.

6. Conclusions

Current work objective is to use a systematic approachto purge modeling. Purge modeling was decoupled intothree sub-components. Purge inlet was analyzed first. Itsgeneral behavior was studied and conclusions weredrawn concerning overall inlet trends. Simulations werethen run and a sub-model was developed to describe theresults. Steady layer motion and diffusion were thenstudied. They were then combined into a comprehensive

J.R. Roth et al. / Acta Astronautica 86 (2013) 188–200200

sub-model that matched their behavior. Next, obstructionflow and, similarly, outlet flow were examined. Anotherset of simulations was run and sub-models were com-posed that conformed to the results. Once the sub-modelswere completed, they were combined into the full model.Finally, the full model validity was demonstrated againstindependent data.

Importance of Reynolds and Froude non-dimensionalparameters in successfully describing the mixing charac-teristics of purge flow is stressed. An algebraic model wasdeveloped and validated with experimental data thataccurately characterized complete purge behavior. A mod-ified Froude number for each flow geometry was found tobe the most successful single parameter for characterizinggeneral purge mixing behavior. The model is most accuratewhen dealing with purges that heavily rely on steady layermotion and have low turbulence.

Future studies will focus on using a purge gas flow rateschedule which begins the purge with a low flow ratewhen first introducing purge gas into the tank to mini-mize mixing and once the layer has been formed andbegins to move away from the inlet flow rates can beincreased to decrease purge time and minimize diffusion

contact time between purge gases and tank gases acrossthe layer.

Acknowledgments

We would like to extend a special thanks to all of theNASA employees involved in the Kennedy InternshipProgram and the helium reduction project, especially BarryMeneghilli, Deborah Morris, and William Notardonato.

References

[1] Isobaric Properties for Helium, Available from NIST Chemistry Webbook:/http://webbook.nist.gov/cgi/fluid.cgi?Action=Load&ID=C7440597&Type=IsoBar&Digits=5&P=1&THigh=100&TLow=2.1&TInc=1&RefState=DEF&TUnit=K&PUnit=atm&DUnit=kg%2Fm3&HUnit=kJ%2Fkg&WUnit=m%2FsS. (accessed 24.08.10).

[2] Ana Campoy, As Demand Balloons, Helium is in Short Supply, TheWall Street Journal. (December 5, 2007) B.1.

[3] J.R. Roth, Non-dimensional parameterization of tank purge behavior,Florida Institute of Technology, Master’s Thesis, Melbourne, FL, May2009.

[4] Richard Arkin, A Monitoring System For Efficient Utilization ofHelium at KSC. Kennedy Space Center: ASRC Aerospace Corporation,Interim Report, 2008.