4

ENGINE IGNITION TRAN

FINAL REPORT

CONTRACT NAS7-467

MAY 1970

BY

T. R. MILLS AND B.P. BREEN

DYNAMIC SCIENCE A D I V I S I O N

OF MARSHALL INDUSTRIES

2400 MICHELSON

I R Y I N E , CALIFORNIA

NATIONAL A

COMPUTER MODELING OF ROCKET ENGINE IGNITION TRANSIENTS

Final Report

Contract NAS7-467 I

May 1970

T . R . M i l l s and B. P . Breen DYNAMIC SCIENCE, A Division

of Marshall Industries 2400 Michelson Drive

b i n e , California

For

NATIONAL AERONAUTICS AND SPACE ADMINISTRATION Jet Propulsion Laboratory

Pasadena, California

FOREWORD

This report was prepared for the National Aeronautics and Space . i

.-. Administration, Jet Propulsion Laboratory, Pasadena, California. Project Monitor on this contract was Richard M. Clayton, Liquid Propulsion Section.

This is the final report of a research program conducted to develop a mathematical model of how design and operating parameters influence combustion chamber pressures during the starting transient of a rocket engine. As such, i t is based upon work completed and reported in two previous interim reports published under this contract (NAS7-467); "Study of Random Wave Phenomena in Hypergolic Propellant Combustion, '' June 1967 (Ref. 16), and "Transients Influenc- ing Rocket Engine Ignition and Popping, 'I April 1969 (Ref. 17).

ii

SUMMARY

The objective of this program was to predict the dominant engineering parameters influencing the occurrence of start spiking in rocket en>gines. A

computer program was written to describe transient propellant flow and the pressure/temperature and O/F histories with the chamber prior to ignition. Experimental tests were performed which confirmed the analytical findings. Ignition spiking occurred with fuel leads at low fuel temperature, and even a t high fuel temperatures with long vacuum leads: while spiking was reduced by controlled valve opening sequences at nominal temperatures .

The analytical study resulted in a propellant transient flow .digital computer program and a chamber pressurization transient digital computer program which was used to obtain the engine starting characteristics. The data from the pressurization program is used in the MASA/Lewis chemical equilibrium/detonation program to predict maximum pressures possible from the transient chamber fuel/oxidizer mixture environment.

TABLE OF CONTENTS

Page N o .

N O M EN C LATURE 1. INTRODUCTION 2 . PROPELLANT TRANSIENT FLOW PROGRAM 3. CHAMBER PRESSURIZATION TRANSIENT PROGRAM 4. EXPERIMENTAL PRO GRAM 5 . CONCLUSIONS 6. REFERENCES

APPENDIX A - USER'S MANUAL FOR PROPELLANT TRANSIENT FLOW PROGRAM

APPENDIX B - USER'S MANUAL FOR CHAMBER PRESSURIZATION TRANSIENT PROGRAM

APPENDIX C - PROPELLANT TRANSIENT FLOW PROGRAM

APPENDIX D - CHAMBER PRESSURIZATION TRANSIENT PROGRAM

V

1 6

3 1

43

56 57

59

65

80

87

DISTRIBUTION 110

NOMENCLATURE

Cross-sectional area of propellant line, in2

Total cross sectional area of orifices, in2 Aa AO

AV

Avo B

Open area of valve (which varies a s the valvq opens) ina

Area of valve when fu l l open, in2

Compressive bulk modulus, lb/in2

cD

cO

Discharge coefficient

LOSS coefficient of orifices

‘rn Capacitance of the propellant manifold (which is variable a s the manifold fills), ft? -in2/lb

cV

D

Loss coefficient of valve

Diffusion coefficient of oxidizer vapors to droplet f P/s ec

Diameter of line, in d

f Friction factor

Gravitational constant, 3 2 . 2 ft/sec2

Concentration of oxidizer vapor surrounding a droplet, mass fraction

K

- K Local concentration of oxidizer in vapor surrounding

a droplet, mass fraction

Loss coefficient for bends and abrupt line s ize changes

Inductance of the propellant line between the tank and the valve, lb-sec2/ft3 -in2

Lm Inductance of the propellant manifold (which is variable a s the manifold fills) , lb-seca/ft3-ina

a Length of propellant line, f t

Length of line over which friction ac t s , f t

Length of propellant manifold ,- in a m Mach number M

Number density of droplets with radius Oi Ni.

V

'a

pC

pf

'i

'1 ine

'm

pV

9

q2

RO

RV

r

T

t

tf

ti

'm

'me

'mo

w*

Ambient pressure, lb/in2

Chamber pressure, lb/in2

Final manifold pressure after filling, lb/ina

Initial manifold pressure before flow starts, lb/ina

Pressure in the line upstream of the valve, lb/in2

Pressure in propellant manifold, lb/in2

Vapor pressure of the propellant, lb/in2

Volumetric flow rate, ft3/sec

Volumetric flow rate of propellants through the valve, fP/sec

Volumetric flow rate of propellants through the orifices, fP/sec

Resistance of the propellant line between the tank and the valve, lb-sec/fF-in'

Resistance of the orifices, lb-sec/ft?-in2

Resistance of the valve (which is variable a s the valve opens), lb-sec/ft3-in2

Radial distance from the surface of the droplet

Temperature of gases in the propellant manifold OR

Time, seconds

Time of final manifold pressure after filling, sec

Time of initial flow into manifold, sec

Volume of propellant manifold, ft3

Empty volume of manifold (which varies a s the manifold fills), in3

Original empty volume of the manifold, ina

Flow rate of gases initially in the propellant manifold, lb/sec

Flow rate through the orifices, lb/sec

Weight of gases initially in the propellant manifold, l b

v i

1. INTRODUCTION

High pressures usually referred to a s pressure spikes or detonation waves can occur during the starting transient of a rocket engine. These high starting pressures can damage the combustion chamber. High pressure spiking has been encountered in both large (Ref. 1) and small scale (Ref. 2) space engines. Engine fixes were made to eliminate the spikes in specific engines while little effort was made to understand the mechanisms involved. At first it was generally accepted that the cause of the pressure waves was the explosion of accumulated propellants in the combustion chamber. However, a s a result of recent experimental investiga- tions , it was found that detonatable chemical reaction intermediates can form under start transient conditions (Refs. 3 , 4 , 5 , and 6) and Perlee (Ref, 4) showed that observed hardware deformations could only be explained on the basis of the presence of highly detonatable material. This information provided evidence for a mechanism to explain start transient spiking: conditions within a rocket engine combustion chamber, during the start transient, that are conducive to the formation of these detonatable mixtures would lead to the magnitude of spikes observed. Thus, what was needed was an analytical model describing the occurrence of these unfavorable conditions and also describing how these unfavorable conditions could be avoided by proper engineering design and/or controlled. The details of this model are aimed at establishing temperature , pressure, and O/F conditions which control preignition and intermediate chemistry , while the overall purpose is to show how smooth starts can be engineered into a rocket engine.

The model developed is spatiallyone-dimensional and is based on t i m e dependent differential equations which describe the physical and chemical processes governing the transient chamber conditions. The overall logic of the model is based on the four processes shown in Figure 1. The equations must account for the four processes shown by Roman numerals I through IV: (I) the liquid propellant transient flow , (11) vaporization, condensation, and freezing of propellants and their effect on the chamber transient pressure and temperature , (111) chemical reaction leading to the formation of detonatable mixtures with the effects of species concentration and temperature considered , and finally (IV) the strength of detonation of the accumulated mixture. The vaporization model incorpo- rates the modeling work of Agosta (Ref. 7) and of Seamans and Dawson (Ref. 8).

The present model is unique in that it incorporates the results of previous chemical

1

t 1 t c 0

c b,

d w d

H

2 i--

VAPOR INJECTOR

v IO _l_g.

d Pc (O,Tclt)

a. Transient Flow Systems (I)

1

VAPOR PHASE IveTc (1) CHEMISTRYAND .

HEAT GENERATION Pc(l)

PREIGNITION LOSS

7

-L Cltl

,$-":.?:::?:E< ..................................... 43; p RE I GN i TI o N $ #

C( ,) ............................ ................... :.:.:...:

CONDENSED PHASE CHEMISTRY AND

HEAT GENERATION

I I

v,cs *

@ pEW, Tc (0

I IF:-., ........... .......... .......... !

PRODUCT GAS GENERATION

GENERATION

b. Chamber Pressurization System (11)

c. Preignition Chemistry System (III)

Figure 2 . Individual Components of Ignition Model

3

intermediate research on hypergolic ignition mechanisms (Refs 3 and 9) and on ignition chemistry (Refs. 4 , 5, and 10). The model contains several constants which have been evaluated from experimental data published in these references.

The solution of the equations describing the model were performed numerically on the digital computer by a finite difference method. The main objectives of this project were to perform analytical and experimental investigations to:

(1)

(2)

(3)

Analytically determine the dominant parameters that influence the production of starting transient chamber pres sure spikes . Determine design criteria for the minimizing of spiking based on study developments. Experimentally verify the analytical results and determine the limitations of the analysis and of the computer programs.

In any practical rocket engine system, which relies upon hypergolic ignition, the engine will start once the liquid entering the chamber meets previously determined ignition criteria conditions of temperature and vapor pressure. From this point of view, the starting of an engine involves two characteristic flow delays :

(1) (2)

line and manifold filling, and the flow of enough liquid sensible heat to overcome hardware and vaporization heat losses,

Essentially, once enough liquid has entered the chamber so that both the fuel and the oxidizer droplet enter a chamber pressure either equal to or greater than their vapor pressure, then they do not flash vaporize and the engine starts within - f 5% of the added two flow delays above.

The individual components of the flow and heat balances are shown in Figure 2 . During the first phase of this work (Ref. 16), these components were identified by calculating controlling time constants and from published experimental observations; thus, the controlling model is formulated in the first interim report of this work (Ref. 16). In the second phase of this contract (Ref. 17), the individual components of Figure 2 were described by an analytical model, and the model was programmed for solution so that the characteristics of each component of Figure 2 could be demonstrated Generally, the importance of the transient flow character- istics was pointed out and it was shorn that once enough liquid sensible heat entered the chamber to overcome the hardware heat capacity, the engine started.

In Section 2 of this report, the line manifold and chamber flow (the first delay) are described, while Section 3 describes the heat balances (the second delay) and resulting chamber copditions which the entering liquld encounters and Section 5 relates these flow and vaporization situations to ex determinations of the occurrence and severity of spiking

5

2 PROPELLANT TRANSIENT FLOW PROGRAM

Chamber pressurization transient predictions require propellant flow into the combustion rchamber as &a functions of were made of the propellant feed syster of a typicral biprope rocket engine. This system is shown schematically in Figure 3. The feed system and the analysis are general and can be used in any gas-pressurized injection scheme regardlesg of the size of the engine. Likewise, the analysis can be used to predict the response of a future system design or analyze an existing system

nowledge of the

Analysis of the feed system of Figure 3 is s i m i l a r to a pipeline flow problem, There are two general methods of approach: the controlling parameters can be assumed to be either (1) distributed along the flow line, or (2) lumped at one point in the circuit. Solution of systems (Ref. 11) by a distributed approach involves partial differential equations in space and t ime. Discontinuities in the system, such as the valves and propellant tank of Figure 3, are the boundary conditions for the problem, Solutions are obtained by methods of Characteristics (such as water hammer analysis , Ref. 1). The difficulties in applying this approach are: (1) the solutions are difficult to generalize or only simple configurations may be generalized, and (2) the flow downstream of the valve requires a separate solution which must be matched at the discontinuity (the valve). This second condition requires detailed knowledge of the pressure wave interactions within the propellant manifolds which are difficult to obtain. The approach may be applied to simple configurations where detailed in formation about the wave inter- action effects are desired but overall the more microscopic nonlinear effects of unfilled vs . filled manifolds and t i m e dependent valve resistance and cavitating flow in the orifice are more important to the starting characteristics of the engine.

Solutions of flow systems by a lumped parameter approach are made by considering solutions of quasi-steady-state flow (Ref. 11) or by use of an electrical analogy model. Quasi-steady-state solutions assume (1) no injector flow until the manifolds are full, (2) all loss terms are linear or constant, (3) no inertia or fluid elasticity effects are considered, and (4) all pressure in and flow out of the manifolds occurs discontinuously. These restrictions are quite severe and the results of such analyses give trends only for design changes and minimal details of the flow transient,

6

f -

By considering a lumped parameter model wherein each element of the fluid system is considered analogous t o those of a passive electrical system, the details of the distributed system are retained with the simplicity of the quasi-steady-state approach (Refs. 13 and 14). Basically, the analog model which was decided upon is described on the following pages.

3

Electrical/Hydraulic Analoq Model: The electricaI/hydraulic analogy Is developed by considering all pressure loss terms lumped in a hydraulic resistance, Rh , all fluid inertia effects lumped in a hydraulic inductance , Lh, and all fluid elasticity effects lumped in a hydraulic capacitance c h ' The lumped hydraulic capacitance can be taken as the compressibility of the vapor because in the case of vacuum starts there always exists a point of cavitation and, therefore, a com- pressible vapor point. For one side (fuel or oxidizer) of the system shown in Figure 3a , an analogous system can be constructed, Figure 3b.

Writing the pressure drops around the loops of the circuit shown in Figure 3b, the following differential equations result:

Converting the analogous terms t9 fluid flow parameters a s follows:

pa L~ = (for the line)

2

-- rn (for the manifold)

R = Kn; p 9?, (for bends and line size changes) 2 S A j

R = f d + p -& (for friction losses)

7

Oxidizer

~

Combustion Chamber

l \ a , Schematic Diagram of Propellant Feed System.

b. Analogous Electrical System to Propellant Feed System Figure 3, Frogellant Feed Systzm. Schematic and Analogous Diagrams.

8

the final differential equations result:

Solution of the Model: Standard digital computer integration procedures are available for solving nonlinear differential equations shown by Equations (3) and (4) e

A standard integration subroutine was found to be perfectly satisfactory The method employed used a 4th order Runge-Kutta start and a 4th order Adams-Moulton fixed step predictor-corrector method used to continue the integration. Comparing predicted and corrected values a t each step, the integration step size was halved, doubled, or maintained the same so that the truncation error would remain within prescribed error bounds. The t ime varying valve area, Av, is prescribed by either an input table or for valves which open nearly linearly, by the equation:

t n A =4r0$-)

vo (5)

Within the framework of this analysis, the following assumptions are made: (1 1 (2

The liquid propellants are incompressible. The compressibility effect in the propellant manifold is due to the vapor in the manifold and is equal to the bulk modulus of vapor. adiabatically. Wave effects within the system have negligible effects on the transient flow. The chamber pressure is constant.

The formation of vapor in the manifold is accomplished

(3 1

(4 1

Parametric Effects: Initial ca ses were calculated to determine the effects of the various system parameters and empirical constants in the analysis. Figures 4 through 10 show the results of these initial cases. Table I shows those parameters which were not varied for these cases. Most of the cases were performed with n = 1.0

(linear valve opening); however, a limited number of cases were run for n = 3.

9

TABLE I

TRANSIENT FLOW PARAMETERS HELD CONSTANT DURING INITIAL PROPELLANT FLOW TEST CASES

line diameter inches DI =e .1875 in. valve coefficient CV = a7 injector coefficient C@ = a 7

orifice diameter I inches DQfI = .02 in. number of orifices xN@w = 4 . 0 steady-gtate flow, lb/sec wss - c .08 lb/sec (oxidizer)

,067 lb/sec (fuel)

10

Figure 4 shows the effect on flow rate of varying KA, the loss coefficient. KR is

approximately 1 , O for one bend or abrupt area change (Ref. 15).

Figure 5 shows the effect on flow rate of varying the valve opening t i m e from 2 .5 to 10 m s . There is little effect on the transient shape in each case except to delay the transient a s the valve opening t i m e is increased.

The effect of the manifold volume is seen in Figure 6 where manifold volumes of .05 , and .025 in” were considered with a valve having an opening t i m e of 10 m s . For the smaller manifold volume steady-state flow is achieved sooner, however, the overshoot of Wo is greater than for the larger volume (.0901 lb/sec vs .0857 lb/sec).

Figure 7 shows the effect of varying the valve area. The effect of reducing the area is to throttle the flow.

Figure 8 shows the effect of varying the valve transient shape for two valve areas. It is seen that by reducing the initial opening rate the valve can more effectively control the flow through the orifices.

Figure 9 shows the effects of temperature on the start transient, Oxidizer a t 540 and 580°R was used for these tests. The differences in transients noted here are due to the difference in vapor pressure (18.5 psia vs 49 psia) of the propellant (Nz04) a t these two temperatures.

The calculations were made for fuel (hydrazine) a t 500°R (Figure 10). Both calculations show flow rate overshoot and extremely rapid flow rise rates. Although both conditions show overshoots , the recovery to steady-state flow is rapid.

Originally the analysis considered the compressibility of the vapors inside the manifold to take place isothermally. Campbell (Ref. 14) showed that rapid compression of results in the following:

gases occur nearly adiabatically. This effect

me where Cm is the capacitance. For nonvacuum starts the propellant manifolds contain air which is expelled a s the manifold is filled with propellant. The capacitance pressure term in the differential equation accounts for the change

11

I

u 0 rn a d

c

3 O

.Ol

, ,001

I

, OD01 10 12

b\. .,. ' . . - Figure 4 . Effect of Loss Coefflci'ent'; KA on Flow Transient.

12

,1

. 0 1

. O O l

0 2 ' 4 6 Time, t; ms

10 12

Figure 5 . Effect of Valve Opening on Flow Transient.

n 1

.01

.001

.oo ' 0

d... n = 1.0 Propellant: N 0 Temperature: 540 R 'i-

. I 1 B = ,050 in3 '

= Volume of Manifold ..

-.

2 4, L

Vm = ' A = ,025 in3 t -

1 : * i

2 4 6 Time,, t , m s

8 10 1.2

Figure 6 , Effect of Manifold Volume on Flow Transient.

.01

4

.

5 iz 0

0 2 4 G ! Tim&, t , ms . .

. . . .

" < i %.'

Figtihe 7. Effect o f Valve USp'en Area on Flow Transient.

. a,

' f a p: c,

3 E: 0

. 0 1

.001

,0001

Legend

Ka= 10 R = .15ft Af = 20 ft . I . ( !

Figure 8 . Effect of Valve Transient and Open Area on Flow Transient ,

. o

.oo

.ooo

Figure9 Effect of Oxidizer Temperature on Flow Transient,

17

. . Time, t , m s Figure 10. Effect of Fuel Temperature on Flow Transient.

18

in the manifold volume due to the incoming propellants and the expelled air. This differential equation is:

where

- - g - - "me

Wg = A o - r @ I& M Y+1

p ? k L 1/2 M = (" [. (F)

Y -1 a (9)

For vacuum stsrts, the manifold pressure was the vapor pressure of the entering propellants until the manifold was full. Thus, the pressure rises from zero to the vapor pressure, remains at vapor pressure until the manifold fills I and then becomes equal to the system fluid pressure.

Valve Opening Effects: Five calculations were made under these conditions (Fjgures 11 through 15) e These cases considered three linear valve openings and two step-wise openings Table I1 shows the conditions. The three linear openings are 10, SO, and 100 ms. Figures 11,12,and 13 show the effect of these opening rates. It is seen that no control of the propellant flow rate is achieved. When the manifold fills a substantial pressure and flow rate overshoot occurs,

To simulate flow control, two step-wise valve openings were considered, Figures 14 and 15. Figure 14 shows the results of a low level step. Under these conditions a substantial reduction in the flow and pressure r ise occurs. For the oxidizer flow, no overshoot occurred, and for the fuel flow, the over- shoot was reduced. When a medium level step-wise opening was used the results were equivalent to a 50 m s valve opening.

From the propellant transient studies it can be concluded that:

Propellant flow from the injector prior to the manifold pressure reaching the vapor pressure is controlled by the valve opening transient. Propellant flow from the injector prior to the manifold filling after the manifold pressure rises to the vapor pressure, will

(1 1

(2 1

19

be controlled by the injector orifices I the and finally by the vapor pressure of the pr manifold. The flow control which is possible during this period therbfore, is by controlling the propellant temperature and thus the vapor pressure. Propellant flow from the injector can be controlled by valves if the initial valve opening area is small.

(3 1

20

TABLE 11

INPUT FOR PROPELLANT TRANSIENT FLOW TEST CMES - . (Sac Figures 9 - 13)

Oxidiser System

density, lb/ft" R@ = 88.9

. . ~ ... . . Fuel System

RQf 62,6

line length, ft XL 8 . XL = 8 . E

vapor pressure , lb/ina PVI =

resistance coeff. XKL = line d ia , , in DI = discharge coeff, cv resistance length, ft XLF E

manifold length, in -MI =C

discharge coeff. co = orifice dia, in DQI viscosity, fb/ftvsaa XMU = manifold volume, ina VMQI =

=

number of orifice XNORF = heat ratio GAM = smbie3t pressure ,

lb/ft PAMBI =

18.5 16000. ,305 .7 8 , 4 . .86

w 02 .00026 1037

4 . 1 .2

8.

PVI = XKL = DI e

CV c

XLF = XLMI = CQ = DO1 XMU = VMOI = mow 9

GAM =

PAMBI =

32 1 $000. .305 07 8 . 4. 1. .02 , 00058

,172 4. 1.4

0 .

2 1

2

2

1

1

1

1

1

I

I

4

r 4

I

Figure T i m e = msec

11, Propellant Flow Transient with Fast Opening Valve.

0

22

2.

- 2 .

1.

1.

1.

a 0 4

x 1. CP, w

2 1, I

a 4

22

20

l e

1€

14

12

L O

8

6

A

2

0

Figure 12 . Time- msec

Propellant Flow Transient with Medium Opening Valve.

23

2 .2

2 . 0

- 1 . 8

1.6

1 . 4

a 0 d

x 1 .2 01-1 rcc

1.c I 4

3 -4 g . E

. I

.4

. 2

22

20

i a

le

14

12

10

8

6

4

2

0

Timew msec Figure 13. Propellant Flow Transient with Slow Opening Valve.

24

2 . 2

2.c

1 . t

1.r

1.1

c

3 4 I 1.

I

.

.

22

Time- msec Propellant Flow Transient with Low Step Opening Valve.

21

2.

2 .

1.

1 .

.

.

22

20

1E

1E

14

12

10

8

6

4

2

'0

Timew msec 0

Figure 15 . Propellant Flow Transient with Medium Step Opening Valve.

Model Applications To explore the model's applicability to simulate the start transient of

real engines exploratory studies were undertaken t o determine if the program was applicable for larger engines , higher density ambient environments , and could predict the preignition pressurization transients .

To accurately predict the initial preignition pressurization transient , it wag found from last year's effort that a very small initial step size was needed. The step size was increased as t i m e increased according to the t i m e step-time formula:

A t = (t+.i) z4 x 1 0 ' ~

However , the step size had to remain small to accurately portray the transient. It was found also in the propellant transient model where the step size was controlled by error bounds, that the step size did not increase sufficiently fast, if the valve opened rapidly , in order t o calculate long transients. While exploring these conditions, the propellant transient was programmed to simulate a water flow test (Ref. 12) in an attempt to determine the empirical constants within the equation. The test was also performed at atmospheric pressure. Figure; 1 6 shows the experimental and analytical results of this study. The propellant transient model was able to perform the calculation only because the valve opening was very gradual. The calculations were not possible when the valve transient of Figure 17 (Ref e 15) was used, since they program an inordinate amount of t i m e to perform.

From a more basic standpoint, i t can be shown that when the propellant flow rate per unit volume of the chamber is low, it is possible for the program to handle the calculations. For instance, if the flow rate per unit volume of the chamber for the experimental engine used in this program is compared to that of the larger engine of Reference 1 2 , it is seen that the flow/volume for the larger engine is twice that of the smaller engine.

Engine Flow Rate Volume Flow/tlolume Large 85 Ib/sec 1.169 ft" 72.7 lb/ft3-sec Small .147 lb/sec .00376 ft' 39.1 lb/fta-sec

Furthermore, the valve opening time and manifold volumes also contribute long transient periods which are difficult to simulate by the techniques developed here. Due to the large amount of computer t ime needed to perform these

27

calculations (the propellant transient model and the chamber pressurization transient model), it was decided that the basic program was not applicable to large run times and was applicable only to short transient studies in its present form. From Figure 25 I it appears that the propellant transient program will handle transients starting at other than vacuum conditions . The chamber pressurization program has been modified to handle other than vacuum starts and I lacking confirmation from any experimental data will handle atmospheric starts within the framework of the model.

28

Figure 16. Comparison Between Experimental and Amfytical W z tst' Flow Tests on a Large Englns (see Ref. 12).

2 9

4.0

3 .O

2.0

1 .o

0 0 Normalized Time, t/Tvo

Figure 17 Valve Opening Transient for Larger Engine (see Ref. 12)

30

3 . CHAMBER PRESSURIZATION TRANSIENT PROGRAM

Vaporization Program

The pressurization of a thrust chamber is treated mathematically as a sequence of steady-state processes in very short t ime intervals. At the start of each new t i m e interval, a new set of drops enter the thrust chamber. These drops undergo vaporization during the t i m e interval as do the drops which entered previously. At any time, each drop has a unique radius, temperature and physical state (solid fraction). The equations used in this part of the program (vaporization) were outlined by Agosta (Ref. 7) and later incorporated into computer programs by Seamans , et a1 (Ref. 8) , and Dynamic Science (Ref. 16).

1

Basically, the vaporization program accounts for massive operation rates during each t i m e interval to compute the chamber pressure for an arbitrary and transient fuel and oscillator input. Condensation on the chamber wall and mass loss through the nozzle are calculated and used to correct the chamber pressure. The temperature of the gas is based on the mass weighted average of gas, while the different temperatures of each droplet of both the propellant and the fuel for each t ime interval is accounted for. In accounting for each t i m e interval drop temperature, the radius and a l so the fraction frozen is accounted for.

Several analytical studies were conducted to improve the operation of the vaporization program and to make it more realistic. These studies investigated the effect of (1) the t ime step s i ze , (2) the number of initial drop s izes , and (3) the heat transfer between the combustion chamber gases and the chamber wall. Mechanistic additions to the previous year's program of Reference 16 to make it more realistic were (1) preignition reactions I and (2) variable propellant flow rate (by means of tabulated flow rates versus t ime and/or an orifice flow equation which depends on the chamber pressure).

The ability to use variable t i m e step was particularly important during the initial or zero pressure starting of the calculation. Reduction in time increments from 2 5 ~ 1 0 ~ ~ seconds down to the range of 5x1OW6 seconds showed significant influence on the solution. Reductions from one microsecond to one-half microsecond showed no significant change in pressurization solution . Calculations based on this short t ime step can be speeded up by drop averaging of drops which have been in the chamber for 5 to 10 t i m e steps because all of these older drops behave in a n average way.

31

The vaporization model was initially set up with a drop s ize distribution containing three radii of 7. O O X ~ O - ~ , 2 . O S X ~ O - ~ , and 4.61~10-~ inches, each radius representing respectively 30% , 40%, and 30% of the t injected. This scheme also resulted in high computing costs. In an effort to reduce these cos ts , a comparison between the t one-drop distribution of radius 2 .05x1 only was infected and from these results there is very little difference in chamber pressure between these two distributions. As a result, the vaporization program now uses a single droplet model having a radius of 2 . O ~ X ~ O - ~ inches.

inches

Preignition Chemistry Preignition chemical reactions were considered so that ignition could

ultimately be achieved. The analytical framework for treating preignition chemistry is as follows: the vapor reaction stoichiometry, heat of reaction and rate of reaction are governed by chamber temperature and reactant vapor partial pressures which are continually computed and followed by the vaporization program Within this framework shown in Figure 18, the chemical and the controlling physical mechanism l i m i t s measured by Zung (Ref. 3) were used.

Preignition reaction intermediates (Refs initiating mechanism for the detonations and the chemical energy t o sustain them. Combination of hardware designs (valve configurations, propellant manifolds and manifold volumes, injector configurations , feed system configura- t ions, etc .) combined with the proper operating modes of the system could produce those conditions which are most susceptible to ignition detonations.

To reduce the number of the engineering variables other studies were

3 , 4 , and 6) provide both the

performed using the Chamber Pressurization Transient Model. Reference 3 , a study of Nz04/N2H4 ignition mechanisms, indicates that hydrazine temperature controls ignition. As the hydrazine temperature is varied, distinct regions (Fig 19 , Ref. 3) are encountered wherein the ignition's mechanisms are different. At the lower temperatures (below approximately 5 SOOR) , reaction between liquid hydrazine and vapor nitrogen tetroxide occurs by reactions on the surface of the hydrazine

nable reaction intermediates

Detonation Program Following the running of the vaporization program to ignltion or for a

specified t ime , detonation properties were computed for various selected t i m e s .

32

Detonation properties were calculated by the NASA/Lewis detonation program given in Reference 16. This program is well documented in References 16 and 17, so a discussion of the basic principles used is not needed here. To fit the data from the vaporization program to the detonation program, some modifications t o the data are necessary. The detonation program is written for gaseous reactants while the reactants calculated by the vaporization program contain liquid droplets in a gaseous atmosphere. Table I11 is a tabulation of some of the data calculated from the vaporization program: the "f" listed in Table 111 is the fraction of a liquid propellant species to the total propellant species (liquid and gaseous). This f factor is used to convert the liquid propellant to a pseudo equivalent amount of gaseous reactants. Inherent with this conversion is that all of the liquid will be consumed in the detonation process. i'

A l l of each propellant species is converted to vapor reactants having a molecular weight in the ratio: weight of liquid + weight of vapor propellant/ weight of vapor propellant (!# +!# /% ). The new propellant enthalpy is obtained by adding the gaseous molar enthalpy t o the liquid molar enthalpy which has been corrected by the liquid to vapor ratio: [H=H +H [& /%) 1. Thus , each liquid propellant species is converted to a pseudo vapor wherein the molecular weight and enthalpy are obtained as outlined above.

d g g

a s k g

Results Ignition transient studies were conducted using the Chamber Pressurization

Transient Program where the propellant temperatures were varied (Ref. 17). In Figure 20, reproduced higher detonation pressures occur as the temperature is decreased. Further, as the t i m e to detonation is increased, and more reaction intermediates are produced , the detonation pressure is increased.

From an empirical standpoint (Refs. 2 and 18) , the occurrence and level of spiking is influenced by the sequence in which propellants enter the combustion chamber. Figure 2 1 from Reference 19 shows the results of these tests. These tests were performed with Nz04/UDMH-NzH4. These results can best be explained by considering the analytical cases shown in Figure 22. When N204 is injected into a vacuum atmosphere, its high vapor pressure results in a low vapor temperature. The subsequent injection of hydrazine into this low temperature results in the formation of liquid phase reaction intermediates. Figure 23 (Ref. 3) shows the effects of oxidizer vapor temperature on the ignition

3:

of N 0 /N H If the N 2 0 4 temperature regions in this figure are lowered to a level indicated in the preignition transient of Figure 24 , no immediate ignition will occur , but reaction intermediates would form until the heat of reaction raises the temperature to a level high enough for ignition. Further- more, it appears that for colder propellant temperatures and for longer fuel leads , the t ime to detonation increases, as well.

2 4 2 4 '

In conclusion, from the analytical studies using the Propellant Transient Flow Program and the Chamber Pressurization Transient Program , the following are considered to be the dominant engineering parameters influencing the occurrence

(1)

(3)

(4)

of start transient spiking. The fuel temperature should be high enough to prevent the formation of detonable reaction intermediates. Short oxidizer leads are conducive to spiking i f , during the lead condition , the gaseous chamber temperature is reduced to a level where reaction intermediates may form. Cold propellant fuel lead conditions become more conducive to spiking than do other lead conditions. Controlled propellant transient to achieve rapid ignition will reduce transient spiking.

34

W I I

m

C O ~ W m h w m h w I l l I l l I l l 0 0 0 O O O * 0 0 0

x x x x x x x x x ~ Y ) N m m ~ NO

N N - . I ~ O N ~ * .

4rlPI H4.d

4?3 9?? 97?

4 W m Nrlh (Ohm

r(NN 4NN 4 N N Y 1 7 ??7 491

$ $

0 0 o w m m 0 0 0 : : z z 0 0 0

m m m w w m

0 0 0 0 0 m m z

8 8 5 m m m

0 0 a :

s s 0 0

0 0 0

: : s 2

0 0 0 0 1 1 w m m

35

400 4 T 530°R O/FS .5

O/F > . S AH = 2220 Btu/lb 63N204+64N2H4 3 80N20+16N0+1 1N2+72H20+28NH4NO3

AH = 1123 Btu/lb 1 9N204+25N2H4 + 10N20+ N0+19NHQ+ 3~ N ~ + ~ H ~ O + ~ N Z H ~ N O ~

530 T S 600'R O B .5 and O/F> . 5 A H = 2605 Btd lb

2N 2 4 0 +4N 2 4 H 3 2N20+NO+ 2$N2+2HZO+NH4NO3+4H2

600 .< T s l O , O O O * R O B +: . S and O/F> a 5

N2O4f2N2H4 + 3N2+4H20

AH = 4860 Btu/lb

' T 1 O e T s T1l

E = 7500 cal/gmole

set of reaction products) la

TI T 5 T2

Set of reaction products for

complete reaction

A Hcornplete reaction (Eact) , (Frequency Factor) 10

T < T S T 3 2

(Eact)2b, (Frequency Factor) 2b

where, T = gas temperature,

S = stoichiometric oxidizer to fuel ratio Figure 18, Temperature and O/F Dependent Reaction Paths

Measured by Zung (Ref. 3)

36

2 0 I- < I- 2 w 0 z 0 0 v) v)

E

0 z

- a

a

d= cu

0.8

0 .7

0.6

0 . 5

0.4

0.3

0 . 2

Re =29 OXIDIZER TEMPERATURE 2i 310°K. BURNER PRESSURE= I atm.

c] IGNITION o NOIGNITION

b

"0 0 0

7 I I * I b I I

2.5 3.0 3.5 I ITOKX 10-3

I I

375°K 350°K 325°K 300'K 275*K

O K

"R 700"R 650"R . 600"R 550°R 5OO"R

. HYDRAZINETEMPERATURE Figure 19 . Ignition Threshold

(From Ref. 3)

37

2000

1800

1600

f I I

- TOX Sample Time Symbol

0 500 OR 1. Oms Open 0 540 OR 2. Oms Half Shaded A 580 OR 3 . 0c.s Shaded

-

Simultaneous Injection -

1200

1000

400 0

38

15oc PEAK PRESSURE

20c

---3L .I.*.--

/ 1 I I

0 4 IO 2 0 FUEL LEAOTWE- OXIDIZER LEAD TfME-

MILL I SLCONOS MILL IS EC OND S

Figure 21. Pressure Peak a s a Function of Oxidizer or Fuel Lead. (From Ref, 19,)

39

cu cu G =I

40

0.8

0.7

v) v)

I 0.4 d- cu 0 z

0.3

3 0 3 O K .[ OX ID1 ZER R e 2 39

BURNER PRESSURE: I atm. * . TEMPERATURE)

0 IGNITION o NO IGNITION

TEMPERATURE)

3.0 3.5 I / T O K X 10-3

I I

375'K 35Q'K 325°K 300°K 275'K

7Q0°R 650"R . 600"R O R

. HYDRAZINE TEMPERATURE

' Figure23 . Ignition Threshold

, +

(From Ref. 3)

500°R

4 .

2000

1800

1600

1400

1200

1000

800

so0

400

200 (Note: Time is M e a s u r e d From Instant Both Propellants are Flawing)

0 1.0 2.0 3 . 0

Time, t, 1Iw

Figure 2 4 . Effect of Propellant Leads and lnithl Temperature Cm ]etaMtion -8-

42

4. EXPERIMENTAL PROGRAM

Experiments were performed wherein engineering assumptions and engine parameters influencing spiking could be evaluated in &der t o determine the applicability of the Start Transient Program& (the Propellant Transient Flow Program and the Chamber Pressurizatibn Transient Program) to predict engine starts.

'

" 1

Hardware and Experimental From the Start Transient Programs, the following variables were important

in influencing the start transient and the start transient spiking behavior: (1) propellant temperature , (2) propellant leads , and (3) the transient behavior of the entering propellants (length and shape of propellant transient). In an attempt to accommodate these assumptions in the experimental hardware, two injectors were fabricated. The first injector (Figure 25), In jF tor Pattern A

(like-on-like) attempts to accommodate the assumption of vapor phase mixing. Pattern A consists of four like-on-like doublet elements which impinge such that the fuel and oxidizer fans do not intersect (Figure 26). This injector .

keeps the liquid propellants apart while they are being injected and vaporiz- ing, but allow mixing of the propellant vapors. Injector Pattern B (unlike), on the other hand, consists of four mixed twin elements. This injector pattern is used in current high-performance attitude control engines. The effects on ,the start transient of these two injectors were observed experimentally. These patterns were drilled into a propellant manifold configuration which is t h e same for both patterns (Fig. 27) Completing the injector-manifold is a cover plate (Fig. 28) which incorporates the instrumentation for the fuel side and which forms the cover for the fuel and temperature conditioning fluid manifolds (Fig. 29). The central oxidieer'inlet and manifold is connected to an AN cross into which is plumbed the main propellant valve, the Freon flush valve , the-gaseous nitrogen purge valve, and the oxidizer manifold pressure port. The fuel enters the backing plate through two inlets which are similarly connected t o an AN cross via two 1/8 inch tubes. The fuel cross is plumbed to the main propellant valve, the gaseous nitrogen purge valve, and the Freon flush valve. During the initial tests, the manifold vo1ume.s consisted of the crosses , t h e connecting tubing, and the injector body. These volumes were .232 in3 and .252 in3 for the oxidizer and the fuel manifolds, respectively.

i

8 1

43

44

Pattern A

Pittern B

Figure 2 6 .. Propellant Spray Patterns from Experimental Injectors,

4 6

47

Figure 29. Exploded View of Combustion Chamber arid Injector Assembly .

48

These volumes were subsequently reduced by solder filling some of the manifqlds. The final tests were conducted wit anifolds having volumes Gf . lo37 in3 for the oxidizer and fuel manifolds, respectively.

* .

Completing the experimental hhrdware are the combustion cha the nozzle (Figs. 28 and 29) . Thi rdware was designed to operate under those condltions listed in Table N. The experimental work was done with a chamber length of 1.75 in. The chamber had two high response pressure transducer ports, a chamber wall thermocouple port and two fluid flow lines leading to the temperature conditioning jacket surrounding the chamber. The assembled components are seen in Figure 30.

+ <

During the initial t e s t s , the main propellant valves used were solenoid valves {Echel Valve AF' 56C-35). Subsequent tests utilized a pneumatically controlled pintle valve. This valve consists of a pneumatic cylinder with the plunger attached to a yoke which, in turn, lifts the tapered pintles, The valve opening time can be controlled by varying the orifice opening and supply pressure to the pneumatic cylinder. Propellant leads can be varied by adjust- $ng each pintle a t the yoke.

The experimental engine was fired downward into an eight cubic foot vacuum tank (Figs. 3 1 and 32). Between each test, the injector manifolds combustion Chamber and vacuum tank were purged with Freon and gageous nitrogen.

The combustion chamber and the propellants were temperature conditioned by circulating heated or cooled water through jackets surrounding the combus- tiQn chamber, the propellant lines , and the injector. High response , flush mounted piezeoelectric pressure transducers (Endevco Model 2 501 Pressure Transducers) provided the hlg 11 response pressure data for the tests. Endevco Model 2 5 0 1 ~ 5 0 0 (0-500 psia pressure range) pressure transducers were used to measure propellant manifold pressures . These transducers were connected to Endevco Model 2808 charge amplifiers with the amplified signal being recorded on a CEC oscillograph using a 7-361 model galvanometer. Chamber pressure was measured by an Endevco Model 2501-200 (0-2000 psia pressure range) pressure transducer with an Endevco Model 2811 charge amplifier and wag recorded on a CEC oscilloscope using a sweep rate of .5p sec/cm and a 7-3 6 1 model galvanometer , and paralleled onto a Tektronix type 535A oscilloscope.

49

TABLE IV EXPE RIMEN TAL OPE RATING CQNDI TIQN S

Oxidizer: Nitrogen Tetroxide, N 2 0 4

Steady State Flow Rate: Wox = .080 lb/sec

Fuel; Hydrazine, N2H4

Steady State Flow Rate: Wf = .067 lb/sec

Mixture Ratio: 1 . 2 (equal stream momentum for equal fuel and oxidigqr orifices)

Steady State Chamber Pressure: 100 psia

Nozzle Throat Diameter: .SO3 in. (Nozzle ThrOat Area: , 2 6 6 in')

Nozzle Area Ratio: 40

Thrust: 50 lbf

Ma nif old Vol um es Oxidizer: 172 in' Fuel: . lo37 in3

50

W e a

a l a z 0 I- u w v)

-

--: ? I- e

v) W 0

-I

e

a n

p' >- o- e

L, Q) Q E a c 0

A. Assembled Experimental Hardware

€3. Experimental Test Stand

Figure a t . Experimental Setup

52

Propellant Temperature Conditioning System

2

Vacuum Tank

+ Vacuum Pump

Figure 32. Experimental Test Stand.

53

Several lower range Taber pressure transducers were used to measure the lower preignition chamber pressure. The signal from the transducer was fed to a Dana amplifier and then recorded on a CEC oscillograph using a 7-346 model galvanometer.

The pressure in the vacuum tank was measured by a General Electric Thermistor Vacuum Gage (Recorder Model 22GC3 10, Vacuum Gage Tube 22GT). Propellant injection temperatures and chamber wall temperatures are measured with Iron-Constantin thermocouples which are recorded on a CEC oscillograph using a 7-349 model galvanometer. The fuel injection thermocouple was located in the injector fuel manifold opposite the injection pressure transducer port. The oxidizer injection thermocouple was located in the AN cross opposite the injection pressure transducer port.

Results Table V shows test conditions and pressures resulting from the experimental

program. The injector used to obtain the data was a like-on-like doublet which most closely simulated the conditions portrayed in the chamber pressurization model. The propellant temperatures were: 540°R (nominal), 580°R, and 5OO0R; the propellant valve openings were varied from 5 m s to 40 m s and the propellant leads were varied. The propellant lead conditions were determined from the t i m e difference between the first noticeable increase in chamber pressure and ignigion and, therefore, includes any ignition delay. The valve opening was measured by a linear potentiometer which coupled to the valve s t e m opening. Propellant temperatures were measured by thermocouples located in the injector manifold

It was found that fuel lead conditions produced highest pressures with cold propellant temperatures (500 to 530OR). The results of this test program demonstrate the influence of fuel leads in the production of detonatable inter- mediates. Low fuel temperature gave consistent spiking, and long fuel leads at even relatively higher fuel temperatures (175OF) a l so lead to spiking. Although relatively little t ime and funding was available for these experiments, the results demonstrate the importance of preignition chemistry and condensed phase reactions of the hydrazine droplet surface. These reactions can be followed with vapor- izing fuel droplets (long fuel leads even at higher temperatures) to analytically determine worst or unacceptable start sequences. The effect of propellant leads are seen where the fuel leads produced ignition spikes while the oxidizer lead conditions at low temperature produced none. Lengthening the valve opening t i m e of the fuel system did not significantly reduce or eliminate the spiking tendency which exists at this condition.

54

TABLE V EXPERIMENTAL RES VLTS

Date T e s t

(6/2 7) 8 9

3 4

(7/2 1 6 7 8

11

1 3 4 5 6 7 8

1 2 13 14 15 16 17 18

(7/1)

(7/3)

P r o p e l l a n t L e a d s ox Fuel

, (msJ (ms)

25 10

21.9 26.6

3-8 7.6

12.1 13.1

7.6 6.2

22.5 10.0 8.3

8.8 34.2 15.5

19.6 19.3 21.8 17.1

9.1 3.8

Valve Opening Time ox Fuel 0 (msr

4.8 4.8 6.0 6.0

17.0 17 .O

21.0 21 .o

12.9 12.9 18.3 28.3 9.0 9.0

43.9 43.9

15.7 15.7 13,2 13 ;2 43.9 16.0 38.2 13.7 31.2 9.2 21.2 12.2 37.4 10.2 44.0 19.5 12.9 39.7 12.4 34.6 13.35 39.9 13.3 36.2 12.6 12.6 13.75 27.2

T e m p e r a t u r e eR) Ox Fuel Wall

540 540 540 540 540 540

540 540 540 546 540 540

540 540 540 ,

540 540 540 540 540 540 540 540 540

540 540 540’ 540 540 540 540 540 540 530 500 540 520 500 540 520 500 540 560 590 540 570 630 540 570 640 540 570 630 540 570 640 540 570 640 540 530 510 540 530 500 540

N o 2900

No NO

I No N o NO N o

N o No N o N o N o Y e s N o N o Yes Yes N o NO 3000 3500

5 5

5 . CONCLUSIONS

A computer program has been written t o describe rocket engine ignition transients. This program is useful in order of magnitude studies t o determine what is influencing t i m e delays and subsequent ISP pulse shape, and, also , the details of chemistry and O k ratios which control the smoothness of ignition and spiking; f inal ly , a short experimental firing program also performed t o demonstrate the predicted trends

The influence of design and operating variables upon what is going on as the engine starts can be evaluated by a computer program which essentially consists of an accounting system of enthalpy and mass balances with arbitrary propellant input. The propellant input may be calculated from a compatible flow program which essentially consists of a lump parameter analog model of the input hardware influences which affect the input flow. These programs, listed in the Appendix, thus describe flow, vaporization , chemistry, ignition, and/or detonation strength. Hardware parameter can be evaluated by one run after another with changing such things as chamber volume, heat capacity, injection velocity , etc .

.

Conclusions

The program is useful in evaluation of such things as an order of magnitude study of what design or physical processes are controlling ignition delay. For example, injected drop s ize or vaporization surface area are not particularly important, because the start is controlled by an enthalpy balance for which the engine starts when the accumulated enthalpy overcomes the engine's heat capacity. Such simplifications can be graphically demonstrated by various size engines, and often the start problem can be reduced t o one of propellant flow and a known t ime delay for enthalpy accumulation. The program is also useful in evaluating the extremes of O k ratio which can be encountered with hardware fuel or oxidizer leads. These calculations can often be used t o interpret the relevance of purely chemical observations.

Chemical observations have shown that condensed phase fuel often reacts without ignition, but with the formation of detonation-sensitive intermediates. This fact was predicted by the computer program and was observed experimentally. Cold fuel gave rise t o severe spiking and, a l so relatively warm fuel, even above 12SoF, showed a tendency to spiking with long fuel leads in vacuum environment.

5 6

6 REFERENCES

1. Bell Aerosystems: Agena Vacuum Start Improvement Program, (1965)

2 .

3.

4.

5.

6.

7.

8.

9.

10.

11.

1 2

13.

.Knox, R.M.; Minton, S, J.; and Zwkk, E.B.: $pace Ignition. Paper presented a t AIAA 2nd Propulsion'Jt . -Spec. Corif. (Colorado Springs , Colo .) (1966).

Zung, L.B.; Breen, B.P.; and Kushida, R.: A Basic Study of Ignition of Hypergolic Liquid Propellants. Western States Section/The Combus tion Institute Paper No. 68-43 (Oct. 1968).

Perlee , Henry E . and Christos , Theodore: Summary of Hypergolic Ignition Spike Phenomena. U. S. Dept. of the Interior, Bureau of Mines, Final Report No. 3982, April 8 to December 31, 1965.

Dauerman, L.; Ray, A.B , ; Koehler, G.; and Salser, G. ..': Evidence for the Formation of Azides in the N2H4/N204 Reaction. AIAA Journal (Nov. 1968), p. 2186.

Seamans, T.F. and Waser, P.C.; Effects of Additives on Ignition Delay and Chamber Pressurization of Space-Ambient Engines. Tech. Rept. AFRPL-TR-69-68, July 1969.

1 ,

Agosta, Vito D.; and Graus , Geo.: An Investigation of the Impulse Bi t Developed by a Pulsed Liquid Propellant Rocket Engine. Cu.rtiss-Wright Corp. (1964).

Seamans, T.F. and Dawson, B.E.: Hypergolic Ignition a t Reduced Pressures. Air Force Tech. Rept. AFRPL-TR-67-175 , (1 9 67).

Stevens, M.R.; Fisher, H.D.; Weiss , H.G.; and Breen, B.P.: Effect of Additives on the Ignition Delay Time of Hypergolic Propellants Western States/The Combustion Institute Paper No. 67-22, (April 1967).

Weiss , H. G. : A Basic Study of the Nitrogen Tetroxide/Hydrazine Reaction. Western States Section/The Combustion Institute Paper No. 65-20 ,

(Oct. 1965.)

Streeter V.L. and Wylie, E . B. : Hydraulic Transients , McGraw-Hill, New York, C 1967.

Clayton, R.M. and Rupe, J. H.: An Experimental Correlation of the Nonreactive Properties of Injection Schemes and Combustion Effects in a Liquid in a Liquid-Propellant Rocket Engine , Part VI The Relation Between the Starting Transient and Injection Hydraulics. Jet Propulsion Laboratory, Tech. Rept, No. 32-255, 29 October 1965.

Aerospace Fluid Component Designer's Handbook , Glen W. Howell, ed. Tech.Documentary Rept. No. RPL-TDR-64-25, May 1964, prepared by TRW Space Technology Laboratories under contract AF04(611)-8385 for the Air Force Rocket Propulsion Laboratory, Research and Technology Division , Edwards , California AD 447995 , pgs 3.16-1 to 3.16-3.

57

14. Campbell, Donald P. SC. D. Process Dynamics , John Wiley & Sons,Inc. London, C 1968, pgS 75-82. ' '

15 Vennard, John K. : Elementary Fluid Mechanics , John Wiley & Sons , Inc, New York, C 1965.

16. Nadig, E. W.; Tkachenko, E,A.;, Breen, B.P.: $tudy of Random Wave Phenomena in Hypergolic Propellant Combustion. Interim Report SN-87 , NASA Contract NAS7-467, Dynamic Science, 1967.

1 7 . Mills, Ignition. Interim Rept. Contract NAS7-467, Dynamic Science, April 30, 1969.

T. D.; Breen, B. P . , et al; Transients Influencing Rocket Engine

18. Propulsion Applications Group, Research Dept, Rocketdyme: Program for the Development of Design Criteria for Eliminating Attitude Control Engine Pressure Spiking Through the Use of Catalysts. No. R-6380P, November 1965.

19. Minton, S. J.; and Swick, E. B.: Hypergolic Combustion Initiated a t Low Pressure , Paper presented a t the Aviation Space Conference of the American Society of Mechanical Engineers, Los Angeles, Calif. March 1965,

58

APPENDIX A USER'S MANUAL

For PROPELLANT TRANSIENT FLOW PROGRAM

This section is divided into the following subsections: 1. Operating Procedures 2 , Description of Program Input 3 . Description of Program Output

1 Operating Procedures

Stapdard FORTRAN 1"V C@MM@N is used for al l input data. ThSs program was developed on the CDC 6400 using FORTRAN IV language.

2 . Description of Program Input

a . Propellant Properties b. Hardware Parameters c. Flow Properties d . Computational Control Information

This program requires the following groups of data.

a . Propellant Properties:

Item Name Input Quantity Units R(d = denqity of propellant a t the 1 b/f I?

temperature considered PVI = vapor pressure of propellant lb/in2 absol.ute

a t the temperature considered XMU = viscosity of the propellant a t 1 b/f t - s ec

the temperature considered GAM = specific heat ratio of the none

vapor propellant

b. Hardware Properties: Item Name Input Quantity Units XL = length of propellant line which f t

XLF length of propellant line over f t

XLMI = length of propellant manifold inches XKL = accumulated pressure loss coefficient none

of system from tank to valve

contains accelerating propellant

which friction ac t s

5 !

DI DO1 XNG~RF VMOI AVO1 TVQ XN

n(1)

AVTI(1)

NT

diameter of propellant line diameter of orifices in injector number of orifices in injector volurric of propellant manifold area of the valve when fu l l open* tinip for valve to open* exponent on valve transient to shape its opening* points in t i m e table used to specify valve transient 5 100"

valve opening areas corresponding to t i m e values TI ~7 100"

number of tabular values used to describe valve opening*

inches inches l?one inches' inches' s B cond s none

seconds

inches'

none

c. FLOW Properties: Item Name> CV co

wss PCSSI

PsSr DPI

TEMP@ X M c T

PAM BI

Units Ipput Quantity discharge coefficient of valve none discharge coefficient for injector orif ices steady s ta te propellant flow rate* lb/sec steady s ta te combustion chamber lb/in2 absolute pressure pressure drop across the injector 1 b/ina overall pressure drop from propellant lb/in2 tank through injector* initial values of volumetric flow rate* ft3/sec Qx(1) = propellant flow out of tank QJ(2) = propel1 t flow out of injector QJ(3) = d/dt f l i ( l ) l QI(4) = d/dt $1(2)1 QI(5) = gas f o out of manifold fP /sec QI(6) = d/dt L- - l ( s ) l temperature of propellants considered* R

molecular weight of propellants* nape (not needed if PAMBI = 0.) initial ambient pressure* lb/in" Tabsolute

*ccc

0

*See computational control information section,

60

d. Computational Control Information: Item Name - Input Quantity Units

. TMAX = maximum computational t i m e seconds ’

TS = starting t i m e for computations , f o seconds HO = initial step size seconds HMIN = minimum step s ize seconds HMAX = maximum step s ize seconds ELR = minimum relative error on integrated none

flow parameters = maximum relative error on integrated none

flow parameters (should be a minimum of 32 t i m e s longer than ELR)

DRP = print suppression index (printout seconds will occur a t every t i m e interval

EUR

D RP)

FLAG = option defining the form of the none flow parameters FLAG = 0. requires that WSS, PCSSI,

and PSSI be input and DPI be undefined .

FLAG = 1.0 requires that DPI be input and WSS, PCSSI, and PSSI be undefined .

FLAGT = option which provides for use of none tabular values of valve areas instead of formula. FLAGT = 1. uses table

XN FLAGT = 0. uses formula

(when FLAGT = 1. option is used, AVOI, TVO, and XN are not needed for input)

AVOI = [time/TVOI

TABLE A-I shows a typical input listing.

3 . Description of Program Output: I tem Name Input Quantity T = t i m e

Units seconds

H = t i m e s tep taken a t t i m e I seconds WI = propellant flow rate from propellant lb/sec

w2 = propellant flow rate from injector lb/sec

= propellant flow rate from propellant ft3/sec Q1

tank

or if ices

tank

propellant flow rate from injector or if i ces the derivative of Q1

t h e derivative of 9 2 thc integral of Q1

the integral of QZ

tho volume of the propellant manifold which is fu l l the volume of the propellant manifold which is empty

the pressure inside the propellant maq ifold the opep area of the valve the amount of gas which has left the propellant manifold if the start occurred in other than vacuum conditions.

f P

1 b/in2- a b s 01 ut e

Et2 lb

the flow rate of gas out of the propellant lb/sec manifold if the start accurred in other than vacuum condition.

TABLE A-I1 shows a typical output using t h e input data from TABLE A-I.

62

TABLE A-I TYPICAL INPUT DATA FOR OXIDIZER FLOW TRANSIENT

63

64

0.3 3 -

d 9 3.3. 0 0 0 3 0 3 a 0.

m .

APPENDIX B

USER'S MANUAL For

CHAMBER PRESSURIZATION TRANSIENT PROGRAM

This section deals with the u s e of the program and is divided into the following subsections :

1. Operating Procedures 2 . Description of Program Input 3 . Description of Program Output

1. Operating Procedures

Standard FORTRAN IV C@MM@N is used for a l l input data. This program was developed on the CDC 6400 using FORTRAN IV language.

2 . Description of Program Input a . Propellant Properties b. Chemical Reaction Parameters c. Transport Properties d Hardware Properties e. Computational Control Information

a . Propellant Properties:

Item Name Input Quantity Units R@N(l I 1) = table of oxidizer density 1 b/f t3

(up to 1 0 values may be used)

to oxidizer density RGN(1 I 1) (up to 10 values may be used)

R@N(1,2) = table of fuel density 1 b/f t3 (up to 1 0 values may be used)

TRaN(1 I 2) = table of temperatures corresponding to fuel density R@N(l12) (up to 10 values may be used)

WQlRQl = number of values used to define none density table used

CPN(1 , I ) = table of specific heat a t constant Btu/lbol% pressure of liquid oxidizer (up to 10 values may be used)

TR@N(1 I 1) = table of temperatures corresponding OR

R 0

65

TCPN(1,l) =

CPN(l,2) =

TCPN(1,Z) =

NaCP E

CPGN(1,l) =

TCPGN(1 1) =

CPGN(1,Z) =

TCPG(1,Z) =

- CPGP c

PVN(1,l) =

TPVN(1,l) =

PVN(1,2) =

TPVN(1,Z) =

table of tempera tures, corresponding to liquid oxidizer specific heat (up to 10 values may be used) table of specific heat a t constant pressure of liquid fue l (up to 10 values may be used) table of temperatures corresponding to liquid fue l specific heat (up to 10 values may be used) number of values used to define liquid propellant specific heat table table of specific heat a t constant pressure of vapor oxidizer (up to 10 values may be used) table of temperatures corresponding to oxidizer vapoe specific heat a t constant pressure(up to 10 values may be used) table of specific heat a t constant pressure of vapor f u e l (up to 10 values rnay be used) -

table of temperatures corre sponding to fuel vapor specific heat a t constant pressure (up to 1 0 values may be used) number of values used to define vapor propellant specific heat table specific heat of vapor product table of vapor pressyre for oxidizer (up to 10 values rnay be used) table of tempera tures corresponding to oxidizer vapor pressure (up to 10 values may be used) table of vapor pressure for fuel (up to 10 values may be used) table of temperatures corresponding to fuel vapor pressure (up to 10 values may be used) number of values used to describe vapor pressure tables specific heat ratio of vapor oxidizer and vapor fuel specific heat ratio of vapor products

R 0

Bt u/l bQR

QR

none

Bt u/l boR

Btu/lboR

"R

none

lb/fta

OR

none

none

none

66

viscosity of oxidizer vapor and fuel vapor thermal conductivity of oxidizer vapor and fuel vapor molecular weight of oxidizer and fuel molecular weight of vapor products heat of vaporization for oxidizer and fue l heat of fusion for oxidizer and fuel heat of sublimation for oxidizer and f u e l freezing temperature of oxidizer and fuel vapor pressure of oxidizer and fuel evaluated a t the chamber wall temperature initial vapor temperatures of the oxidizer and the f u e l initial partial pressure in the chamber due to oxidizer vapor, and fue l vapor

b. Chemical Reaction Parameters: ItemName - CFQIRPR = R M - -

Input Quantity

1 b/f t - s e c:

Q Btu/f t -seC R

none

none Btu/lb

Bt ullb Btu/l b

OR

lb/ina

OR

1 b,ha

Units - stoichiometric oxidizer to fuel ratio none experimentally determined exponent none for fue l concentration in reaction rate equation expe rimenta 11 y de term ined exponent for . oxidizer concentration in ~

reaction rate equation activation energy for each preignition reaction path Arrhenius reaction rate constant for each preignition reaction path relative formula weights of species in balanced preignition reactions for oxidizer rich reactions relative formula weights of species in balanced preignition reactions for fuel rich reactions I corresponds to reaction paths within the temperature range TTAPLE (I) and TTABLE (I+l). Maximum I is NN

none

ft/lb/mole

cc/mole-sac

6

TTABLE(~) =

YREACT(~ , I)=

YREACT(~ 2)=

C@NCR G

- TCR -

- HEA'IX - HFLIQ(1) =

J corresponds to specified species in balanced reaction. Maximum J is 1 2 , where J=1 is reactant species on which the enthalpy of reaction i s based, J=2 species is second reactant species. Al l other species are unspecified. table of temperatures which define reaction paths (must be NN+1 values) enthalpy of reaction for fue l rich reactions enthalpy of reaction for oxidizer rich reactions critical oxidizer vapor concentration none below which liquid fuel and oxidizer vapor reaction takes place (concen- tration of oxidizer vapor/concentration of all vapors) critical temperature below which liquid fue l and oxidizer vapor reaction takes place heat of reaction for liquid fue l - oxidizer vapor reaction heat of formation of liquid oxidizer and fue l

QR

Btu/lb

Btu/lb

Bt u/l b

calories/mole

c. Transport Properties:

VDRGP (1 ) ALPHA

RGI (1)

Input Quantity

heat transfer coefficient between oxidizer vapors and wall when Tw > and wall when Tw gaseous products and wall when Tw > Tg

Tg, between oxidizer vapors Tg, apd between

heat transfer coefficient between Btu/fP - s ~ c O R fuel vapors and wall when Tw>Tg, between fuel vapors and wall when ' IWC Tg, and between gaseous products and wall when Tw < Tg

velocity of oxidizer and fuel drops accommodation coefficient (fraction nor18 of vapor that impinges on chamber wall and remains a s condensate) initial radius of oxidizer and fuel droplet

ft/see

f t

68

WLIQ(1,l) =

NLIQ(1) =

WLIQ(1,2) =

PGADDT(1 I 1 )=

PGADDT(1 , 2)-

table of transient propellant flow rates of first entering species (up to 25 values may be used) t i m e table corresponding to values of WLIQ(1,l) (up to 25 values may be used) number of entries in WLIQ(1,l) table table of transient propellant flow rates of second entering species (up to 25 values may be used) t i m e table corresponding to values of WLIQ(1,Z) (up to 25 values may be used) numbeq of entries in WLIQ(1,Z) table table of t i m e variable backpressures affecting the oxidizer transient pressure (up to 10 values may be used) time table corresponding to values of PGADD(~ I 1) (up to 10- values may be used) table of t i m e varlable backpressures affecting the fuel transient pressure (up to 10 vQlues may be used) t i m e table corresponding to values of PGADD(1,Z) (up to 1 0 values may be used) initialized flow rate of oxidizer and fue l (small number needed to start program)

.

d , Hardware Properties:

Item Name Input Quantity

AC = c ombustion chamber internal surface

VC = combustion chamber volume w = combustion chamber wall temperature ASTAR = chamber nozzle throat area

area

lb/sec

sec

none

lb/sec

sec

none

lb/ina -absolute

sea

lb/ina-absolute

sec

1 b/s ec

Units - fP

ft" OR

fta

69

e. Computational Control Information:

Item Name

NN

TMAX DELTN ND1

ND2

ND3

IUNIT

MSPEC

IFPLQIT

PLTIME

IDEBUG

T D E T @ N ( ~ ) =

TCRIT(I) =

R C R I T ( ~ ) =

XCRIT(1) =

Input Quantity

number of preignition paths used (up to 10 paths may be specified) starting t i m e in terms of number of calculations for oxidizer and fuel maximum running t i m e initial step s ize first integration step to be selected for print last integration step to be Selected for print print every ND3rd step between ND1 and ND2 unit on which punched output will be written number of chemical species (must be 10) option for plot routine IFPL@T=I will plot

real t i m e for plot generation such that job does not run to maximum t i m e plots are generated provides intermediate output when IDEBUG=T or . TRUE. specifies t i m e a t which detonation calculations are to be performed (up to 40 values may be specified) normalized averaging criteria based on stored droplet temperature for oxidizer and fuel normalized averaging criteria based on stored droplet radius for oxidizer and fuel normalized averaging criteria based on stored droplets' percent frozen for oxidizer and fue l

Units

none -

none

sec sec none

none

naaa

real sw

none

sec

none

n w e

none

A typical input listing is shown in Table B-I

70

3 . Description of Program Output

Item Name Output Quantity

P G T ~ T A L

TFI NAL

TAVERG

TG

TQP

WT@TAL REACT

t i m e ratio of liquid propellant species to total propellant (liquid and gaseous) species mass of propellant evaporated mass of propellant condensed partial pressure due to oxidizer partial pressure due to fue l vapors partial pressure of gaseous reaction products total pressure due to oxidizer, f u e l , and product vapors temperature of gaseous chemical species in chamber after reaction temperature of gaseous chemical species in chamber before reaction temperature of vapors in chamber (when only one propellant is flowed) temperature of gaseous products amount of material which has reacted total accumulated propellant flow

Table B-TI shows typical output from this program.

Units

m ill i 8 econd s none

-

l b l b lb/in’-absolute lb/inz -absolute lb/inz=absolute

lb/ina-a bsol ut e

OR

R 0

OR

OR

lb lb

71

s PI 5 0

72

I F4

I

h

m I a

w c-l m 5

I M

I

n a Q) =I c: .r( c,

u

m

Y

I 4 1

w I 4

c 0 3 + w m 3 0

e 0 fa + 4 in .i 3

D 3 3 + w m 0 ,

.3

m 3 3 + AI> In 3 or

m 3 3 + &I n 3

m 3. 3 + *&I ;n

3 0

n

V8

3 t l

> 3 z n

41

t a a

74

=& I

* U

I P 4- N 9

4

.c

h

W

z c h'

11 n 11

7 7 0 0 + +

N *I)*

II I1 I t It

75

z W n

II

2 3 3:

a

I

?

n

% 1 E: 3

n; 'I N

o. a c W! Y *rl

1i

* (u *a I rl

0 3

c N 0 I

W N

0 r;$

11

c Y a a 0 ,

e

0 ' 3

0

c 9

3 0

m 3 0 3

* 0 3

3

L 3

3 0

c 7

3 0

m e 3 3

m o a 3

m m 3 3 0 . 0 3 a

I? a

3 3 4 s3 I;. a

77

I h I

78

II

3

.J 3

H

11

3 c - l . -J

. i - 1

e -

0 0 cum E Z

N aN r r

80

C

C

C

15

I 6

C C

21

2 C

C 1fi

3

C

CALL QUXSUC LEO CALL PRINT 11)

81

a2

81

84

81

SlJBROUf INE PRINT ( L ) c

C C

X F ( L c N E o 0 ) GO TO 1 C

960

1

3

963 9r! 91

C

PNEXTPTI~.*URP W R I T E ( 6 9 9 0 0 1 FORMAT ( 1 H l ,40Xg23HTRANSIENT FLCW ANALYSIS*//

1 9 0 T W l Q l 2 I Q l VMF PVV 3 9 9 H w2 Q2 4 IQ2 VME A V

CONT JNUE I F ( T e L T . PNEXT) RETURN PNEXTxP&EXT+DRP L=L*1 00 2 I " 1 9 2 w (1 ) =Q ( I 1 U R O PVVI=PVV/144,

RETURN ENR

86

OUOUU:!

000117 OdG121 000145 000172 O i ) O l ? i !

.

8

000345 000346 OUQ3SO Q$r)3S2

8!

0 0 0 6 5 1 0 ~ 0 6 6 0 000S63 OUO665 0 0 0 7 0 1 0 3 0 7 u 2 000711 O b 0 7 1 1 ouo71s OUci725 000731 000734 000740 O O Q 7 5 U Ob0 156 a00762 000765 000772 000773 uou775

o # l o r o

001066 001077 ObllO'IS

001122 001122

01126 00 1126

001131 001142 001152 061162 001177 461177 Ob1202 OP)li?d7

001214 001214 ob1214

91

01)1220 001223 001226 031226 001230 001236 001243 00124j 001247 001251 OU1253 031254 001260 001262 Ott1276 001277 001301

001321 ou1322 001336 ou1337 001341

OUi361 001362 001367 001371 001373 001314 0[314(12 001411 001414 001417 001423

001427 001430

oo14aS

001430 001433 001444 0111447 001453 001461 001463

001473 o o i 4 7 i

001521

001522 001526 01)1541 001541 OOlS4S 001557

92

091623

(101641 o w 6 4 2 001651 0~1054 OUlb54

OU1657 001666 (101 I O 3 80170.3 U U l l O ?

001711 001713 001717 0 0 17 2 1 001723 001732 0 0 1 7 3 5 001735

001735 001737 601746 001747 Qd1147 001751 001752 Oil1754 Ob1766q 091764 001766 002010 002012 Ob2015 OilZUl.6 002040 002042 602045 0 0 2 0 4 0

002074

93

0021 17

002121 002124 002126 002130

002132 002136 002144 0132244

002144

002213 002215 OU2216 002222 092224

002226

002230 . 002233

002234

4

OU2LS2 C C C

832260 002263

C

9246

G C C

OU231C1 002312

c , c c c

OU22314 502317 002322 03Z32t4

002327 002331

925s C C C

C C G

002335

002342 002346 062351 OI)ZJS4 oil2354 Olp2356 OD2347 002370 0 ti! 3 7 Z 002374 002376 002377

95

002403 00140 I

0\)2*33 002434 00243s 002436 U1)244Z 0d2454 002457 00246ti 002.465 0024b7 OU25UO Oi125U4 062506 OUd.5513 032523 002S25 OdZS2 7 Od2S31 002534 002542 OOL540 002551 932553 002562 002571 002600 002602 002605 GO2605 #02b12 002612 002613 002621 002634

. 002635 032636 002637 00264 1 002644 OIiL646

002666

002671 OQ2674

0 ir 0 4)U2705

96

1110

1120

1130

1135

1140

C

C C C C

4341

l l S 0 C

TEST FOH PUNCH DATA FOR UETON~TLON CALC

I F ~ T I ~ E o L T * T D E T O ~ ~ I U E l ~ ~ ) ) '90 TO 4341

fF(IUETONaLTe40) TON = IDETON + 1 CALL OUTX

CONTINUE

CONTINUE

97

C

C

C

C

c

5 c

C

C

C

c

c c

98

99

100

030044 000047

0 0 0 0 I 2

o i l 0 0 7 7

000102

000244 000251 000251 000271 0 0 0 2 t l 000311 000311 000331

14 C C C

176

2bil c C

9 G O C C C c

191 430

192 C C C

193 C

C C C

194

195

196

197

COi"1UTk RELaT I V E wt;IGHTS

vJHITE HEACTANT CARDS'

TI T F I i v A L / 108 P I = PcjToTAL

102

103

oil11020

cruoozu

ouao2c)

104

105

996 IPLl 'I = 0

EbJ\ri) HETURN

#OECK,SCAC

106

107

C 0 9 0 3 3 3

C C c C f, c C C c C C C

000013 C

000\)32 ou0044 000044 000045 oouosz 0 0 0 0 5 4 000057 000061

O O U O 6 3 OUO(163 OU0065 000066 O ~ o d ? o

C c C

C

C C c

1 0

C C C

I uli

20 C C C

SUdQOUTlNIE TAbGEN ( I F L A a r L T A e L € , X T U e c Y T A W , L 4 ~ ~ ~ ~ X ~ Y c I E R R O W )

DIMENSICrlv X T A t ) ( l ) r Y T A 8 ( 1 )

i f L a t i uI~NUTES THE TYPE OF €NTRY TO T M i S SUBROUTINEo ( 3 TYPES)

,

IFLAG = -1 F I R S T ENTHY FOR A PARTlCULAFZ TABLE IFLaG = u NOHMAC ENTRY (NE1THk.H F I R S T NOR LAST ENTRY) 1FLub = + 1 LAST ENTRY TO THE SUBROUTINE FOR T H I S TAQLE

THE A W V E OPTIONS ALLOW THE ASSURANCE THAT THE F I R S T AND LAST EVENTS & I L L ALWAYS BE TAQULATEO I N THtj FINAL f A Q & , E o

IF THIS IS TtiE FIMST ENTRY TO T H I S SUBF4QUl'IMEr MUST INITIALIZE FLAGS AIVU V A M I A ~ L E S ~

I F ( I . P L A G . N E ~ ~ ~ ) GO T O 10

IV = u LUSEU = 0 IENTER = 0 I X M O O 1 IFVENT = 0 1 E V P ' i l = ir I E V L S T r: o

08

3 I) c C C

35

4l) 999

' 109

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115