Two approaches to modeling turbofan engine component volume dynamics are explored and compared with a view toward application to real-time simulation of short take-off vertical landing (STOVL) aircraft propulsion systems. The first (and most popular) approach considers only heat and mass balances; the second approach includes a momentum balance and substitutes the heat equation with a complete energy balance. Results for a practical test case are presented and discussed

Drummond, Colin K.

English

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NASA Technical Memorandum 102397
STOVL Propulsion System Volume
Dynamics Approximations
Colin K. Drummond
Lewis Research Center
Cleveland, Ohio
Prepared for the
1989 Winter Annual Meeting
sponsored by the American Society of Mechanical Engineers
San Francisco, California, December 10-15, 1989
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STOVL PROPULSION SYSTEM VOLUME DYNAMICS APPROXIMATIONS
Colin K. Drummond
National Aeronautics and Space Administration
Lewis Research Center
Cleveland, Ohio 44135
ABSTRACT
Two approaches to modeling turbofan engine component volume dynamics are explored
and compared with a view toward application to real-time simulation of short take-off vertical
landing (STOVL) aircraft propulsion systems. The first (and most popular) approach considers
only heat and mass balances; the second approach includes a momentum balance and substitutes
the heat equation with a complete energy balance. Results for a practical test case are presented
and discussed.
INTRODUCTION
An accurate propulsion system simulation for short take-off vertical landing (STOVL)
aircraft is a critical element for research on design methodologies for integrated STOVL aircraft
flight and propulsion control systems. Such a s_mulation must, in principle, mimic steady-state
and transient sub-system performance and be executable in real-time. For modern real-time
system analyses, it is important that the STOVL simulation include the dynamics of component
feeder ducts, engine inter-component volumes, and the tailpipe.
Early engine simulations on analog computers often included intercomponent volume
dynamics modules, but the intent was more often for the purpose of coupling static components
than for an accurate solicitation of gas dynamics effects. As such, the traditional approach draws
only on the continuity equation and a simplified form of the energy equation. Later, simulations
on digital computers relaxed the "complete" form of the initial value problem by dropping
intercomponent approximations and employed iterative schemes to balance the engine. The
latter approach is not appropriate for simulations on modern real-time computers (such as the
Applied Dynamics International AD-100 machine) and is the impetus for the present investi-
gatmn. Problem formulations for real-time STOVL systems must contain accurate volume
dynamics approximations.
Feeder ducts and tailpipes of STOVL engine configurations are likely to exhibit different
dynamic behavior than inter-component volumes and therefore may not be accurately charac-
terized by traditional (analog) volume dynamics representations. There is a need for a volume
dynamics model with the simplicity and computational speed of the traditional approach, but
with the capability to incorporate more detailed heat transfer and fluid-dynamic effects that are
likely features of STOVL systems.
In the present work, two approachesto modeling volume dynamicsare explored and
comparedwith aview toward apphcationto real-time propulsion systemsimulation. The first
andsimplestmethodemploysthe traditional approachin theproblemformulation; in thesecond
approacha momentum oalance is included and the heat equation is replaced with a complete
energy balance. These approaches are applied to a typical ejector feeder pipe for a proposed
ejector-configured STOVL propulsion system. A third method under development is also
mentioned which employs an entropy balance in place of the energy equation.
PROBLEM FORMULATION
Some traditional approaches to the transient volume dynamics problem are represented
by the lumped volume work of Szuch et al.[1], the finite difference analysis of Cheng and
Bowyer[2] and the control volume approach of Thompson[3].
In order to more easily accommodate multiple inlet and exit flows, the present approxi-
mations for mass, momentum, and energy balances are discussed within a control-volume
framework. An integral approach allows complicated aero-thermodynamic physics to be more
simply and robustl_¢ be described by a gross relation involving a group of particles rather than,
say, a flow streamline approach.
For the intent of the present simulation, it is reasonable to proceed with a one-dimensional
gas flow assumption. This sets the stage for simplified control volume equations. Consider the
control-volume k shown in Fig. 1. Multiple inlets are permissable at surface i and multiple
discharges atj. To apply the assumptions above, first define control-volume mass flux as
m = -fspu.n_aA (1)
so, for example, the mass influx is
N
m, = + _. P.vnA,, (2)
n-|
The governing balances of mass, momentum, energy, and entropy can now be written in the
form
d fvpdV=rtz_-mj (3)
-_t fvPU_clV = {v,rn,- u/m,,} + {p,A,- p jA /} + F (4)
t,L(P ho- dV=miho,i-rnjho,i (U)
a fv BQ_'s > o (6)psdV-m_s_+m/s/ T -
Further simplification of the system of equations hinges on discussion regarding the choice of
state variables and the treatment of the time-dependent volume integrals.
BASIC HEAT EQUATION ANALYSIS
Two particularly simple differential equations for the basic heat equation (BHE) analysis
result from the application of two assumpnons. The first assumption ts that changes in flow
kinetic energy are negligible; this reduces the first law of thermodynamics to the heat equation.
A very basic analysis follows from the second assumption in which momentum changes are
neglected. Since many mechanical effects that influence the flow are discarded, we expect the
approach is most appropriate for short ducts of nearly uniform cross-section.
For a spatially uniform density approximation the volume integral in eqn.(3) can be
evaluated. If it is also assumed the volume of region k is of fixed size, the governing equation
for the density derivative is
dp) = m,-m.j = m,-mj (7)k Vk _Ax
where an overbar indicates a volume-average quantity.
In the absence of mechanisms to influence momentum loss, state chan_.es arise through
changes in thermal energy, not mechanical energy. For a zero momentum deficit, the pressure
within a given control volume is subsequently uniform (quasi-steady), and the computation for
P is simply
P = pRT (8)
Changes in pressure are therefore a direct result of changes in density and temperature.
When the mechanical power equation (the dot product of the velocity and Navier-Stokes
equation) is subtracted from the general power equation (the first law of thermodynamics, eqn.5)
there results the heat equation; in integral form the adiabatic result is
podV = - pev.ndA- pv.ndA (9)
In the ideal case of a perfectly mixed one-dimensional flow of small axial temperature gradient
(and a uniform pressure throughout), an average enthalpy h can be introduced. This yields
the traditional result for the temperature derivative
ctT) _ ¥- 1 {m,(h _-_)+ RT(m _mi) } (lO)k Rmcv
Equations (7) and (10) constitute the differential equations for the basic heat equation analysis,
and are the typical equations one might see in early analog simulations of engine inter-component
volumes.
MOMENTUM/ENERGY EQUATION ANALYSIS
The momentum/energy equation (MEE) approach to the duct analysis includes a balance
of momentum and replaces the simple heat equation of the BHE approach with the general
energy equation.
Flow momentum changes in ducts are generally attributable to variations in cross-sectional
area or the friction associated with real flows; the governin,_ differential equation is a vector
expression, but with the flux momentum nomenclature of Fig. 1 in mind (see [3] for details),
there results the scalar balance
d (pVV)k = Mi- M j + fi (11)
where the scalar form of the momentum is
M = vm + PA
In this work an idealized expression for the internal resistance of the duct shown is given by
- 1
P = PdA _ 2"''_-(P'+Pi_rAj-A'_
where the absence of frictional effects should be noted. Carrying through the differentiation in
time and re-arranging results in the following equation
-6-[) a odo _ __1 (Mi_Mj+I_)___.._ - (12)
k oAAx pc:It
The characteristic velocity _ is a weighted average of the inlet and exit control volume velocities
i
v = _v,+(1-_)vj
where _ is a weighting parameter ranging in value from 0 to 1.
The general power equation includes representations of thermal and kinetic energy,
(13)
where
The time-dependent term can be rearranged to read
a-t P h+ .... +_v--+
2 p k y-1 dt dt 2 cltJk
and from this an expression for the pressure derivative obtained
4
1 dp = {£,-Ej}- vm+ - (14)
V- I -'_ , dt 2 at k
Equations (7), (12), and (14) are the differential equations of interest in the momentum/energy
equation analysis.
REMARK ON ENTROPY ANALYSIS
Traditionally, the entropy equation is employed as a check on the validity of multiple
solutions (subsonic flow, supersonic flow) extracted from the general energy balance. However,
except for the mathematical inconvenience of the inequalit_¢ in eqn.(6), there should be no reason
the entropy equation cannot replace the general form otthe energy equation. An analysis is
in-progress to investigate replacement of the lost-work-energy term so that
--AAxd(pS)dt m_s,+rit/sj = Cl>0- (15)
where C 1 is an empirical constant (that replaces the lost-work term) associated with a specific
duct configuration. When a reference entropy point has been established, the ideal gas relations
permit evaluation of entropy at any other desired state. Here, the proposed benefit is in con-
densing the otherwise scattered real flow effects (friction, heat transfer) into one constant,
expediting computations for a given duct. It remains to establish whether computations for
entropy at each point is faster than the quadratic solution previously required for the velocity
(from the energy equation).
RESULTS
Duct system response to step-function inputs are considered in this work since these
changes in duct flowrate are coincident with typical STOVL flight scenarios. In the present work,
flow conditions representative of previous NASA Lewis ejector tests provide baseline data for
a realistic test case. We ,therefore consider a step change in flowrate from 8.48 Kg/s to 9.91 Kg/s
that occurs with an incr,.ase in static pressure from 106 ]_Pa to 108 kPa and at a constant inlet
temperature of 400K. A constant area duct of 0.102 m z is used for all calculations; also, all
numerical calculations proceeded with a time step of I ms. Two cases presented are where the
duct volume is first contained within one finite-volume and then partitioned into several finite
elements.
Our first result points out a potential hazard in simplifying the time derivatives of the
control-volume integrals with the "characteristic" field variables (v, 0). Figure 2 illustrates pre-
dictions of exit flowrate for ducts of 1.5m and 4.6m in length. Note the absence of momentum
exchange in the BHE approach essentially provides a quasi-steady duct flowrate response. The
MEE predictions reqmre twice as much computer time and seem more reasonable, but the
discharge of the 1.5m duct which lags its 4.6m counterpart reflects the inaccuracy of the assumed
value of the weighting scalar _ = 0.5 for very long ducts; after one time step the incoming fluid
has penetrated only 2% of the 4.6m duct, not the 50% implied in the calculation. When _ = 0.9
the situation corrects to the shorter duct reaching a steady-state before the longer duct does.
In Fig. 3 it appears the pressure response of the BHE approach is flawed by the absence
of momentum exchange; pressure changes must inadequately communicate through the heat
equation. Since Fig.3 is based on _ = 0.5 the trend in pressure response for the MEE approach
is intuitively reversed, but, as mentioned above, corrects when _j= 0.9. The cautionary note from
5
Figs. 2 and 3 is that althou._h the BHE calculations ap.pear stable in the analysis of very long
ducts, this by no means imphes the results are necessarily accurate. If, however, analytic interest
is focused only on accurate representation of flowrate, use of the BHE approach may then be
appropriate.
Figure 4 illustrates flowrate predictions with the MEE approach for a 3m long duct divided
into 5 control-volumes. In this case the reduced length of the individual control volumes partially
compensates for the inaccuracy of results for the assumed _j = 0.5; generally, the "correct" _ to
use is not known apriori. In practice, 5 control volumes require the same multiple of computations
that a single-volume computation does. It therefore remains to balance in propulsion applications
whether or not the need for machine speed solicits pre-processing _ for greater single-volume
duct analysis accuracy.
It appears from the computations that the BHE apprach is not adequate to describe the
essential transient flow features required to accurately s_mulate propulsion system feeder ducts
and tailpipe responses, but will suffice for traditional inter-stage engine component coupling.
The more detailed (and computationally intensive) MEE approach is necessary for simulating
STOVL-specific propulsion system components.
CONCLUSION
The modeling approaches presented provide rapid characterization of ejector/duct field
variable time dependencies. These models are potentially useful for real-time STOVL pro-
pulsion simulation development efforts. If, however, the basic assumptions of each approach
are not appreciated in application, the net result is the rapid computation of the wrong answer.
A
E
P
ho
h
KE
L
m
inca
A,!
A/J cu
P
t?
S
t
lJ
I F
X
Ax"
P
NOMENCLATURE
cross-sectional area
energy flux
internal resistance of the duct
total enthalpy, = h + u 2/2
specific enthalpy
kinetic energy
total duct length
mass flowrate
control volume mass
momentum flux
control volume momentum
pressure
gas constant
entropy
time
velocity
volume of control-volume
streamwise coordinate
duct incremental length
density of gas
weighting parameter for average velocity calculation
6
Subscripts
i
J
k
n
Superscript
inflow
outflow
control volume designation
dummy index
averaged quantity
REFERENCES
1. Szuch,J., Krosel,S., and Bruton,W., "Automated Procedure
Computer Simulations of Turbofan Engines," NASA TP-1851, 1982.
for Developing Hybrid
2. Cheng, L. and Bowyer,J., "TUBE-Transient Compressible Flow Code," Fluid Transients
& Acoustics in Industry., ASME, Dec. 1978.
3. Thompson, P., Compressible Fluid Dynamics, McGraw Hill, New York, 1972.
i k
T,P,v
Wall
E
Wall
--.ID,* X
L
T,P,v
--P" n
Fig.1 Control-volume approximati6n.
t_
e_
v
or}
t_
10.22-
8.76
7.29
Fig.2
= 0.5
BHE,Ax = 4.6m
9.91 kg/s "_
"_ ,-'t"- _ --'------- •
BHE ,Ax = l.Srn
Ax 4.6m
l _MEE,Ax = 1.Sin
---- 8.48 kg/s
| i
0 3 6
BHE - Basic Heat Equation
MEE Momentum/Energy Equation
! | ! I ! ..... | • - _l
9 12 15 18 21 24 27 30
Time (ms),
Solution for duct exit flowrate as function of time.
o
t_
ta_
0
116.2"
111.1
105.3
Fig.3
MEE,Ax = 1.5m
//MEE,Ax = 4.6m
__/_nlet Pressure
/./
,Ax = 1.Sm
,Ax = 4.6m
0
i i ! i | • ! | • •
3 6 9 12 15 18 21 24 27 30
Time (ms)
Solution for duct exit pressure as function of time.
= 0.5 Duct Length = 3m
O
oO
10.22
8.76
Influx
Im
7.29 [ , ° , , , , , , , ,
0 3 6 9 12 15
Time (ms)
Fig.4 Solution for duct flowrate as function of time for three points along the duct.

Report Documentation PageNational Aeronaullcs and
Space Admlntstratlon
1. Report No. 2. Government Accession No. 3. Recipienl's Catalog No.
NASA TM- 102397
5. Report Date4. Title and Subtitle
STOVL Propulsion System Volume Dynamics Approximations
7. Author(s)
Colin K. Drummond
9. Performing Organization Name and Address
National Aeronautics and Space Administration
Lewis Research Center
Cleveland, Ohio 44135-3191
i12. Sponsoring Agency Name and Address
National Aeronautics and Space Administration
Washington, D.C. 20546-0001
6. Performing Organization Code
8. Performing Organization Report No.
E-5147
10. Work Unit No.
505-62-71
11. Contract or Grant No.
13. Type of Report and Period Covered
Technical Memorandum
14. Sponsoring Agency Code
15. Supplementary Notes
Prepared for the 1989 Winter Annual Meeting of the American Society of Mechanical Engineers, San Francisco,
California, December 10-15, 1989.
16. Abstract
Two approaches to modeling turbofan engine component volume dynamics are explored and compared with a
view toward application to real-time simulation of short take-off vertical landing (STOVL) aircraft propulsion
systems. The first (and most popular) approach considers only heat and mass balances; the second approach
includes a momentum balance and substitutes the heat equation with a complete energy balance. Results for a
practical test case are presented and discussed.
17. Key Words (Suggested by Author(s))
STOVL
Real-time simulation
Duct flow
Unsteady flow
t8. Distribution Statement
Unclassified- Unlimited
Subject Category 07
19. Security Classif. (of this report) 20. Security Classif. (of this page) 21. No of pages
Unclassified Unclassified 11
NASA FORM 1626 OCT86
*For sale by the National Technical Information Service, Springfield, Virginia 22161
22. Price*
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STOVL propulsion system volume dynamics approximations

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