# Nasa tech briefs ksk 11495, simplified model of duct flow

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### Transcript of Nasa tech briefs ksk 11495, simplified model of duct flow

John F. Kennedy Space Center Kennedy Space Center, Florida 32899

Technical Support Package

Simplified Model of Duct Flow

NASA Tech Briefs KSC-11495

NI\S/\

National Aeronautics and SpaceAdministration

Technical Support Package

For

SIMPLIFIED MODEL OF DUCT FLOW

KSC-11495

NASA Tech Briefs

The information in this Technical Support Package comprises the

documentation referenced in KSC-11495 of NASA Tech Briefs. It is

provided under the Technology utilization Program of the National

Aeronautics and Space Administration to make available the results

of aerospace-related developments considered to have wider

technological, scientific, or commercial applications.

Additional information regarding research and technology in this

general area may be found in Scientific and Technical Aerospace

Reports (STAR) which is a comprehensive abstracting and indexing

journal covering worldwide report literature on the science and

technology of space and aeronautics. STAR is available to the

public on subscription from the Superintendent of Documents, U.S.

Government Printing Office, Washington, D.C. 20402.

NOTICE: This document was prepared under the sponsorship of the National Aeronautics and Space Administration. Neither the United States Government nor any person acting on behalf of the united States Government assumes any liability resulting from the use of the information contained in this document or warrants that such use will be free from privately owned rights.

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SIMPLIFIED MODEL OF DUCT FLOW

INTRODUCTION

Analysis of the safety of hydrogen disposal in the Space Shuttle Main Engine exhaust duet at Vandenberg was made difficult by the complexity of the transient fluid flow through the duct at critical times. Finite element analysis gave information on overall trends and on local flow, but did not match test data very well, and was much too expensive to u~e for adjusting input to match data.

A simple one-dimensional program was developed, using a perturbation of duct exit area to account for duct friction loss, which could be used to iterate aspiration until inlet and exit momentum are balanced. The transient flow can then be calculated as a perturbation of the quasi-steady (equilibrium) flow computed by iteration. Only after the total transient airflow through the duct is known, can local conditions for combustion or explosion be evaluated.

'-\ DESCRIPTION ~ ~ A description of the analysis and listings of the computer programs is given in ~, MCR-81-536, No. 084859, Vol. 1, 1/1-Scale VLS Duct Steam Inerting System, Phase III ~ Tests, Appendix C, which is attached. Also attached is a copy of Section 1.5 - Task V

{ Duct Transient Tests, from the same report, which~hows the application of this ~ analysis to the actual problem. ~ The first novel feature of this analysis is the inclusion of duct friction loss in

an effective duct exit arca, so that the inviscid conservation of inlet momentum can .~ be used to make the solution iteration very simple. The second novel feature is

~ relating the transient duct velocity to the quasi-steady state (equilibrium) velocity ~ with'a simple differential equation. This separation of transient and equilibrium ~ velocity enormously simplifies the converg~nce problem.

~\ However, the most important aspect of this work is to again demonstrate that the \J~simplest analysis that captures the important features of a problem is the best

analysis.

,APPLICATIONS This technique is applicable to any situation in which the knowledge of the

transient behavior of average fluid parameters is important, and for situations in which finite element analysis is impractical beca~se of time or cost.

The same technique c.an be extended to any' situation in which 'the average properties of a solution to sets of partial differential equations is required, and in which finite difference solutions ar~ impractical. In practice, this usually means solutions in at least three dimensions.

KSC-11495

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MCR-87-536, No. 084859, Vol. Duct Stream Inerting System,

1, 1/7-Scale VLS Phase III Tests

APPENDIX C AIR ENTRAINMENT ANALYSIS

The a~entrainmen[ analysis requires establishment of a uasi-stead flowrate driven by the SSME and steam nozzle flows. A momentum balance iterauon between ~t inlet and exit. incorporating the engine and SIS flows and including aerodynamic shock loss of engine momentum, provides the quasi-steady velocities through the operational envelop~_ O~ce the quasi-steady velocities are calculated, ttansient velocities can be calculated_ An iteratIon to match transient velocity is used to determine the total duct airflow. Acceptable results are provided by a conscious effon to keep the analysis as simple as possible, emphasizing fIrst-order effects and one-dimensional flow_ Data from the Martin Marietta In-scale test series suppons the analysis.

The equation for the ll-nnsient duct ,oelocit) can be simply exp,cssed in terms of the equilibrium duct ,,-elocity in the follo\lin

The duct pressure loss coefficien[~ K, is determined using steam-air and helium-air test data. Values of K are selected for the computation of velocities arising from a known system flow and the resulting entrained air flow.

. . dv

V

Scenario: Three Engines at RPL I Engine...-E 160

::5 -4lc::'c;, -... 140 c::::t: w ...~ 0c:: 120 ....

4l at i90 c::

at~ 100 C;;>c::::t: ...

':I 80 0 v .:J :CI); I... lit 60(!I

Shutdown Sequence-No.1, No.2. No.3

Eu.. 139 :;/, Max Detrimental ., o Unburned GH~ Flow Rate E ...- ~~--~--------------------

E u..

, ...... ..........

C(H11bined Detrimental-0 Unburned GH l -1 ............... /all ". w ..~ /

"t2 ........, ..... .....-:-~-....... / ..... ......,

4l

40c:::; /' fQ.., :~>/ ....B .(.:" ', .....'l-.......-J.....- ............... ..... .......... ......

.Q c:: / ._... "" '. .... "filii'" -_. ...... 0 ..... - ,

::l 20 . L Engine 1 Engine 2 Engine 3 ........, '.'0. , Profile Profile Profile ., '. ,0

o 1 2 3 4 6 7 Time. I

Figure C..l. FRF Shutdown Sequence from RPL (Case 2)

Now, suppose the actual exit area is divided by the factor (l+K)1IZ so that the exit velocity is increased by the same factor. The exit dynamic head will be increased by the factor (1 + K) so that the dumping loss with the adjusted ex i ~ area is exacdy equal to the acmal total duct resistance. Thus a simple equality of inlet and exit momenmm can be used to iterate a solution to determine the aspirated air flow. The Manin Marietta steamaair tests are used to evaluate the effective inlet momentum of the steam jets, using the same adjusted exit area and thus accounting for duct friction loss in that evalu~tion.

rilvOUT =(rilAIJI +1i1.m:.w +m".o)vour

Iilvour(l + K.)1IZ =thvlN' where IilvlN' = mvlla0+mvAIII.

with vAlR =0

Once steam momentum is known, the momenmm of propellants at full scale or helium at

In-scale injected through the SSME nozzles can be added. Evaluation of the nozzle flow

momentum entering the duct is uncenain because of the variation in shock train losses as the

-engine chamber pressure drops. A simple, conservative (approximately 6% greater loss than

calculating multiple shocks) procedure is used (Ref 1). The ratio ofentrained air to engine

propellant flow is 6.28 with a shock versus a ratio of 9.72 without the shock. This is consistent

with previous results of 6.0 obtained at MSFC. The nozzle exit flow passes through a single,

normal shock to get[IhC appro:riatc ]IOSS in total pressure,

* (M-2)'''' Pc =Pc

(.!tM2 _!:! }T-.

1+ I 1+1

KSc-11495

-3A

'.

where

and Pc =engine chamber pressure p. = ambient pressure.

The flow is then expanded back to a static pressure equal to ambient to get an adjusted Mach number

M* is a dimensionless velocity ratio (Ref 2)

fonned with the speed of sound at sonic conditions (M = 1) -so that for a given chamber temperature, M* is proportional to velocity. Thus the ratio

is just the effect of shock loss on flow velocity, where

, Since momentum is mass flow times velocity, the M* ratio is also the effect of the shock loss on momentum.

.' Momentum = Momentum x M

M

The components of an energy balance, Figure C-2, are evaluated at static equilibrium at the exit, establishing exit momentum. The In-scale test results limit additional combustion of un burned hydrogen and air to 20% of the air available. Iteration convergence of momentum between inlet

) and outlet is accomplished by adjusting entrained air flow . .'

KSC-11495

-4A

---Hl HlOVapor (:to'

H: Air

------- HlOVapor H20Liquid 183F -..... ---- N, 10% H2 0 Oropou,

Figure C-2. Complex Duct Flow Chemistry which Quickly [nerts Unburned Hydrogen

Once the quasi-steady exit velocity for the abott condition is calculated, the transient air flow and velocity can be determined. The duct loss coefficient dc;tenmnes the aspiration decay rate for the entrained air. The resulting transient velocity curve is used to determine total air flow through the dUCl A duct velocity balance is used to detennine conditions in the duct matching the transient velocity. This calculated transient air flow is compared to the quasi-steady airflow at me time of interest to detennine the air flow ratio. .

Figure e-3 displays validation of the momentum balance-calculation

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