Filling Accuracy Analysis of the Rocket Propellant

based on the Flowmeter Measuring Model

Xiang Youhuan, Zhang Ping, Liu Weidong and Cui Benting

Technical Department, Taiyuan Satellite Launch Center, Taiyuan, China

Keywords: Propellant Filling System, Flowmeter Measuring Model, Filling Accuracy, Valve-closed Delay.

Abstract: The high filling accuracy of rocket propellant is an important guarantee for the success of the rocket launch.

In view of the factors that affect filling accuracy of the rocket propellant in the filling system of the

spaceflight launch site, the algorithm of propellant filling accuracy calculation based on the flowmeter

measuring model is proposed in this paper. It respectively carries through mathematical analyses for the

different factors affecting the filling accuracy. Through the proposed algorithm, numerical calculation has

been carried on the comprehensive filling accuracy of rocket propellant under the existing filling process. It

can provide theoretical basis and data support for optimizing filling control process and improving filling

accuracy in the launch site, so as to further improving the success rate of rocket launch.

1 INTRODUCTION

The rockets propellant filling system is an important

part of the spaceflight launch site. It mainly fulfills

the task of the rocket propellant filling. High filling

accuracy of rocket propellant is an important

guarantee for the success of the rocket launch, so the

precision is a basic requirement for the filling

system (Deng, 2012). Therefore researching filling

accuracy of the rocket propellant is of great

significance to ensure complete success of the rocket

launch.

The basic filling quantity of rocket propellant is

measured by the level gauge of rocket tank, and the

quantitative-filling quantity is measured by the

flowmeter in the filling storeroom. It starts

quantitative-filling filling when reaching the

specified level. The valve automatically closes when

the flowmeter measures to the quantitative-filling

quantity. The existing filling system adopts the

filling model of volume-level, which measures the

filling quantity by flowmeter, to meet the needs of

filling quantity (Zhuang, 2005).

There are some factors that affect the filling

accuracy of rocket propellant in the propellant filling

system of the spaceflight launch site. It could

increase the risk of rocket filling and launch.

Therefore, filling accuracy of the existing filling

system in the launch site needs to be analyzed. The

factors that influence the filling accuracy need to be

improved, to improve the accuracy of the rocket

filling quantity, so as to improve the safety and

reliability of rocket filling and launch.

The rest section of the paper is organized as

follows: Section 2 introduces the related work on

filling accuracy of rocket propellant. Section 3

introduces the proposed algorithm, which is the

algorithm of filling accuracy based on flowmeter

measuring model. Section 4 analyzes the actual

filling accuracy of rocket propellant. Finally, section

5 makes conclusion.

2 RELATED WORK

At present, there are few special researches on actual

filling accuracy of propellant filling system.

However, the researches on the some factors that

affect the accuracy of propellant filling have been

carried out.

The filling measuring model based on weight

measurement is proposed in literature (Xiang, 2014).

It designs and analyzes the filling measuring model,

and analyzes the filling accuracy based on the

proposed model. It also compares the filling accuracy

with the existing volume-level measuring model, and

improves the filling accuracy. However, there are

some problems in the proposed model as follows:

First, it does not consider the system error that

caused by other equipment when calculating the

181

Youhuan X., Ping Z., Weidong L. and Benting C..

Filling Accuracy Analysis of the Rocket Propellant based on the Flowmeter Measuring Model.

DOI: 10.5220/0005505801810187

In Proceedings of the 12th International Conference on Informatics in Control, Automation and Robotics (ICINCO-2015), pages 181-187

ISBN: 978-989-758-123-6

 2015 SCITEPRESS (Science and Technology Publications, Lda.)

filling accuracy. For the literature, the filling

accuracy affected by the equipment can be ignored

when carries through comparison between the two

models, because the measuring error caused by these

equipments are consistent. Actually, equipment

performance can cause certain error value of filling

quantity. Second, when calculating the filling

accuracy, whether or not taking the volumetric

measurement err

or (Ma, 2013) into account. For the

literature, it needs to compare the filling accuracy

based on the existing model with the filling accuracy

based on the proposed model, and the weight

measurement model eliminates the effect of the

volumetric measurement error. So it must take the

volumetric measurement error into account when

calculating the filling accuracy. When analyzing the

filling accuracy of propellant filling system, it does

not need to consider the effect affected by

volumetric measurement error, if we take the filling

quantity given by the rocket department as reference.

In order to exactly calculate actual filling

accuracy of the rocket propellant in the spaceflight

launch site, the algorithm of propellant filling

accuracy calculation based on the flowmeter

measuring model is proposed in this paper. It takes

the factors that affect filling accuracy of the rocket

propellant into account. The factors include

flowmeter measuring, valve-closed delay,

maintenance of flowmeter set-zero and leakage of

pipeline. It respectively carries through numerical

analyses and mathematical calculation for the

different factors affecting the filling accuracy.

Through the proposed algorithm, the actual filling

accuracy of the existing rocket propellant filling

system has been figured out. It can provide

theoretical basis and data support for optimizing

propellant filling control process and improving

filling accuracy in the launch site. The following

analyses the factors that affect the filling accuracy.

The first is flowmeter measuring. The filling

quantity is measured by vortex-flowmeter in the

filling system. (Yang, 2004) The vortex-flowmeter is

a kind of new type speed instrument on the basis of

the principle of fluid oscillation. Its output signal is

pulse frequency signal or standards current signal

that is proportional to the flow, and can be

long-distance transmission. The output signal is only

related with the flux, not affected by temperature,

pressure, composition, viscosity and density of the

liquid. The measuring accuracy of vortex-flowmeter

is only 1%, the measuring accuracy is not high, and

can lead to higher error.

The second is valve-closed delay. The valves

used in the filling system are high pressure

pneumatic ball valve. Its working principle is that

opens or closes the flow path of the propellant under

the pneumatic pressure. When the rocket propellant

filling finished, in view of the time when the valve

closed, the filling automatic control process is

designed as follow. When the filling finished and the

PLC received the end signal, the filling-valve and

overflow-valve are closed at the same time.

Meanwhile, the relevant valves on the filling

pipeline are closed. When flowmeter measures to the

filling quantity, PLC sends out the instruction of

close-valve. It has a certain time delay from PLC

instruction issued to the valve fully closed, the

valve-closed delay could cause error of propellant

filling.

The third is maintenance of flowmeter set-zero.

Filling control system adopts PLC control model.

Take the second-level quantitative-filling (Yan, 2004)

for example, when PLC receives the second-level

signal, firstly the secondary instrument of the

flowmeter is set zero, and the set-zero operation

cannot be instantly restore, which need to keep 0.5

seconds, to ensure that the secondary instrument

performs normal set-zero action. The maintenance of

flowmeter set-zero could cause error of the

propellant filling.

The fourth is leakage of pipeline. The pipeline of

filling system in the spaceflight launch site is longer.

In the process of propellant filling, it’s hard to avoid

leakage of pipeline, including the outer leakage and

the inner leakage. The leakage of pipeline could

cause certain error of the propellant filling.

3 ALGORITHM OF FILLING

ACCURACY BASED ON

FLOWMETER MEASURING

MODEL

Through analysis on the factors that affects the

filling accuracy, the specific error value of filling

quantity caused by each factor has been calculated,

including the error value caused by flowmeter

measuring, the error value caused by valve-closed

delay, the error value caused by maintenance of

flowmeter set-zero and the error valve caused by

leakage of pipeline, etc. Then the actual filling

accuracy of rocket propellant can be calculated.

When carrying through numerical calculation, the

filling quantity given by the rocket department is

taken as the reference, taking no account of the

influence of

volumetric measurement error. The

specific analysis is as follow.

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3.1 Numerical Analysis of Error

Caused by Flowmeter Measuring

The existing filling system adopts the filling model

of volume-level. Namely, it measures filling quantity

by flowmeter, meanwhile adopts the liquid-level

quantitative-filling way. Flowmeter start measure

from zero when it receives the liquid-level signal,

until flowmeter counts to the certain value. General

the second liquid-level is taken as the liquid-level of

quantitative-filling. Therefore, the measuring value

of the flowmeter before the quantitative-filling

liquid-level does not affect the actual filling

accuracy, only affects actual effect of display.

Actually, the error value of flowmeter measuring

equals the error value of quantitative-filling

measuring. The value could be calculated according

to the metering accuracy of flowmeter, namely 1%.

Define: the error value caused by flowmeter

measuring is E

(L), the quantitative-filling quantity

is b (L), the measuring accuracy of flowmeter is m.

The calculation formula of error value caused by

flowmeter measuring is as follow:

mbE ×=

(1)

Specific calculation data are shown in table 1.

Table 1: Error value caused by flowmeter measuring.

Rocket

level

Quantitative-filling

quantity

Theoretical value (L)

Flowmeter

accuracy

Error value

(L)

R1 2560 1% 25.6

R2 1190 1% 11.9

R3 1130 1% 11.3

Y1 1390 1% 13.9

Y2 1160 1% 11.9

Y3 1230 1% 12.3

3.2 Numerical Analysis of Error

Caused by Valve-Closed Delay

3.2.1 Mathematical Analysis

The high pressure pneumatic valve of filling system

conforms to the quick-opening flow characteristic

when valve closes. Valves provided with the flow

characteristic have larger flow when the opening is

smaller. With the increase of the opening, the flow

increases rapidly and is close to the largest soon.

Keep on adding the opening, the change of flow is

small. Therefore it is called quick-opening flow

characteristic (Pan, 2011). The function relationship

between the relative flow and f relative excursion

is:

dlKqdq

1−

= . Generating into the boundary

conditions, we can obtain the function relationship

of quick-opening flow characteristics, the formula is

as follow:

()

⋅−+=

⋅−+==

max

(2)

In the above formula, R is the ratio that valve can

control between maximum flow and minimum flow,

namely the adjustable ratio. Q is the flow that passes

through the valve. Qmax is the maximum value of

flow that passes through the valve.

max

is the

relative flow.

max

is the relative excursion.

For the valve of quick-opening flow

characteristic, the gain K is proportional to the

reciprocal of flow Q, or

∝

. With the

increase of flow, the gain decreases.

The flow characteristic curve when valve closes

is as follow:

0 20406080100

100

percentage of maximum flow (%)

percentage of maximum opening (%)

— flow characteristic curve

Figure 1: Flow characteristic curve when valve closes.

3.2.2 Numerical Calculation of the Error

From experiment we can get the time delay is 1.5s,

the transmission speed of electrical signal is quite

fast, and it can be ignored.

Table 2: Error value caused by valve-closed delay.

Rocket

level

Flow velocity

when filling finished

(L/min)

Time

(s)

Error value

(L)

R1 300 1.5 5.6

R2 300 1.5 5.6

R3 150 1.5 2.8

Y1 300 1.5 5.6

Y2 300 1.5 5.6

Y3 150 1.5 2.8

FillingAccuracyAnalysisoftheRocketPropellantbasedontheFlowmeterMeasuringModel

183

Define: the error value caused by valve-closed delay

is E

(L). Then the error value can be calculated

through the above formula. The specific calculation

data are shown in table 2.

3.3 Numerical Analysis of Error

Caused by Maintenance of

Flowmeter Set-zero

Filling control system adopts PLC to control. Take

the second-level quantitative-filling for example,

when PLC receives the second-level signal, the

secondary instrument of flowmeter is set zero. The

set-zero operation cannot be instantly restore, it need

to keep 0.5 seconds, to ensure that the secondary

instrument perform the set-zero action. The

maintenance of flowmeter set-zero could cause the

error of propellant filling quantity.

Define: The error value caused by maintenance

of flowmeter set-zero is E

(L). The flow velocity

when receives the second liquid-level signal is v

(L/min). The time of valve-closed delay is t

(s).

Then the error calculation formula caused by

maintenance of flowmeter set-zero is as follow:

333

tvE ×= (3)

Specific calculation data are shown in table 3.

Table 3: Error value caused by maintenance of flowmeter

set-zero.

Rocket

level

Flow velocity

(L/min)

Time

(s)

Error value

(L)

R1 300 0.5 2.5

R2 300 0.5 2.5

R3 150 0.5 1.25

Y1 300 0.5 2.5

Y2 300 0.5 2.5

Y3 150 0.5 1.25

3.4 Numerical Analysis of Error

Caused by Leakage of Pipeline

3.4.1 Mathematical Analysis

In order to calculate the error value of propellant

filling quantity caused by leakage of pipeline, the

pipeline leakage model needs to be established, as

shown in Fig.2. When the fissure of equipment is

regular, and the fissure size, physical and chemical

properties and parameters of the leakage material are

known, the leakage quantity can be calculated

according to related equations of the hydrodynamics.

When the fissure of equipment is irregular, the

fissure size can be instead of equivalent size. (Ma,

2008)

,ρ

P,T,u,ρ

Leakage

hole

Pipeline

external

Pipeline

internal

Figure 2: Leakage model of the filling pipeline.

Fig.2 shows the gas leakage process of filling

pipeline. The gas inner pipeline is nitrogen, and

there is a small leakage hole somewhere on the

pipeline. As is shown in Fig.2, the parameter (P, T, u,

ρ) respectively express the pressure, temperature,

leakage velocity and gas density nearby the leakage

hole which on the pipeline internal. The parameter

, T

, u

, ρ

) respectively express the pressure,

temperature, leakage velocity and gas density nearby

the leakage hole which on the pipeline external.

In the process of the filling pipeline gas tightness

check, gas flow process can be taken as reversible

and adiabatic process of ideal gas. It follows the

state equation and Poisson equation of ideal gas. The

following equation can be obtained through the

energy conservation equation and momentum

conservation equation













−+













(4)

In the above formula, D is diameter of the

pipeline (mm). K is the specific heat capacity. f is

the friction coefficient. u is the gas leakage rate

(m/s). G is the gas flow (m

/s). R is the gas constant.

In the pore model, in view of the aperture is

smaller, pressure is not affected by gas leakage, and

the gas expansion process is isentropic. Therefore

gas leakage rate is constant, and is equal to the initial

maximum leakage rate (Dong, 2002).

a) The gas leakage calculation

The leakage rate that gas leak from the fissure is

related to its flow state (Zou, 2010). Therefore, it

needs to determine the gas flow belongs to sonic

flow or subsonic flow when calculating the leakage.

The former is called the critical flow, the latter is

called the subcritical flow (Beirami, 2006), (Boonen,

2009).

In allusion to the filling pipeline gas tightness

check, from numerical calculation we can

get:

−













. Therefore, the gas leakage of

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filling pipeline belongs to the sonic flow. In the

formula, p is the medium pressure within the

pipeline (Pa).

is the environmental pressure

(Pa). k is the gas adiabatic index, that is, the ratio

between Cp and Cv.

When the gas flow is the sonic flow, the leakage

is:

−













kRT

ApCQ

(5)

In the above formula,

C is the gas leakage

coefficient, if the fissure shape was

round,

00.1=

C , if the fissure shape is triangle,

95.0=

C , if the fissure shape is rectangle,

90.0=

C . M is the molecular weight. p is the

medium pressure (Pa). R is the gas constant (J/(mod

• K)). T is the gas temperature (K).

If considering the leakage rate that affected by

the gas decrease or pressure reduce inside the

pipeline, the calculation of leakage rate is too

complex (Cazauran, 2009), (Zhang, 2010). In

process of the filling pipeline gas tightness check, in

view of pressure of pipeline internal is higher, and

the leakage is very small, so assume that the gas

pressure inner the pipeline is invariable when carries

through calculation.

b) Liquid leakage calculation

The liquid leakage rate can be calculated by

Bernoulli equation of hydromechanics (

Ben-Mansour,

2010), the leakage rate is as follow:

ACQ

)(2

−

(6)

In the above formula,

is the liquid leakage

rate (kg/s).

C is the liquid leakage coefficient. A is

the area of fissure (m

). ρis the density of the

liquid leakage (kg/m

). p is the gas pressure inner

the pipeline (Pa).

is the environmental pressure

(Pa). g is the acceleration of gravity (9.8 m/s

). h is

the liquid-level height above the fissure (m).

3.4.2 Numerical Calculation of the Error

From the above analysis we can know the specific

calculation process, it is as follow. First of all, we

calculate the equivalent fissure size according to the

pressure drop values and gas leakage formula.5 in

the process of gas tightness check. The actual

pressure drop value is within 1%, so the value of 1%

is used in the calculation. Then we calculate the

liquid leakage rate according to the liquid leakage

formula.6. Finally we calculate the error value of

propellant filling according to the actual

quantitative-filling time.

Define: the error value of filling quantity caused

by leakage of pipeline is E

(L). The liquid leakage

rate is

. The quantitative-filling time is t

(s). The

quantitative-filling velocity is v

. The

quantitative-filling quantity is b. Assuming that the

liquid leakage rate is constant in the process of

quantitative-filling. According to the real

experimental data, gas pressure drop within 1% in

half an hour in the process of gas tightness check.

The quantitative-filling time can be calculated

through the quantitative-filling quantity and the

quantitative-filling time velocity. The error value

caused by leakage of pipeline before the

quantitative-filling liquid-level does not affect the

actual filling accuracy, only affects the actual display

effect. Calculation formula is as follows:

0404

QtQE ×=×=

(7)

Specific calculation data are shown in table 4.

Table 4: Error value caused by leakage of pipeline.

Rocket

level

Quantitative-filling

quantity

Theoretical value (L)

Time

(s)

Error value

(L)

R1 2560 512 3.20

R2 1190 238 1.49

R3 1130 452 1.41

Y1 1390 278 1.73

Y2 1160 232 1.45

Y3 1230 492 1.54

4 NUMERICAL ANALYSIS OF

THE ACTUAL FILLING

ACCURACY

From the above numerical calculation and analysis

we can know, the infection of different factors to the

actual filling accuracy is different, and it is positive

or negative that the infection effect of different

factors to the error value of filling quantity.

Define: Fac1 expresses the error caused by

flowmeter measuring. Fac2 expresses the error

caused by valve-closed delay. Fac3 expresses the

error caused by maintenance of flowmeter set-zero.

Fac4 expresses the error caused by leakage of

pipeline. Then, the influence factor of Fac1 is “±”,

FillingAccuracyAnalysisoftheRocketPropellantbasedontheFlowmeterMeasuringModel

185

the influence factor of Fac2 is “+”, the influence

factor of Fac3 is “+”, the influence factor of Fac4 is

“±”.

Define: the actual filling error of rocket

propellant is E (L). The formula can be got as

follow:

)()()(

0332

4321

QtvEmb

EEEEE

×±×++×±

=±++±=

(8)

The error calculation results of rocket propellant

filling under the existing filling process are shown in

table 5.

Table 5: Actual filling accuracy of rocket propellant.

Rocket

level

(L)

Total error

(L)

Filling

accuracy

±25.6

+5.6 +2.5

±3.20 -20.7～33.7 -0.81%～1.32%

±11.9

+5.6 +2.5

±1.49 -5.29～20.0 -0.44%～1.68%

±11.3

+2.8 +1.25

±1.41 -8.66～15.35 -0.77%～1.36%

±13.9

+5.6 +2.5

±1.73 -7.53～22.0 -0.54%～1.58%

±11.9

+5.6 +2.5

±1.45 -5.25～20.0 -0.45%～1.72%

±12.3

+2.8 +1.25

±1.54 -9.79～16.35 -0.79%～1.33%

In order to more intuitive reveal the influence

that the actual filling accuracy affected by different

factors, we convert the data in the above table into

graph form, as shown in Fig.3.

123456

-20

-10

Error value of filling quantity (L)

Rocket level

Error 1

Error 2

Error 3

Error 4

Total error

Figure 3: Filling accuracy contrast fig of the rocket

propellant.

From the data in Table5 and Fig.3, we can get

that the infection of different factors to the actual

filling accuracy is different. Fac1 has the greatest

influence on the filling accuracy, followed by Fac2,

Fac3 and Fac4 has smaller influence on the filling

accuracy.

From the above mathematical analysis and

numerical calculation, we can know that the actual

filling accuracy of rocket propellant is related with

the quantitative-filling quantity and

quantitative-filling velocity. In order to further

analyze the relationship between filling accuracy

and quantitative-filling quantity and

quantitative-filling velocity, on the one hand, the

numerical calculation of the filling accuracy is

carried through in the case of 1/2 and 1/4 of the

original quantitative-filling quantity, and the

calculated results are compared with the filling

accuracy under the original quantitative-filling

quantity. The results are shown in Fig.4. On the

other hand, the numerical calculation of the filling

accuracy is carried through in the case of 1/2 and 1/4

of the original quantitative-filling velocity, and the

calculated results are compared with the filling

accuracy under the original quantitative-filling

velocity. The results are shown in Fig.5.

-20

-10

Error value of filling quantity (L)

Rocket level

original quantitative-filling quantity

1/2 original quantity

1/4 original quantity

Figure 4: Filling accuracy contrast fig in the case of

different quantitative-filling quantity.

123456

-20

-10

original quantitative-filling velocity

1/2 original velocity

1/4 original velocity

R3R2

Error value of filling quantity (L)

Rocket level

Figure 5: Filling accuracy contrast fig in the case of

different quantitative-filling velocity.

Fig.4 shows the filling accuracy contrast in the

case of different quantitative-filling quantity, Fig.5

shows the filling accuracy contrast in the case of

different quantitative-filling velocity. As is shown in

the Fig, the actual filling accuracy of rocket

propellant is related with the quantitative-filling

quantity and quantitative-filling velocity. The

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186

quantitative-filling quantity has much influence on

the filling accuracy, and reduce the

quantitative-filling quantity can significantly

improve the filling accuracy. The quantitative-filling

velocity has smaller influence on the filling accuracy,

but it can adjust the peak of filling error value.

Therefore reduce the quantitative-filling quantity can

reduce the maximum of filling error, so as to

improve the filling accuracy.

5 CONCLUSIONS

In terms of rocket propellant filling, this paper

analyzes the factors that affect the accuracy of the

propellant filling in the filling system of the

spaceflight launch site. It calculates the error value

of filling quantity caused by the different factors,

and carries through numerical calculation and

analysis for the actual filling accuracy of rocket

propellant. It is helpful to optimize filling model and

filling process, and provides theoretical basis and

data support for the research of improving the filling

accuracy. Through numerical analysis we can get

that the equipment performance has much influence

on the filling accuracy, in the case of definite

equipment performance, reduce the

quantitative-filling quantity and quantitative-filling

velocity can also improve the filling accuracy.

However, it does not consider the influence of

the gas-liquid two-phase flow and the propellant

temperature rise when calculating the actual filling

accuracy. The next research direction is to get the

error value of filling quantity caused by the

gas-liquid two-phase flow and the propellant

temperature rise through simulation calculation, to

perfect the factors that affect the accuracy of

propellant filling, put forward more effective

targeted measures, so as to further improve the

filling accuracy of rocket propellant.

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