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i

NASA/TM—2012–217473

Liquid Acquisition Device Design

Sensitivity Study

M.K. Van Dyke

Marshall Space Flight Center, Huntsville, Alabama

L.J. Hastings

Alpha Technology, Inc., Huntsville, Alabama

November 2012

National Aeronautics and

Space Administration

Marshall Space Flight Center • Huntsville, Alabama 35812
ii

Available from:

NASA Center for AeroSpace Information

7115 Standard Drive

Hanover, MD 21076–1320

443–757–5802

This report is also available in electronic form at

<https://www2.sti.nasa.gov/login/wt/>
iii

TABLE OF CONTENTS

1. INTRODUCTION ............................................................................................................. 1

1.1 Liquid Acquisition Devices Background ....................................................................... 1

1.2 Study Objective ............................................................................................................. 2

2. ANALYTICAL APPROACH ............................................................................................. 3

2.1 Candidate Screen Geometries and Physical Parameters ................................................ 3

2.2 Screen Channel Pressure Drop Sources ......................................................................... 3

2.3 Analysis Sequence and Assumptions ............................................................................ 5

3. ANALYTICAL RESULTS ................................................................................................. 7

3.1 Head Pressure Losses .................................................................................................... 7

3.2 Flow Across Screen Losses ........................................................................................... 8

3.3 Stepwise and Linear Regresssion Modeling .................................................................. 9

3.4 Flow-Through Screen Loss and Bubble Point Combination ......................................... 11

3.5 Screen Parameter Influences ......................................................................................... 13

4. CONCLUSIONS ................................................................................................................ 14

APPENDIX A—STATISTICAL PROCEDURES AND TERMS DEFINITION ................. 16

A.1 Regression Analysis ..................................................................................................... 16

A.2 Multiple and Nonlinear Regressions ............................................................................ 16

A.3 Residual ....................................................................................................................... 17

A.4 Multiple Regression Correlation Coefficient ................................................................ 17

A.5 Stepwise Regression ..................................................................................................... 17

APPENDIX B—MINIMUM LIQUID ACQUISITION DEVICE WIDTH RESULTS ........ 18

APPENDIX C—STEPWISE REGRESSION RESULTS ....................................................... 20

C.1 Backward Stepwise Regression ..................................................................................... 20

C.2 Forward Stepwise Regression ....................................................................................... 21

APPENDIX D—LINEAR REGRESSION EQUATION RESULTS ..................................... 22

D.1 Regression Analysis ..................................................................................................... 22

D.2 Analysis of Variance .................................................................................................... 22
iv

TABLE OF CONTENTS (Continued)

APPENDIX E—‘FLOW THROUGH THE SCREEN LOSS’ CONTRIBUTION

AS A FUNCTION OF ‘BUBBLE POINT PRESSURE’ ANALYSIS ......... 23

APPENDIX F—SCREEN CORRELATION PARAMETER ANALYSIS ............................ 25

REFERENCES ....................................................................................................................... 29
v

LIST OF FIGURES

1. Screen-channel-type LAD propulsion system example application .............................. 2

2. Twilled Dutch screen weave pattern ............................................................................. 3

3. Individual pressure drop contributors .......................................................................... 4

4. Histograms for minimum LAD widths with three screen meshes ................................. 9

5. Residuals versus LAD width using linear regression model ......................................... 10

6. Residuals histogram for LAD width using linear regresison model .............................. 11
vi
vii

LIST OF TABLES

 1. Individual pressure drop terms .................................................................................... 4

 2. Variable requirement levels used in analysis ................................................................. 6

 3. Screen constants for twilled Dutch screens .................................................................. 6

 4. Isopropyl alcohol head height at bubble point breakdown ........................................... 7

 5. Minimum LAD widths versus performance requirements ........................................... 8

 6. Stepwise regression significant variables ....................................................................... 10

 7. Ratio of DPFTS to PBP under various conditions ......................................................... 13

 8. Minimum LAD width results ...................................................................................... 18

 9. Predictor and response variables .................................................................................. 23
viii

NOMENCLATURE

a surface area to unit volume ratio of screen wire, m–1 (ft–1) constant for a given screen

B screen thickness, cm (ft); constant for a given screen

D hydraulic diameter, cm (ft)

d measured pore diameter, cm (ft); represents the average or effective open space 

between the wires

e flow friction factor (dimensionless); constant for a given screen

g ratio of actual acceleration to acceleration of Earth gravity, dimensionless

gc dimension conversion constant, 980 m/s2 (lbm·ft/lbf·s2)

h LAD height, m (ft)

L LAD distance between screen and liquid level, m (ft)

n number of channels in LAD

PBP screen bubble point, kPa/m2 (lb/ft2)

Pscreen screen pressure

Ptotal total pressure

R2 multiple regression correlation coefficient

V volumetric flow rate, L/s (ft3/s)

W LAD width, m (ft)

a viscous resistance coefficient; experimental constant

b inertial resistance coefficient; experimental constant

DPD pressure losses due to dynamic flow

DPFR pressure losses associated with friction as the fluid flows down the channel
ix

NOMENCLATURE (Continued)

DPFTS pressure losses associated with flow through the screen

DPH pressure losses due to head

e screen volume void fraction; ratio of open space volume between wires compared 

to wire volume

μ fluid viscosity, Newton-s/m2 (lbm/ ft·s)

r density of fluid, kg/m3 (lb/ft3)
x
1

TECHNICAL MEMORANDUM

LIQUID ACQUISITION DEVICE DESIGN SENSITIVITY STUDY

1. INTRODUCTION

1.1 Liquid Acquisition Devices Background

In-space propulsion can require reduced gravity engine startups, propellant transfer, and 

venting for pressure control, all of which can necessitate special provisions for liquid acquisition. 

The special provisions can be one of either of two categories: (1) Use of a settling acceleration 

to ensure the desired liquid-vapor positioning or (2) use of a capillary liquid acquisition device 

(LAD), which takes advantage of surface tension forces to either position the bulk liquid and 

vapor (a vane device) or to act as a barrier to vapor flow (a screen channel device), permitting the 

passage of liquid only. Settling acceleration forces, either intermittent or continuous, have been 

implemented on cryogenic upper stages to support one to two main engine starts and pressure 

control venting. However, future cryogenic applications, such as on-orbit transfer and a reaction 

control system (RCS), cannot necessarily use acceleration due to conflict with other vehicle requirements and/or because of the random nature of RCS thrust directions and durations. In such cases, 

a LAD, either vaned or screened, must be considered. 

Vane devices are designed to take advantage of surface tension forces to favorably position 

both liquid and gas within a tank, but typically encompass almost the entire tank volume. Therefore, vane devices historically have been used only in special cases, i.e., as small storable propellant 

tanks operating with low acceleration forces and flow rates. 

Screen channel LADs with fine mesh screens are designed to act as capillary barriers that 

allow gas-free liquid to be expelled regardless of the liquid’s position within the tank. Referring 

to figure 1, pressurized outflow is typically used to push liquid from the tank into the channel and 

then to the feed system outlet. The channels typically consist of rectangular or triangular stainless 

steel tubing with screen-covered openings on one side. The screened openings allow fluid to enter 

the channel while simultaneously surface tension blocks the passage of vapor.
2

Screen-Covered

Outer Surface

of Channels

Screen Communication

Window

Barrier

Radial Plate Sponge

& Bubble Trap

Channels

Figure 1. Screen-channel-type LAD propulsion system example application.

Screen channels have been implemented extensively for storable propellant orbital maneuvering and reaction control flight systems. Despite extensive on-orbit experience with storable propellants, experience with cryogenic applications is currently limited to ground testing. Although the 

principles of surface tension are the same for both storable and cryogenic liquids, there are additional thermal control challenges inherent in the cryogen application. The results presented herein 

have application to both storable and cryogenic propellants, assuming that the cryogen technology 

exists to remove the thermodynamic uncertainties. 

1.2 Study Objective

The objective of this study is to define an analytical approach for selecting the best screen 

mesh for representative LAD performance requirements, wherein the best screen is defined as one 

that results in the smallest LAD area when compared to any other screen candidates. For example, 

under what conditions is a 325×2,300 screen mesh the best choice when designing a LAD? The 

approach for achieving this objective is discussed in the following sections.
3

2. ANALYTICAL APPROACH

The analysis of a screen channel necessitates a basic understanding of the candidate screen 

geometries, their physical parameters/notations, and the pressure drop sources and equations. 

These elements, along with the analytical sequence, are discussed in this section.

2.1 Candidate Screen Geometries and Physical Parameters

Available screens are identified by the weave pattern used to generate the mesh. The wires 

are denoted as warp or shute, depending on their direction in the weave; warp and shute wires 

are perpendicular to one another. Weave patterns can be plain square, full twill, plain Dutch, 

and twilled Dutch (each shute wire travels over two warp wires before going under a warp wire). 

The weave pattern of a twilled Dutch screen is shown in figure 2. 

(ds+dw) i1s

  i 2s

Warp Wire

Shute Wire

Figure 2. Twilled Dutch screen weave pattern.

In addition to being identified by its weave pattern, a screen is identified by the number of 

wires per inch associated with the shute and warp wires. A 325×2,300 twilled Dutch screen means 

that, for every square inch of wire, there are 325 wires in the warp direction and 2,300 wires perpendicular to the warp direction, or in the shute direction. A 325×2,300 screen has a very fine mesh 

weave, whereas a 160×800 screen has a very relatively coarse mesh weave. If a screen-type device is 

chosen for the LAD, then as described in subsequent sections, the LAD designer must determine 

the appropriate number of channels, the best screen mesh, and the channel dimensions.

2.2 Screen Channel Pressure Drop Sources

Choosing a screen mesh is not always straightforward. The total pressure drop of the LAD 

has four different components (fig. 3): (1) Pressure losses due to head (ΔPH), (2) pressure losses 

associated with flow through the screen (ΔPFTS), (3) pressure losses associated with friction as the 
4

Tank Wall

Channel

∆Pflow through screen

∆Pdynamic

∆Pfriction

Tank Wall

Channel

Gas

Liquid

Inflow

∆Phead

∆Pflow through the screen

∆Pdynamic

∆Pfriction

h

g

Figure 3. Individual pressure drop contributors.

fluid flows down the channel (DPFR), and (4) pressure losses due to dynamic flow (ΔPD). As shown 

in equation (1), the summation of these four components (Ptotal) must be less than the screen 

bubble point pressure (PBP) to avoid screen breakdown and vapor ingestion into the LAD channel:

PBP > ΔPtotal = ΔPH + ΔPFTS + ΔPFR + ΔPD . (1)

Table 1 identifies equations for each individual pressure drop.

Table 1. Individual pressure drop terms.

Pressure Drop Term

(lb/ft2) Physical Representation Equation

ΔPH Pressure losses due to head ρgh

ΔPFTS Pressure losses due to flow through 

the screen (into the channel) βαμa2

V

ε

2

nLWgc

+ βBρV 2

n

2

L

2

W 2ε

2

dgc

ΔPFR Pressure losses due to friction from the flow 

down the LAD channel (to the engine)

96μV

2g

c

D2nW

+ ρV2

n

2

LW2 8g

c

D(log(3.7D / e))2

ΔPD Pressure losses due to dynamic flow down 

the LAD channel ρV2

2L

2

W 2n2g

c
5

Integration of the table 1 equations into equation (1) yields the following:

Ptotal > ρgh + βαμa

2

V

ε

2

nLWgc

+ βBρV 2

n

2

L2W2ε

2

dgc

+

96μV

2gcD2

nW

+ ρV 2

n

2

LW28gcD(log(3.7D / e))2 + ρV 22L2W2n

2

gc

. (2)

Application of the preceding relationships and definitions are discussed in the following 

section. 

2.3 Analysis Sequence and Assumptions

The terms used in the statistical modeling applied herein are defined in appendix A. Because 

pressure losses due to head are independent of screen choice, pressure losses due to head were 

examined first. In cases in which acceleration was not the major contributor to the total pressure 

drop, a statistical regression analysis was used to determine which predictor variables (conditions) 

and variable interactions are drivers for screen LAD widths. At first glance, it would appear that 

the predictor variables of interest in the regression would be as defined in table 1: g, h, β, α, a, V, e, 

n, L, B, d, e, and PBP

. However, because some predictor variables are determined by other choices 

(e.g., α is determined by screen choice), the choice of which predictor variables to use in the regression model were not straightforward. 

The physical factors that could be varied are as follows: percent tank fill and the total LAD 

length (which determine L and h), liquid flow rate (V), the number of LAD channels (n), the acceleration (g), and the screen choice (which determines β, α, a, e, B, d, e, and PBP). Although the 

number of channels is known to affect the LAD width, earlier studies indicate that the LAD width 

multiplied by the number of channels is a constant.2,3 Therefore, the effect of the number of channels is already understood and was removed as a variable in this study. Data from reference 3 was 

used in this current study.

Data for the regression analysis were obtained from a series of computer calculations using 

equation (2) to determine a minimum screen width versus the imposed conditions. The predictor 

variables chosen for the regression were the conditions that the engineer could change. These were 

acceleration, flow rate, percent fill, and type of screen. The regression model included only the 

main variables and two-way interactions. The acceleration levels and LAD heights were chosen (for 

the regression model) such that the ΔPH losses did not dominate ΔPtotal. To maintain computer 

computations at an acceptable level, only twilled Dutch weaves and isopropyl alcohol as the liquid

were included in the analysis. The values of β, α, a, e, B, d, e, and PBP were treated as constants 

dependent upon the screen choice. Minitab, a piece of computer software, was used to analyze the 

data. Table 2 shows the predictor variable levels used for the analysis, while table 3 shows the screen 

constants for the Dutch twilled screens.
6

Table 2. Variable requirement levels used in analysis.

Main Variable Low Level High Level

Flow rate, kg/hr (lb/hr) 1,633 (3,600) 7,711 (17,000)

Fill level, % 5 95

LAD length, m (ft) 0.305 (1) 0.475 (1.557)

Acceleration, g 0.025 0.0095

Table 3. Screen constants for twilled Dutch screens.

Screen Types

Constants* 165× 800 200× 1,400 325× 2,300

β 0.17 0.2 0.19

α 3.3 4.2 3.2

a 12,606 19,930 33,598

e 0.426 0.248 0.245

B 0.000575 0.00050 0.000292

d 0.000082 0.0000328 0.0000164

e 0.012 0.0096 0.006

PBP 4.95 12.23 17.66

* English units
7

3. ANALYTICAL RESULTS

The screen channel design sensitivity results due to head pressure (due to acceleration), the 

flow through the screen losses associated with fill level and flow rate, screen mesh, and bubble point 

are presented in the following sections.

3.1 Head Pressure Losses

The pressure losses due to head pressure, ΔPH, are functions of LAD height and acceleration only. Although ΔPH is not dependent on screen choice, there are limitations on the ΔPH that 

each screen can tolerate. Setting ΔPtotal equal to PBP

, the coarser screens (e.g., the 165×800 mesh) 

cannot sustain as much head before breakdown because of the reduced surface tension retention 

capability, or PBP. To demonstrate this trend, a sensitivity analysis was conducted with isopropyl 

alcohol; the results are shown in table 4. Because the head losses do not depend on channel width, 

the calculations show the uncovered LAD height (h) each screen can sustain at the specified acceleration levels before breakdown. Note that, for this analysis, the acceleration levels were chosen 

such that the ΔPH losses dominate ΔPtotal. (For the regression analyses in sections 3.2 and 3.3, the 

acceleration levels are chosen such that the ΔPH losses do not dominate ΔPtotal.) 

Table 4. Isopropyl alcohol head height at bubble point breakdown.

Screens 165×800 200×1,400 325×2,300

PBP, kPa (psf) 0.24 (4.95) 0.59 (12.23) 0.85 (17.66)

Acceleration Uncovered LAD height (or head) at breakdown, cm (in)

0.01 g 22.6 (88.93) 55.8 (219.6) 80.57 (317.2)

0.1 g 2.26 (8.893) 5.58 (21.96) 8.06 (31.72)

1 g 0.23 (0.8893) 0.56 (2.196) 0.81 (3.172)

Table 4 shows that, as the acceleration increases an order of magnitude, so do the uncovered screen heights. The fine mesh screen held almost four times as much head as the coarse screen 

before breakdown. Therefore, it is apparent that some screens can be ruled out on the basis of 

acceleration requirements alone.
8

3.2 Flow Across Screen Losses

While table 4 showed that a finer mesh screen is better for large head retention requirements, 

or ΔPH, it may not be the best choice if flow loss across the screen, or ΔPFTS, is considered as an 

additional requirement. Using the predictor variables in table 3 and equation (2), minimum LAD 

widths necessary to avoid screen breakdown for various predictor variable level combinations were 

calculated and are listed in table 5. The data significance can best be visualized if it is presented in 

the form of a histogram, which is a graphical representation showing a visual impression of the 

distribution of data. As presented in figure 4, the data were arranged to show relative frequencies, 

or the proportion of cases versus channel width for each of the three meshes evaluated. Further 

details regarding individual pressure drops for each LAD width are presented in appendix B.

Table 5. Minimum LAD widths versus performance requirements.

Independent Variables (Performance Requirements) Dependent Variables—Screen Width, cm (in)

Flow Rate 

kg/hr (lb/hr)

Percent

Fill

LAD Length

m (ft)

Acceleration

g

Screen 1

165×800

Screen 2

200×1,400

Screen 3

325×2,300

 1,633 (3,600) 5 0.305 (1) 0.025 6.86 (2.7) 12.45 (4.9) 10.7 (4.2)

 1,633 (3,600) 5 0.305 (1) 0.0095 5.84 (2.3) 11.68 (4.6) 10.4 (4.1)

 1,633 (3,600) 5 0.475 (1.557) 0.025 5.39 (2.2) 8.64 (3.4) 7.11 (2.8)

 1,633 (3,600) 5 0.475 (1.557) 0.0095 4.06 (1.6) 7.62 (3) 6.86 (2.7)

 1,633 (3,600) 95 0.305 (1) 0.025 1.27 (0.5) 1.02 (0.4) 1.02 (0.4)

 1,633 (3,600) 95 0.305 (1) 0.0095 1.27 (0.5 1.02 (0.4) 1.02 (0.4)

 1,633 (3,600) 95 0.475 (1.557) 0.025 1.27 (0.5) 1.02 (0.4) 1.02 (0.4)

 1,633 (3,600) 95 0.475 (1.557) 0.0095 1.27 (0.5) 1.02 (0.4) 1.02 (0.4)

 7,711 (17,000) 5 0.305 (1) 0.025 32.26 (12.7) 59.2 (23.3) 50.8 (20)

 7,711 (17,000) 5 0.305 (1) 0.0095 27.18 (10.7) 55.37 (21.8) 48.8 (19.2)

 7,711 (17,000) 5 0.475 (1.557) 0.025 25.85 (10.1) 40.64 (16) 34.3 (13.5)

 7,711 (17,000) 5 0.475 (1.557) 0.0095 18.8 (7.4) 36.32 (14.3) 31.75 (12.5)

7,711 (17,000) 95 0.305 (1) 0.025 2.8 (1.1) 3.3 (1.3) 3.05 (1.2)

 7,711 (17,000) 95 0.305 (1) 0.0095 2.8 (1.1) 3.3 (1.3) 3.05 (1.2)

 7,711 (17,000) 95 0.475 (1.557) 0.025 2.54 (1) 2.54 (1) 2.29 (0.9)

 7,711 (17,000) 95 0.475 (1.557) 0.0095 2.54 (1) 2.54 (1) 2.29 (0.9)
9

0 26 60

15

10

5

0

Frequency

165 × 180 200 × 1,400 325 × 2,300

LAD Width (cm)

Figure 4. Histograms for minimum LAD widths with three screen meshes.

The coarsest mesh screen always returned the smallest LAD width for the conditions specified in table 2. In other words, for a given length, percent fill, flow rate, etc., the coarsest mesh 

screen would be the screen of choice because its LAD width is the smallest out of the three screens. 

This is because the flow through a coarse mesh screen is less impeded than the flow through a finer 

mesh screen; thus, the coarse mesh screen widths do not need to be as large to sustain flow. The 

data also show that, with the exception of the third data point (see app. B), all LAD widths greater 

than 25.4 cm (10 in) occur when the flow rate is high and the fill level is low. The high fill level 

exhibits a similar pattern when combined with high flow rates. This suggests that flow rates and fill 

levels may drive the LAD widths. Therefore, the preceding results were used to guide inputs for the 

‘stepwise and linear regression modeling’ described in the next section (see app. A for definitions 

of statistical terms).

3.3 Stepwise and Linear Regression Modeling

With 5 main variables and 10 two-way interactions, a total of 15 terms could be used as predictor variables for the regression model. Including all these candidates is cumbersome and would 

not reveal any information on the most influential factors. Therefore, only those variables and/

or interactions that highly influence LAD widths need to be included. Minitab offers a procedure 

called a ‘stepwise regression,’ which uses both forward selection and backward elimination techniques to identify a useful subset of predictor variables to use in the linear regression model. Both 

stepwise techniques were performed, and the predictor variables identified as significant variables 

to include in the linear modeling are listed in table 6, with further stepwise modeling details listed 

in appendix C.
10

Table 6. Stepwise regression significant variables.

Backward Stepwise Regression Forward Stepwise Regression

Backward and Forward Stepwise Regression 

Common Predictor Variables

Screen Percent fill Flow rate

Flow rate Flow rate Flow rate×percent fill

Screen×flow rate Flow rate×percent fill Flow rate×LAD length

Screen×percent fill Flow rate×LAD length Screen×flow rate

Screen×LAD length Screen×flow rate Percent fill×LAD length

Flow rate×percent fill Percent fill×LAD length Screen×percent fill

Flow rate×LAD length Screen×percent fill –

Percent fill×LAD length – –

As expected, the flow rate and percent fill are the major drivers in both stepwise regression 

procedures. The screen choice and LAD length also affect the LAD width. Using the predictor 

variables identified in both regression techniques, a linear regression was performed and resulted 

in a model with a 92% R2 value. The plot of the ‘residuals’ versus LAD widths and a histogram 

of the residuals are presented in figures 5 and 6, respectively (see app. D for further details). The 

residuals look fairly normal, and the high R2 value for the regression model indicates that the variables chosen as the main drivers for the LAD widths are correct.

5

0

–5

0 25 50

LAD Width (cm)

Residual

Figure 5. Residuals versus LAD width using linear regression model.
11

15

10

5

0

–4 –3 –2 –1 0 1

Residual

Frequency

2 3 4 5 6

Figure 6. Residuals histogram for LAD width using linear regresison model.

Regardless of the screen chosen, the flow rate and percent fill are major drivers for determining the screen widths. Physically, this is easy to understand. For example, with a high flow rate 

and a low fill level (which leaves a large portion of the screen exposed), both ΔPH and ΔPFTS are 

at a maximum. Because ΔPFTS is inversely proportional to the screen width, the screen width needs 

to be large enough to accommodate the flow requirements and avoid breakdown. If the width is 

too small, ΔPFTS, in combination with the other pressure drop terms, will exceed ΔPBP and cause 

screen breakdown. If the acceleration is low enough so that ΔPH is a minor influence, then ΔPFTS

and ΔPFR are the largest contributors to ΔPtotal, making the coarse mesh screens a better choice. 

What is peculiar about the data is that the finest mesh screen is the second best choice 

(e.g., the next-smallest LAD width). If lack of flow impedance is the reason why the coarsest mesh 

screen is better than the finest mesh screen, then it should reason that the second-most coarse 

screen should give the next-smallest LAD width for the same set of conditions. This trend is consistent throughout the data (i.e., at any variable level combination, the coarsest mesh screen always 

has the smallest LAD width, the finest mesh screen has the next-smallest LAD width, and the 

middle mesh screen has the largest LAD width). Therefore, the study described below was conducted to more closely investigate the combined design sensitivity of flow losses across the screen 

and bubble point. 

3.4 Flow-Through Screen Loss and Bubble Point Combination

To investigate the combined influence of flow losses across the screen and bubble point, the 

ratio of ΔPFTS to PBP for a constant LAD width was compared. The three screens at all the combination of variable levels from table 2, with the exception of the high flow rates and low fill level 

combinations, were examined. If the LAD width was set to the largest LAD width, then the comparisons would not be meaningful, as the ratio of ΔPFTS to PBP would be too small in magnitude 

for most of the conditions. Ignoring the high flow rate and low fill level combinations, all other 

LAD widths are less than 12.5 cm (5 in), and so a constant LAD width of 12.5 cm was used for 
12

the calculations. Table 7 shows the ratio of ΔPFTS to PBP for the various combinations of conditions from table 2. Note that, for these calculations, ΔPtotal will always be less than the PBP of each 

screen. Appendix E contains further details on the total pressure drop, the ratio of ΔPFR to PBP, 

and the ratio of ΔPFTS+FR to PBP.

Table 7 shows that the coarsest mesh screen returns the smallest ratio of ΔPFTS to PBP, 

followed by the finest mesh screen, and then the middle screen. Therefore, the screen that will yield 

the smallest width for a given LAD design will be the screen that has the smallest ratio of ΔPFTS

to PBP. This implies the designer must have a basic idea of the LAD configuration before beginning calculations for comparing screens. Note that the comparisons must be based on the same 

LAD geometry (i.e., same lengths and widths), or some means to correct for the different LAD 

geometries must be taken into account. A designer cannot compare screens based on PBP and pressure head losses (H) alone. For example, if a designer tried to subtract the pressure head losses (H) 

from the bubble point pressure, and set this equal to the ΔPFTS losses, the ratio of ΔPFTS to PBP

would not follow the same trend as table 7. This is because the ΔPFTS losses would be based upon 

different widths, and therefore different LAD performance capabilities. The effects of other screen 

parameters on the ratio of ΔPFTS to PBP are discussed in the following section.

Table 7. Ratio of DPFTS to PBP under various conditions.

Independent Variables

Dependent Variables (Ratio of ΔPFTS

to PBP), Dimensionless

Flow Rate

kg/hr (lb/hr)

Percent

Fill

LAD Length

m (ft)

Acceleration

g

Screen 1

165×800

Screen 2

200×1,400

Screen 3

325×2,300

1,633 (3,600) 5 0.305 (1) 0.025 0.26 0.84 0.73

1,633 (3,600) 5 0.305 (1) 0.0095 0.26 0.84 0.73

1,633 (3,600) 5 0.475 (1.557) 0.025 0.15 0.48 0.42

1,633 (3,600) 5 0.475 (1.557) 0.0095 0.15 0.48 0.42

1,633 (3,600) 95 0.475 (1.557) 0.025 0.01 0.03 0.03

1,633 (3,600) 95 0.305 (1) 0.0095 0.01 0.03 0.03

1,633 (3,600) 95 0.475 (1.557) 0.025 0.01 0.02 0.02

1,633 (3,600) 95 0.475 (1.557) 0.0095 0.01 0.02 0.02

7,711 (17,000) 95 0.305 (1) 0.025 0.05 0.16 0.14

7,711 (17,000) 95 0.305 (1) 0.0095 0.05 0.16 0.14

17,000 95 0.475 (1.557) 0.025 0.03 0.10 0.09

17,000 95 0.475 (1.557) 0.0095 0.03 0.10 0.09
13

3.5 Screen Parameter Influences

To investigate the potential effects of the screen constants on the ratio of ΔPFTS to PBP, 

a correlation analysis using Minitab was performed on the results of table 7 and correlation details 

are presented in appendix F. However, no strong correlations were indicated (0.7 or higher) between 

the screen constants (b, α, a, e, B, d, e, and PBP) and the ratio of ΔPFTS to PBP. Because the high 

flow rate and low fill level combination data were not included in the analysis (see explanation in 

the previous section), the correlation was calculated using only the data for the 95% fill level with 

both the high and low flow rates. Only flow rate showed a strong correlation with the ratio of 

ΔPFTS to PBP. The calculation was repeated with the 1,633 kg/hr (3,600 lb/hr) flow rate and including both 5% and 95% fill. The fill level showed a strong correlation to the ratio of ΔPFTS to PBP. 

Therefore, as expected, the flow rate and fill levels drive the values for the ratio of ΔPFTS to PBP. 

However, it is cautioned that, because the flow rate and fill levels are such strong drivers, the screen 

constant effects may be ‘masked.’

Therefore, to understand the potential effects of the screen constants, the correlation 

analysis was performed with the following conditions: (1) 1,633 kg/hr and 5% fill, (2) 1,633 kg/

hr and 95% fill, and (3) 7,711 kg/hr and 95% fill. In all three cases, the ratio of ΔPFTS to PBP was 

highly correlated with β, e, d, and PBP. Because screen widths correlate to the ratio of ΔPFTS to 

PBP, the values of β, e, d, and PBP could be very influential in determining screen widths at a given 

flow rate and fill level. Accurate determination of these screen constants is very important.
14

4. CONCLUSIONS 

It was confirmed that optimum screen mesh selection is highly dependent on screen channel LAD performance requirements. For example, a high expulsion rate at low fill levels’ drives the 

LAD channel width to larger values to mitigate flow losses, regardless of screen choice. If accelerations are high during LAD expulsion, a screen with a high bubble point is desired to accommodate 

the large head retention requirement. After ruling out some screens on the basis of acceleration 

requirements alone, candidate screens were identified by using statistical regression analyses 

to compare the ratios of ΔPFTS to PBP for given constant conditions, i.e., through comparisons 

at fixed flow rates and fill levels. 

Within the same flow rate and fill level, the screen constants, that is, screen thickness (B), 

flow friction factor (e), effective pore diameter (d), and bubble point (PBP), can become the driving forces for the ΔPFTS to PBP ratio. Note that the comparison of these ratios for different screens 

must be based on the same LAD geometry (i.e., same lengths and widths), or some means for correcting for the different LAD geometries must be taken into account. This implies that the designer 

must have a basic idea of the LAD configuration before beginning calculations for comparing 

screens. The designer may wish to run several minor modifications to the LAD geometries to determine if the optimum screen choice changes for the given application. Analysis did indicate that 

coarse mesh screens may offer an advantage over fine mesh screens if the head retention requirement (ΔPH) does not exceed the screen’s bubble point (PBP). Therefore, it is generally recommended 

that sensitivity studies always include the coarsest mesh screen that can support the head retention 

requirement as a candidate.

As noted above, the statistical analyses assumed fixed magnitudes for some mission requirements that actually are likely to be transient. Therefore, it is imperative that the conditions for 

which the LAD is expected to operate be clearly defined before beginning any analysis. An analysis 

for the expected screen widths, comparing a few candidate screens (using the procedures defined 

in the previous paragraph), can be performed using the following approach:

Step 1—Determine the worst-case acceleration requirement and the tank conditions at the 

time of the experienced acceleration (flow rate, tank fill level at end of maneuver, etc.). Calculate 

a minimum LAD width for several screen candidates. 

Step 2—Determine the worst-case flow rate requirement (highest flow rate) and conditions 

at the time of the experienced flow rate (acceleration, tank fill level at end of maneuver). Calculate 

a minimum LAD width for several screen candidates.

Step 3—Determine the worst-case tank fill level requirement and corresponding conditions 

(flow rate and acceleration) at the end of the maneuver. Calculate a minimum LAD width for 

several screen candidates.
15

Step 4—Take the largest minimum LAD width from steps 1–3 for each screen candidate 

and choose the screen that results in the smallest channel width.

Step 5—Verify that the screen choice for the chosen LAD width was correct by comparing 

the ratios of ΔPFTS to PBP using the LAD width chosen from step 4 for each screen candidate. 

Step 6—As a final check, verify that the LAD would not break down at other various stages 

in the mission.

Note that the evaluation of screen channel LAD performance described herein did not 

address any manufacturing aspects, tank sizes, or thermal conditions of the propellant and/or tank, 

all or any of which could also drive LAD design sensitivities. However, in the case of cryogenic 

propellants, for example, if tank conditioning is such that thermal effects are neutralized, then the 

results presented herein can be considered applicable.
16

APPENDIX A—STATISTICAL PROCEDURES AND TERMS DEFINITION

The various statistical procedures and terms implemented to assist in the evaluation LAD 

design sensitivities are described below. 

A.1 Regression Analysis

In statistics, ‘regression analysis’ includes many techniques for modeling and analyzing 

several variables, when the emphasis is on the relationship between a dependent variable and one 

or more independent variables.4 More specifically, regression analysis assists in understanding how 

a typical value of the dependent variable changes when any one of the independent variables is 

varied, while the other independent variables are held fixed. Most commonly, a regression analysis 

is used to estimate the conditional expectation of the dependent variable given the independent 

variables, i.e., the average value of the dependent variable when the independent variables are fixed. 

In all cases, the estimation target is a function of the independent variables called the regression 

function. In regression analysis, it is also of interest to characterize the variation of the dependent 

variable around the regression function, which can be described by probability distribution.

Regression analysis is also used to understand which among the independent variables are 

related to the dependent variable and to explore the forms of these relationships. A substantial 

number of techniques for performing regression analysis has been developed. Familiar methods 

such as ‘linear and least ordinary squares regressions’ are parametric, in that the regression function is defined in terms of a finite number of unknown parameters that are estimated from the 

data. 

The performance of regression analysis methods in practice depends on the form of the 

data-generating process, and how it relates to the regression approach being used. Since the true 

form of the data-generating process is generally not known, regression analysis often depends, to 

some extent, on making assumptions about this process. These assumptions are sometimes testable if a large amount of data are available. Regression models for predictions are often useful even 

when the assumptions are moderately violated, although the results may not be optimal. 

A.2 Multiple and Nonlinear Regressions

The intent of a ‘multiple linear regression’ is to find a linear relationship between a response 

variable and several possible predictor variables. The intent of a ‘nonlinear regression’ is to describe 

the relationship between a response variable and one or more explanatory variables in a nonlinear 

fashion.
17

A.3 Residual

The term ‘residual’ (or error) represents unexplained (or residual) variation after fitting 

a regression model. It is the difference (or left over) between the observed value of the variable 

and the value suggested by the regression model. A ‘residual plot’ is a graph that shows the residuals on the vertical axis and the independent variable on the horizontal axis. If the points in a residual plot are randomly dispersed around the horizontal axis, a linear regression model is appropriate 

for the data, otherwise, a nonlinear model is more appropriate. Residual plots show three typical 

patterns. A random pattern indicates a good fit for a linear model. Plot patterns that are nonrandom (U-shaped and inverted U) suggest a better fit for a nonlinear model.

A.4 Multiple Regression Correlation Coefficient

The ‘multiple regression correlation coefficient,’ R2, is a measure of the proportion of variability explained by, or due to, the regression (linear relationship) in a sample of paired data. It is 

a number between zero and 1; a value close to zero suggests a poor model. However, a very high 

value of R2 can arise even though the relationship between the two variables is nonlinear. 

The fit of a model should never simply be judged from the R2 value. 

A.5 Stepwise Regression

A ‘best’ regression model is sometimes developed in stages. In such applications a list of 

several potential explanatory variables are available and is repeatedly searched for variables that 

should be included in the model. The best explanatory variable is used first, then the second best, 

and so on. This procedure is known as ‘stepwise regression.’
18

APPENDIX B—MINIMUM LIQUID ACQUISITION DEVICE WIDTH RESULTS

Table 8 gives minimum LAD width results; note that units of measure are not metric.

Table 8. Minimum LAD width results.

Predictor Variables Response Variables

Screen 

Flow

Rate

Percent

Fill

LAD

Length

Acceleration

(g)

LAD

Width DPH DPFTS DPFR DPD

PRP/

Pscreen

165 ×800 3,600 5 1 0.025 2.7 1.59 3.08 0.17 0.11 1.61

165×800 3,600 5 1 0.0095 2.3 0.6 3.94 0.25 0.16 1.26

165×800 3,600 5 1.557 0.025 2.2 2.47 2.2 0.21 0.07 2.25

165×800 3,600 5 1.557 0.0095 1.6 0.94 3.44 0.44 0.13 1.44

165×800 3,600 95 1 0.025 0.5 0.08 0.55 4.31 0.01 9.09

165×800 3,600 95 1 0.0095 0.5 0.03 0.55 4.36 0.01 9.04

165×800 3,600 95 1.557 0.025 0.5 0.13 0.33 4.49 0 14.87

165×800 3,600 95 1.557 0.0095 0.5 0.05 0.34 4.56 0 14.76

165×800 17,000 5 1 0.025 12.7 15.9 3.12 0.13 0.12 1.59

165×800 17,000 5 1 0.0095 10.7 0.6 4.01 0.18 0.16 1.24

165×800 17,000 5 1.557 0.025 10.1 2.47 2.227 0.13 0.08 2.18

165×800 17,000 5 1.557 0.0095 7.4 0.94 3.62 0.25 0.14 1.37

165×800 17,000 95 1 0.025 1.1 0.08 1.5 3.22 0.04 3.29

165×800 17,000 95 1 0.0095 1.1 0.03 1.51 3.36 0.04 3.27

165×800 17,000 95 1.557 0.025 1 0.13 0.96 3.84 0.02 5.16

165×800 17,000 95 1.557 0.0095 1 0.05 0.97 3.91 0.02 5.11

200×1,400 3,600 5 1 0.025 4.9 1.59 10.54 0.07 0.03 1.16

200×1,400 3,600 5 1 0.0095 4.6 0.6 11.51 0.08 0.04 1.06

200×1,400 3,600 5 1.557 0.025 3.4 2.47 9.62 0.11 0.03 1.27

200×1,400 3,600 5 1.557 0.0095 3 0.94 11.12 0.14 0.04 1.10

200×1,400 3,600 95 1 0.025 0.4 0.08 5.27 6.87 0.01 2.32

200×1,400 3,600 95 1 0.0095 0.4 0.03 5.28 6.91 0.01 2.32

200×1,400 3,600 95 1.557 0.025 0.4 0.13 3.46 8.63 0.01 3.53

200×1,400 3,600 95 1.557 0.0095 0.4 0.05 3.48 8.7 0.01 3.52

200×1,400 17,000 5 1 0.025 23.3 1.59 10.5 0.11 0.03 1.16

200×1,400 17,000 5 1 0.0095 21.8 0.6 11.47 0.12 0.04 1.07

200×1,400 17,000 5 1.557 0.025 16 2.47 9.61 0.13 0.03 1.27

200×1,400 17,000 5 1.557 0.0095 14.3 0.94 11.11 0.15 0.04 1.1

200×1,400 17,000 95 1 0.025 1.3 0.08 9.61 2.51 0.03 1.27

200×1,400 17,000 95 1 0.0095 1.3 0.03 9.64 2.53 0.03 1.27
19

Predictor Variables Response Variables

Screen

Flow

Rate

Percent

Fill

LAD

Length

Acceleration

(g)

LAD

Width DPH DPFTS DPFR DPD

PRP/

Pscreen

200×1,400 17,000 95 1.557 0.025 1 0.13 7.75 4.33 0.02 1.58

200×1,400 17,000 95 1.557 0.0095 1 0.05 7.79 4.37 0.02 1.57

325×2,300 3,600 5 1 0.025 4.2 1.59 15.93 0.1 0.05 1.11

325×2,300 3,600 5 1 0.0095 4.1 0.6 16.9 0.11 0.05 1.05

325×2,300 3,600 5 1.557 0.025 2.8 2.47 14.99 0.16 0.04 1.18

325×2,300 3,600 5 1.557 0.0095 2.7 0.94 16.49 0.18 0.05 1.07

325×2,300 3,600 95 1 0.025 0.4 0.08 7.72 9.85 0.01 2.29

325×2,300 3,600 95 1 0.0095 0.4 0.03 7.73 9.89 0.01 2.28

325×2,300 3,600 95 1.557 0.025 0.4 0.13 5.09 12.44 0.01 3.47

325×2,300 3,600 95 1.557 0.0095 0.4 0.05 5.1 12.51 0.01 3.47

325×2,300 17,000 5 1 0.025 20 1.59 15.89 0.14 0.05 1.11

325×2,300 17,000 5 1 0.0095 19.2 0.6 16.86 0.15 0.05 1.05

325×2,300 17,000 5 1.557 0.025 13.5 2.47 14.98 0.17 0.04 1.18

325×2,300 17,000 5 1.557 0.0095 12.5 0.94 16.49 0.19 0.05 1.07

325×2,300 17,000 95 1 0.025 1.2 0.08 14.08 3.47 0.04 1.25

325×2,300 17,000 95 1 0.0095 1.2 0.03 14.11 3.48 0.04 1.25

325×2,300 17,000 95 1.557 0.025 0.9 0.13 11.4 6.11 0.03 1.55

325×2,300 17,000 95 1.557 0.0095 0.9 0.05 11.44 6.15 0.03 1.54

Table 8. Minimum LAD width results (Continued).
20

APPENDIX C—STEPWISE REGRESSION RESULTS

C.1 Backward Stepwise Regression

F-to-Enter: 1,000 F-to-Remove: 4

Response is W (LAD w on 15 predictors, with N=48

Step: 1 2 3 4 5 6 7

Constant: –1.629 –1.114 –2.563 –1.983 –1.983 –1.983 –2.598

Screen: 2.6 2.3 2.7 2.7 2.7 2.7 2.5

T-Value: 1.37 1.36 2.22 2.24 2.26 2.25 2.1

Flowrate: 0.00110 0.00110 0.00113 0.00110 0.00113 0.00119 0.00117

T-Value: 4.53 4.59 5.14 5.30 5.58 5.99 5.9

% Fill: –0.028 –0.028 –0.025 –0.028 –0.037 –0.037

T-Value: –0.77 –0.78 –0.72 –0.83 –1.17 –1.17

LAD Length: –1.1 –1.1

T-Value: –0.35 –0.35 

accel-er: 63 34 34

T-Value: 0.54 0.44 0.45

sc*fr: 0.00009 0.00009 0.00009 0.00009 0.00009 0.00009 0.00009

T-Value: 1.81 1.83 1.85 1.87 1.88 1.88 1.87

sc *%fil: –0.0206 –0.0206 –0.0206 –0.0206 –0.0206 –0.0206 –0.0246

T-Value: –2.72 –2.76 –2.79 –2.83 –2.84 –2.83 –3.79

sc*LL: –1.04 –1.04 –1.36 –1.36 –1.36 –1.36 –1.06

T-Value: –0.85 –0.86 –1.74 –1.76 –1.77 –1.76 –1.44

sc*accel: –15 

T-Value: –0.34 

fr*%fill: –0.00001 –0.00001 –0.00001 –0.00001 –0.00001 –0.00001 –0.00001

T-Value: –10.12 –10.26 –10.39 –10.50 –10.56 –10.53 –11.31

fr*ll: –0.00031 –0.00031 –0.00034 –0.00034 –0.00034 –0.00034 –0.00032

T-Value: –2.11 –2.14 –2.65 –2.68 –2.69 –2.69 –2.52
21

fr*accel: 0.0031 0.0031 0.0031 0.0048 0.0031

T-Value: 0.58 0.59 0.6 1.34 1.09 

%fill*ll: 0.066 0.066 0.063 0.063 0.063 0.063 0.044

T-Value: 2.96 3 3.11 3.14 3.16 3.15 3.78

%fill*ac: –0.69 –0.69 –0.69 –0.51

T-Value: –0.87 –0.88 –0.89 –0.78

S: 1.93 1.9 1.88 1.86 1.85 1.85 1.86

R-Sq: 93.83 93.81 93.79 93.75 93.65 93.44 93.21

C.2 Forward Stepwise Regression

F-to-Enter: 4 F-to-Remove: 0

Response is W (LAD w on 15 predictors, with N = 48

Step: 1 2 3 4 5 6 7

Constant: 9.633796 4.804070 –0.007152 –0.007152 –0.007152 –0.007152 –0.007152

% fill: –0.093 –0.093 0.003 0.003 0.003 –0.059 –0.029

T-Value: –5.85 –7.57 0.19 0.21 0.22 –2.1 –0.96

Flowrate: 0.00047 0.00094 0.00133 0.00115 0.00137 0.00126

T-Value: 5.66 11.42 9.15 7.80 8.28 7.76

fr*%fill: –0.00001 –0.00001 –0.00001 –0.00001 –0.00001

T-Value: –7.67 –8.42 –9.11 –9.62 –10.15

fr*ll: –0.00031 –0.00031 –0.00048 –0.00048

T-Value: –3.17 –3.43 –4.35 –4.59

sc*frL: 0.00009 0.00009 0.00014

T-Value: 2.88 3.05 3.99

%fill*ll: 0.049 0.049

T-Value: 2.43 2.56

sc *%fil: –0.0153

T-Value: –2.37

S: 4.98 3.85 2.55 2.32 2.14 2.03 1.92

R-Sq: 42.67 66.50 85.66 88.37 90.30 91.52 92.56
22

APPENDIX D—LINEAR REGRESSION EQUATION RESULTS

D.1 Regression Analysis

The regression equation is:

W (LAD width) = –0.215 + 0.00119 flowrate – 0.000010 fr*%fill – 0.000425 fr*ll

+0.000150 sc*fr + 0.0336 %fill*ll – 0.0180 sc *%fill

Predictor Coef StDev T P

Constant: –0.2149 0.7290 –0.29 0.770

Flowrate: 0.0011924 0.0001456 8.19 0

fr*%fill: –0.00000963 0.00000087 –11.05 0

fr*ll: –0.00042475 0.00008921 –4.76 0

sc*fr: 0.00015043 0.00003401 4.42 0

%fill*ll: 0.03364 0.01094 3.07 0.004

sc *%fil: –0.018030 0.005810 –3.10 0.003

S = 1.921 R-Sq = 92.4% R-Sq(adj) = 91.3%

D.2 Analysis of Variance

Source: DF SS MS F P

Regression: 6 1836.84 306.14 82.97 0

Error: 41 151.28 3.69

Total: 47 1988.11

Source: DF Seq SS

Flowrate: 1 473.76

fr*%fill: 1 1228.99

fr*ll: 1 54.02

sc*fr: 1 38.21

%fill*ll: 1 6.33

sc *%fil: 1 35.53

Unusual Observations:

Obs Flowrate W LAD w Fit StDev Fit Residual St Residual

 10 17,000 10.7 14.652 0.866 –3.952 –2.31R

 25 17,000 23.3 17.119 0.703 6.181 3.46R

 26 17,000 21.8 17.119 0.703 4.681 2.62R

R denotes an observation with a large standardized residual.
23

APPENDIX E—‘FLOW THROUGH THE SCREEN LOSS’ CONTRIBUTION 

AS A FUNCTION OF ‘BUBBLE POINT PRESSURE’ ANALYSIS

The predictor and response variables are given in table 9; note that units of measure 

are not metric.

Table 9. Predictor and response variables.

Predictor Variables Response Variables

Screen

Flow 

Rate

Percent

Fill

LAD 

Length

Acceleration

(g) DPFTS/PBP DPFR/PBP

DPFTS+ DPFR/

PBP DPtotal

165×800 3,600 5 1 0.025 0.26 0.01 0.27 2.96

165×800 3,600 5 1 0.0095 0.26 0.01 0.27 1.98

165×800 3,600 5 1.557 0.025 0.15 0.01 0.15 3.25

165×800 3,600 5 1.557 0.0095 0.15 0.01 0.15 1.71

165×800 3,600 95 1 0.025 0.01 0 0.01 0.14

165×800 3,600 95 1 0.0095 0.01 0 0.01 0.09

165×800 3,600 95 1.557 0.025 0.01 0 0.01 0.17

165×800 3,600 95 1.557 0.0095 0.01 0 0.01 0.09

165×800 17,000 5 1 0.025 – – – --

165×800 17,000 5 1 0.0095 – – – --

165×800 17,000 5 1.557 0.025 – – – --

165×800 17,000 5 1.557 0.0095 – – – --

165×800 17,000 95 1 0.025 0.05 0.02 0.06 0.41

165×800 17,000 95 1 0.0095 0.05 0.02 0.06 0.35

165×800 17,000 95 1.557 0.025 0.03 0.01 0.04 0.34

165×800 17,000 95 1.557 0.0095 0.03 0.01 0.04 0.26

200×1,400 3,600 5 1 0.025 0.84 0.01 0.85 11.99

200×1,400 3,600 5 1 0.0095 0.84 0.01 0.85 11

200×1,400 3,600 5 1.557 0.025 0.48 0 0.48 8.38

200×1,400 3,600 5 1.557 0.0095 0.48 0 0.48 6.85

200×1,400 3,600 95 1 0.025 0.03 0 0.03 0.47

200×1,400 3,600 95 1 0.0095 0.03 0 0.03 0.42

200×1,400 3,600 95 1.557 0.025 0.02 0 0.02 0.38

200×1,400 3,600 95 1.557 0.0095 0.02 0 0.02 0.3

200×1,400 17,000 5 1 0.025 – – – –

200×1,400 17,000 5 1 0.0095 – – – –

200×1,400 17,000 5 1.557 0.025 – – – –

200×1,400 17,000 5 1.557 0.0095 – – – –
24

Predictor Variables Response Variables

Screen

Flow 

Rate

Percent

Fill

LAD 

Length

Acceleration

(g) DPFTS/PBP DPFR/PBP

DPFTS+ DPFR/

PBP DPtotal

200×1,400 17,000 95 1 0.025 0.16 0.01 0.17 2.14

200×1,400 17,000 95 1 0.0095 0.16 0.01 0.17 2.37

200×1,400 17,000 95 1.557 0.025 0.10 0.01 0.11 1.42

200×1,400 17,000 95 1.557 0.0095 0.10 0.01 0.11 1.33

325×2,300 3,600 5 1 0.025 0.73 0 0.73 14.51

325×2,300 3,600 5 1 0.0095 0.73 0 0.73 13.52

325×2,300 3,600 5 1.557 0.025 0.42 0 0.42 9.9

325×2,300 3,600 5 1.557 0.0095 0.42 0 0.42 8.36

325×2,300 3,600 95 1 0.025 0.03 0 0.03 0.58

325×2,300 3,600 95 1 0.0095 0.03 0 0.03 0.53

325×2,300 3,600 95 1.557 0.025 0.02 0 0.02 0.45

325×2,300 3,600 95 1.557 0.0095 0.02 0 0.02 0.37

325×2,300 17,000 5 1 0.025 – – – –

325×2,300 17,000 5 1 0.0095 – – – –

325×2,300 17,000 5 1.557 0.025 – – – –

325×2,300 17,000 5 1.557 0.0095 – – – –

325×2,300 17,000 95 1 0.025 0.14 0.01 0.15 2.68

325×2,300 17,000 95 1 0.0095 0.14 0.01 0.15 2.63

325×2,300 17,000 95 1.557 0.025 0.09 0 0.09 1.76

325×2,300 17,000 95 1.557 0.0095 0.09 0 0.09 1.68

Note: Shaded areas represent conditions excluded from analysis, i.e., low fill level with high flow rate.

Screen Type PBP

165 × 800 4.95

200 × 1,400 12.23

325 × 2,300 17.66

Table 9. Predictor and response variables (Continued).
25

APPENDIX F—SCREEN CORRELATION PARAMETER ANALYSIS

(Pearson) correlations between the ratio of ΔPFTS to PBP, and ΔPFTS to various screen 

parameters: 

Using all data results from table 7:

 ratio fts beta alpha a voidfrac d B

fts 0.959

beta 0.325 0.367

alpha 0.186 0.089 0.693

a 0.214 0.386 0.515 -0.261

voidfrac -0.324 -0.423 -0.940 -0.406 -0.776

d -0.302 -0.433 -0.839 -0.189 -0.899 0.974

B -0.190 -0.366 -0.434 0.348 -0.996 0.715 0.855

e -0.228 -0.396 -0.564 0.204 -0.998 0.811 0.923 0.989

Pbp 0.270 0.423 0.716 -0.007 0.967 -0.911 -0.981 -0.940

flowrate -0.296 -0.261 0.000 0.000 -0.000 0.000 0.000 0.000

fill lev -0.807 -0.712 -0.000 0.000 0.000 0.000 0.000 -0.000

lad heig -0.209 -0.185 0.000 0.000 0.000 -0.000 -0.000 0.000

accelera -0.000 -0.000 0.000 -0.000 0.000 0.000 0.000 -0.000

 e Pbp flowrate fill lev lad heig

Pbp -0.980

flowrate -0.000 0.000

fill lev -0.000 0.000 0.500

lad heig 0.000 -0.000 -0.000 -0.000

accelera -0.000 0.000 0.000 0.000 -0.000

Using data results with 95% fill from table 7 (includes 3,600 and 17,000 flowrate values)

 ratio fts beta alpha a voidfrac d B

fts 0.949

beta 0.456 0.495

alpha 0.249 0.107 0.693

a 0.314 0.537 0.515 -0.261

voidfrac -0.460 -0.578 -0.940 -0.406 -0.776

d -0.433 -0.594 -0.839 -0.189 -0.899 0.974

B -0.281 -0.511 -0.434 0.348 -0.996 0.715 0.855

e -0.334 -0.550 -0.564 0.204 -0.998 0.811 0.923 0.989
26

Pbp 0.391 0.584 0.716 -0.007 0.967 -0.911 -0.981 -0.940

flowrate 0.752 0.635 -0.000 0.000 0.000 0.000 -0.000 -0.000

lad heig -0.251 -0.212 -0.000 0.000 0.000 -0.000 -0.000 -0.000

accelera 0.000 0.000 -0.000 0.000 -0.000 -0.000 0.000 -0.000

 e Pbp flowrate lad heig

Pbp -0.980

flowrate -0.000 -0.000

lad heig -0.000 -0.000 -0.000

accelera -0.000 0.000 0.000 -0.000

Using data results with 3,600 lb/hr flowrate from table 7 (includes 5% and 95 % fill)

 ratio fts beta alpha a voidfrac d B

fts 0.957

beta 0.352 0.394

alpha 0.202 0.096 0.693

a 0.231 0.414 0.515 -0.261

voidfrac -0.350 -0.455 -0.940 -0.406 -0.776

d -0.326 -0.465 -0.839 -0.189 -0.899 0.974

B -0.205 -0.393 -0.434 0.348 -0.996 0.715 0.855

e -0.246 -0.426 -0.564 0.204 -0.998 0.811 0.923 0.989

Pbp 0.292 0.454 0.716 -0.007 0.967 -0.911 -0.981 -0.940

lad heig -0.232 -0.204 -0.000 0.000 0.000 -0.000 -0.000 -0.000

accelera 0.000 0.000 -0.000 0.000 -0.000 -0.000 0.000 -0.000

fill lev -0.801 -0.702 0.000 -0.000 0.000 -0.000 0.000 -0.000

 e Pbp lad heig accelera

Pbp -0.980

lad heig -0.000 -0.000

accelera -0.000 0.000 -0.000

fill lev -0.000 0.000 0.000 0.000

Using data results with 3,600 lb/hr flowrate from table 7 (95 % fill)

 ratio fts beta alpha a voidfrac d B

fts 0.936

beta 0.818 0.726

alpha 0.363 0.079 0.693

a 0.664 0.878 0.515 -0.261

voidfrac -0.866 -0.883 -0.940 -0.406 -0.776

d -0.841 -0.929 -0.839 -0.189 -0.899 0.974

B -0.610 -0.845 -0.434 0.348 -0.996 0.715 0.855

e -0.695 -0.895 -0.564 0.204 -0.998 0.811 0.923 0.989

Pbp 0.784 0.930 0.716 -0.007 0.967 -0.911 -0.981 -0.940

lad heig -0.408 -0.286 0.000 -0.000 0.000 -0.000 -0.000 0.000

accelera -0.000 0.000 -0.000 0.000 0.000 -0.000 0.000 -0.000
27

 e Pbp lad heig

Pbp -0.980

lad heig -0.000 -0.000

accelera -0.000 0.000 -0.000

Using data results with 3,600 lb/hr from table 7 (includes 5% fill)

 ratio fts beta alpha a voidfrac d B

fts 0.927

beta 0.804 0.755

alpha 0.466 0.188 0.693

a 0.523 0.788 0.515 -0.261

voidfrac -0.800 -0.869 -0.940 -0.406 -0.776

d -0.744 -0.887 -0.839 -0.189 -0.899 0.974

B -0.464 -0.747 -0.434 0.348 -0.996 0.715 0.855

e -0.558 -0.810 -0.564 0.204 -0.998 0.811 0.923 0.989

Pbp 0.665 0.866 0.716 -0.007 0.967 -0.911 -0.981 -0.940

lad heig -0.536 -0.394 0.000 -0.000 0.000 -0.000 -0.000 0.000

accelera 0.000 0.000 -0.000 0.000 0.000 -0.000 0.000 -0.000

 e Pbp lad heig

Pbp -0.980

lad heig -0.000 -0.000

accelera -0.000 0.000 -0.000

Using data results with 17,000 lb/hr from table 7 (includes 95% fill)

 ratio fts beta alpha a voidfrac d B

fts 0.926

beta 0.847 0.777

alpha 0.478 0.183 0.693

a 0.567 0.823 0.515 -0.261

voidfrac -0.848 -0.898 -0.940 -0.406 -0.776

d -0.793 -0.920 -0.839 -0.189 -0.899 0.974

B -0.504 -0.781 -0.434 0.348 -0.996 0.715 0.855

e -0.603 -0.845 -0.564 0.204 -0.998 0.811 0.923 0.989

Pbp 0.712 0.900 0.716 -0.007 0.967 -0.911 -0.981 -0.940

lad heig -0.474 -0.337 0.000 -0.000 0.000 -0.000 -0.000 0.000

accelera -0.000 -0.000 -0.000 0.000 0.000 -0.000 0.000 -0.000

 e Pbp lad heig

Pbp -0.980

lad heig -0.000 -0.000

accelera -0.000 0.000 -0.000
28
29

REFERENCES

1. Armour, J.C.; and Cannon, J.N.: “Fluid Flow Through Woven Screens,” AIChE Journal, Vol. 14, 

No. 3, pp. 415–420, May 1968.

2. Blatt, M.H.; and Walter, M.D.: “Centaur Propellant Acquisition System Study,” NASA 

CR-134811, General Dynamics, Lewis Research Center, Cleveland, OH, June 1975.

3. Cady, E.: “Study of Thermodynamic Vent and Screen Baffle Integration for Orbital Storage 

and Transfer of Liquid Hydrogen,” NASA CR–134482, McDonnell Douglas Astronautics 

Company, Huntington Beach, CA, August 1973. 

4. Draper, N.; and Smith, H.: Applied Regression Analysis, 2nd ed., John Wiley and Sons, Inc., 

1981.
30

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Liquid Acquisition Device Design Sensitivity Study

M.K. Van Dyke and L.J. Hastings*

George C. Marshall Space Flight Center

Huntsville, AL 35812

National Aeronautics and Space Administration

Washington, DC 20546–0001

Unclassified-Unlimited

Subject Category 20

Availability: NASA CASI (443–757–5802)

Prepared by the Propulsion Systems Department, Engineering Directorate

*Alpha Technology, Inc., Huntsville, AL

M–1349

Technical Memorandum

NASA/TM—2012–217473

low gravity propellant management, orbital propulsion, capillary screen channel liquid acquisition 

devices, capillary screen selection

01–11–2012

UU 44

NASA

U U U

In-space propulsion often necessitates the use of a capillary liquid acquisition device (LAD) to assure that gas-free liquid propellant is available to support engine restarts in microgravity. If a capillary screen-channel device is chosen, then the designer must determine the appropriate 

combination screen mesh and channel geometry. A screen mesh selection which results in the smallest LAD width when compared to any other 

screen candidate (for a constant length) is desirable; however, no ‘best’ screen exists for all LAD design requirements. Flow rate, percent fill, and 

acceleration are the most influential drivers for determining screen widths. Increased flow rates and reduced percent fills increase the ‘throughthe-screen’ flow pressure losses, which drive the LAD to increased widths regardless of screen choice. Similarly, increased acceleration levels and 

corresponding liquid head pressures drive the screen mesh selection toward a higher bubble point (liquid retention capability). After ruling out 

some screens on the basis of acceleration requirements alone, candidates can be identified by examining screens with small ‘flow-loss-to-bubble 

point ratios’ for a given condition (i.e., comparing screens at certain flow rates and fill levels). Within the same flow rate and fill level, the screen 

constants inertia resistance coefficient, void fraction, screen pore or opening diameter, and bubble point can become the driving forces in identifying the smaller flow-loss-to-bubble point ratios. 

STI Help Desk at email: help@sti.nasa.gov

STI Help Desk at: 443–757–5802

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George C. Marshall Space Flight Center

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