NASA Technical Reports Server (NTRS) 20040066085: High Energy Boundary Conditions for a Cartesian Mesh Euler Solver

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AIAA 2004-
High Energy Boundary Conditions
far a Cartesian Mesh Euler Solver
Shishir A. Pandya
NASA Ames Research Center, Moffett Field, CA
Scott M. Murman
ELORET, Moffett Field, CA
Michael J. Aftosmis
NASA Ames Research Center, Moffett Field, CA
22nd AlAA Applied Aerodynamics
Conference and Exhibit
16-19 August 2004 / Providence, RI
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For permission to copy or republish, contact the American Institute of Aeronautics and Astronautics
1801 Alexander Bell Drive, Suite 500, Reston, VA 201 91-4344
AIAA 2004-
High Energy Boundary Conditions for a Cartesian Mesh Euler
Solver
Shishir A. Pandya
YXSA Ames Research Center, Moffett Field, CA
Scott M. Murmant
ELORET,M offett Field, CA
Michael J, -AftQsmis
N.lSX Ames Research Center, Moffett Field, CA
Abstract
Inlets and exhaust nozzles are often o.m.i tte.d or fared over in aerodynamic sim-
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.U.Il-Aa:b--l-u 115 u-Pi a-i:l t-iaft dii~to the coxplexities iz-vro!-vd i~ the m~dr!icg cf S Z ~ ~ Z S
details such as complex gometry and flow physics. However, the assumption is
often improper as inlet or plume flows have a substantial effect on vehicle aero-
dynamics. A tool for specifying inlet and exhaust plume conditions through the
use of high-energy boundary conditions in an established inviscid flow solver is
presented. The effects of the plume on the flow fields near the inlet and plume
are discussed.
Iiitroduction important in obtaining accurate forces and mo-
ments. Thus, there is a need for proper modeling
Inlets and exhaust nozzles are common place in
of high energy boundaries in the flow field. The
the world of flight. However, for the purposes of
lack of a plume can also create an evacuated base
aerodynamic simular;ion, iniexs and exhausts are
region thus effecting both drag and pitching mo-
often fared over and it is assumed that the flow
ment values.
differences resulting from this approximation are
Often the lack of proper modeling of the inlet
minimal. While this is an adequate assumption
and exhaust conditions is due to the complex-
in many cases, the presence of an inlet that draws
ity of having to model a turbine engine. Often
flow in or an exhaust with a substantial plume can
it is the details of the chemical processes in the
have a notable effect on the flow field and thus the
combustion that keep engineers from modeling
forces and moments of the vehicle. One such ex-
a plume. Thus, an engineering approximation
'ample is a jet-plume-induced flow separation on
that captures the aerodynamic effects of an inlet
the surface of the vehicle [l]. The flow field in
or exhaust on the vehicle without the complex-
and near the base region is often mis-predicted
ity of modeling an engine's internal processes is
resulting in incorrect base drag. For example,
needed. To remedy this, inlet and exhaust capa-
today's missiles have engines which produce an
bility is added to an existing aerodynamic simula-
under-expanded plume which creates a blockage
tion package with the goal of accurately modeling
to the main flow. This blockage is unaccounted
these effects on vehicIe aerodynamics. This goal
for without the modeling of the plume and can be
is achieved by employing a high-energy bound-
a?y condition at a.compressor face within an inlet
*Aerospace Engineer, hlember AIAA
'Sznior Research Scientist, Nember AIAA duct and at-a planar face within the nozzle.
,!Aerqspace Engineer, hlember AIAA .-. . The capability is added to 'the Cartesiae-. .
. - . -*
mesh based aerodynamic Gmulation package
coqr.Tighhist ppraopteerc tiiso na mw otrhbe o Uf nthitee dU SSta tGeso 2v0er0n4m ent and IS not sub~ectt o CART3D[2]. 'The CART30 package consists of -1 .
a set of tools for akromaticaliy and efficiently then conibiiied by intersecring the component tri-
generating a Cartesian solume mesh from com- angulations. At the end of the intersection pro-
punenr t;riariquiations The flow solver within the cess. a single. closed, triangulated surface is ob
CA4RT3Dp ackage is an efficient. parallel. inviscid tained on which each triangle‘s origin can be iden-
soher for a Cartesian meshj3. 41. tified by its component number.
The method for specifying the high-energy A simple and effective strategy for identifying
boundary conditions consists of a components an inlet plane or an exhaust nozzle in this context
based approach where each triangle is assigned is to assign a separate component number to the
a component number. These component numbers triangles that belong to an inlet or exhaust plane.
are assigned a boundary condition and a refer- However, inlet and/or exhaust planes are usually
ence state in the flow solver. The flow solver is not modeled as separate components during the
modified to use this information to produce the CAD process and often the geometry is an old
appropriate inlet or exhaust behavior at the given triangulation that does not have its components
boundary using a characteristics based approach. identified. For these cases, a tool to extract the
-4m ethod for marking the inlet or exhaust plane inlet and exhaust planes as components is used.
triangles as separate components and the modifi-
Presently, the tool allows the user to specify
cations to the flow solver are discussed.
either a bounding box(a rectangular cube) or a
The use of the present tool is demonstrated
sphere to mark an inlet or exhaust region. Any
with v&&ti~n test c ~ e s -4 ~itnft ype inlet &c-~:-~--al l;;l-we. <ll+ihll:l-l ,l, ,.I+bllcaG regions is marked “uji the toz!
and a wedge-shaped diffuser for which the con-
according to the user specification.
ditions are predictable based on the normal and
Figure l(a) shows a legacy geometry where at
oblique shock relations show the capability of the
the back end of a shuttle orbiter the exhaust
method for inlet cases. The solution of the flow
planes for the 3 Space Shuttle Main Engine noz-
about an ogive shaped missile body is compared
zles need to be extracted as separate components.
to an experiment[5] to demonstrate the exhaust
The user specifies a sphere as shown in Fig. l(b)
capabilities of the tool. A space shuttle in ascent
to extract the exhaust plane of the top nozzle as a
configuration is also computed to further show the
separate component. Figure 2 shows the resulting
usefulness of the tool in real world scenarios.
component-marking. Each component is shown in
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a distinct color.
Method
A Riemann based boundary condition where Flow solver algorithm
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the user can specify the known state at the bound-
The boundary in the CART3D package is de-
ary is used. A high energy state can be specified
scribed by the surface triangulation. When the
by the user at the boundary. The solution of the
Cartesian mesh is generated, a set of cut cells is
Riemann problem subsequently determines the
computed by intersecting the triangulation with
conditions in the cells next to the boundary re-
the Cartesian cells forming a set of cut cells
sulting in either inlet or exhaust.
around the surface of the geometry. These cut
Two tasks need to be accomplished in order to
cells are arbitrary polygons in 2D and polyhedra
implement such a boundary condition. First, the
in 3D.
set of triangles making up an inlet or an exhaust
At an inlet or an exhaust plane, the user spec-
nozzle need to be marked appropriately so that
ified reference state is the flow condition at the
the flow solver can easily distinguish them from
boundary. As shown in Fig. 3 the flow condi-
other triangles. Second, the flow solver must treat
tion at the boundary is denoted UL. The flow
these triangles in an manner appropriate to the
condition in the cut-cell next to the boundary is
conditions specified by the user.
reconstructed from the flow variables in the lo-
Marking the triangulation cal neighborhood and is denoted UR. A Riemann
CART33 relies on a component wise approach problemis then solved to compute the flux across
to compose triangulated surfaces. In this ap that Piece of the Cut cell.
proach, each component of the geometry is sep The resdt is $hat far supersonic flow the bomd-
arately triangulated. All triangulated parts are ai-y reference sate spe-cified by the user hecomes
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Fig. 1 Marking the triangles as inlet or Exit
Fig. 2 Marking the triangles as inlet or Exit
the state at an exhaust plane. At a supersonic in- aligned plane, the velocity sent to the Riemann
let. the result of the Riemann solver is to simply soh-er must be rotated into the coordinate system
suck in whatever fluid is seen by the inlet plane. aligned with the normal to that boundary face.
For subsonic flon7, the Riemann solver compures Once the Riemann problem is solved. the resulting
an appropriate boundary value based 011 the char- flux must be rotated back to the original frame of
acteristics of the flow and the specified boundary reference and then added to the appropriate flux.
state.
An additional. complication is that when th-e -
Riemann problem is solved in a non Cartesian- - . -
A.
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.American Insrirute of Aeronautics and -Astronautics
Fig. 3 A typical cut cell. The Cartesian cell is
cut by a boundary forming a cut cell.
Fig. 4 The pitot intake
Resuit s
Supersonic intake design depends heavily on
results in a normal shock at the lip. This condi-
the shock-systems that develop in the flow field.
tion is also called the maximum flow condition.
For this reason, two supersonic intakes are used
In the fourth case, the pressure in the channel is
to validate the method. -4 pitot intake is used
lower than the critical case resulting in a delayed
vu- w 3c1l,1nw-vrv7 t rrt c.Il,,e mIII,G,tLbI.-I,wrlu 1.s mpablc af predictkg shock. Thus, the shock occurs well inside the in-
the correct shock behavior. For a more complex
take channel.
shock system. a Wedge shaped diffuser where an
The computation of these cases is performed on
oblique shock off the lip of the wedge slows the
a Cartesian mesh which wm refined in and near
flow initially and a strong shock at the lip of the
the intake channel to capture the shocks properly.
cowell reduces the flow speed to subsonic.
The free stream Mach number for all four cases
Following the inlet results, two exhaust valida-
is 1.4. The critical condition for the test case is
tion test cases are presented followed by a Space
derived based on the normal shock relations as
Shuttle in the ascent configuration. An ogive
follows. For khch number of 1.4, we obtziin a
shaped missile body at Ad = 0.9 for ::.hich the
Mach number in the channel of 0.7397 from the
plume effects the pressure on the rear part of
normal shock relations. The saise relations also
the body is simulated for several plume shapes.
provide the pressure and density ratios as 2.1199
The plume size is controlled by the pressure in
and 1.6896 respectively.
the plenum chamber. The results are compared
Figure 5(a) shows pressure contours from a
to an experiment by Burt[5]. Finally, the full
computation of the case where the intake is not
space shuttle stack with all the details of attach-
lezting flow through. It can be seen that a bow
ment hardware etc. is modelled with the plume
shock well ahead of the intake lip has formed as
on to demonstrate the ultimate usefulness of the
expected. and the flow behind the bow shock is
method.
subsonic as expected. Four particle traces are
Pitot intake released to verify that the flow is indeed going
The pitot intake can often be attractive to a around the lip. The conditions at the intake
designer due to its low drag. It is also an at- tube wall are specified to be zero velocity for the
tractive test case for validation as its behavior is blocked intake case.
predictable. The behavior of the pitot intake is The pressure contours for the subcritical case
depicted in fig. 4 for four cases. In case one, the are shown in fig. 5(b). Here a bow shock is seen
intake is blocked. The flow can not go though the just ahead of the intake lip. The particle traces
intake. This results in a bow shock well ahead of verify that air is flowing through the intake, but
the intake. In case two, there is flow through the some air spills to the outside. A higher than
intake. there is still some spillage resulting in a criti4 pressure is used to specify the boundary
bow shock closer to the intakelip. -This case is conditions for the sub-critical case. -- -
termed sub-critical. The third case, termed crit- The pressure contours for the crixical case are
ical. does not let flow spill around the lip. This shown in fig. 5(c). Here a normal shock forms 'at
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American Institute of Aeronautics and -4stronautics
2) blocked b) sub-critical
c) critical d) super-critical
Fig. 5 The pitot intake at hfm = 1.4
A T
the intake lip as expected, To verify that the max-
imum flow condition has been achieved, particle
traces are shown, The particle traces verify that
M-20-
no air from the area directly in front of the in-
P1 .s"s
take spills to the outside. The critical conditions PI 8
discussed above are specified for this test case.
The pressure contours for the super-critical case
Fig. 6 The two shock Wedge diffuser
are shown in fig. 5(d). Here the normal shock is
seen inside the intake channel. The particle traces
verify that no air spills to the outside of the lip. A across the shock as well as the speed of the flow
lower than critical pressure is used to create the behind the shock are obtained using the oblique
super-critical conditions. shock relations. When a second so called normal-
shock occurs at the lip of the inlet, the condition
Two-shock wedge diffuser is deemed to be the maximum flow condition as
the flow through the inlet duct for this case cor-
The normal shock diffuser is depicted in fig.
responds to the maximum possible flow in the
6. A 5' wedge shaped inlet results in an oblique
capture &ea(Z,). The second shock is in real-
shock followed by a normal shock at the cowell
ity is a strong shock solution of the oblique shock
lip. The weak.shock solution can be found from
relations for a th-n-angle of 5" which corresponds . ..
the oglique shock tables[6] for a free stream speed
to a shock-apgk of 86S6". The flow .behind the'
of ME = 2.0. The pressure and d.ensity r&tk
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American Institute of Xeronautics and Astronautics
shock is subsonic.
Based on the maximum flow condition, the area
of che iniet is computed using the conservation
relation,
f’lulzs = P3u3Ztube (11
-4 geometry of the wedge and inlet duct that cor-
responds to this area is created and the reference
condition computed based on the oblique shock
relations is specified at the inlet face. The results
of the simulation are plotted as contours of the
Mach number in figure 7. The expected solution
corresponding to the maximum flow condition has Fig. 8 Density contours on the surface of the
been obtained with the appropriate shock angles FESTIP and the center plane at A L = 2.98
and speeds. compared to Experiments[7]
FESTIP
ropean Space Transporxation Investigation Pro-
In addition to the being able to predict the
gram(FEST1P) at Mach 2.95 is simulated with
inlet flows correctly, the method is also capable
plume conditions specified [7]T. he resulting flow
of accurately predicting the esects of an exhaust
field is shown in fig. 8 and %-illb e compared to
plume. MTe first focus our attention on the gen-
a Schlieren photograph to show that the plume
eral features of the flow field with the plume on.
shape. size and its effects on the flotv field are
In order to verify that we obtain a properly sized
properly captured.
plume and that we are able to capture the effects
of the plume on the flow field, the Fu’ture. Eu-
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American Institute of Aeronautics and Astronautics
Ti;
2.004 2.5
1-1.309-1
Fig. 9 The geometry of the ogive
) ig. 1U I'he pressure contours behind the oghe showing tkie plume
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American InsTiwre sf AL+vr,naq-Lcasn d &xr?naurics
Ogive
To further i-alidate the phne capabilitj- of the
high-merz- boundary conditions. n-e look at a
case for ~vhicht he effect of the plume on the sur-
face of the body is esperinientallj- documented for
several plume conditions. Xs the pressure in the
plenum chamber is increased. a larger plume re-
sults and subsequently effects the pressure on the
cyndrically shaped back part of the missile shaped
ogive body. These changes in pressure effect the
moments on the vehicle and are thus important
to capture accurately.
-4 strut mounted body of revolution (see Fig. 9) Fig. 11 Pressure on the surface of the ogive
at Mm = 0.9 compared to Experiments[5] (x=O
with a cylindrical after-body is used in an exper-
is the base of the ogive body)
iment by Burt [5] at -If = 0.9 and M = 1.2 with
zero angle of attack. This case has been more re-
cently computed by Raghunathan et. al [SI using
a viscous technique. The model has a 4caliber
mngent ogive nose attached to a %caliber cyiin-
drical body. A 20 deg conical nozzle with a design
Mach umber of 2.7 is modeled to match the ex-
periment.
Conditions are specified at the vertical face in
the plenum chamber which correspond to the ex-
perimental conditions including the Pressure ratio
betrveen the plenum and the free stream. The I
specification of the pressure in the plenum pro- r) ', I3 II 0
vides the mechazism by n-hich the air is pushed
through the throat and the nozzle. The result- Fig. 12 Pressure on the surface of the ogive
ing plume is depicted by Mach number contours at Ma = 1.2 compared to Experiments[5] (x=O
in Fig. 10 where blue denotes a slow speed flow is the base of the ogive body)
such as that in the plenum, white denotes the high
speed flow at appro-ximately Mach 7 and the col-
ber 1.2 is also shown in figure 12. For this su-
ors in between denote intermediate values.
personic speed case, the vehicle develops a shock
The pressure on the surface of the cylindri-
on the cylindrical after-body due to the block-
cal after-body is reported by the experiment [5].
age from the under-expanded plume. Due to the
The lowest pressure ratios correspond to an over-
boundary layer development, the compression in
expanded plume while high pressure ratios corre-
the experiment is not as strong as the inviscid
spond to aa under-expanded plume. A blochge
simulation and as is well-known, the shock loca-
to the main flow develops as a result of the under-
tion is not well-predicted by the solution of the
expanded plume. The plume grows larger with
Euler equations.
higher pressure ratios. Thus, at high pressure
ratios the plume has a larger effect on the aerody- In the experiment by Burt, a strut is used to
namics in the region of the cylindrical after-body. mount the model in the wind tunnel [5]. The pres-
This effect can be seen by examining the changes ence of the strut also has an effect on the flow field
in pressure on the after-body. The pressure on of the cylindrical after-body. This effect is inves-
the after-body is therefore compared to the ex- tigated in the present work and shows that the
periment and shows good agreement in both trend .pressure on the Cylindrical after-body rises ear-
and value. lier. A small bump in pressure is visible due to
A similar plot on the same body for Mach num- this early rise as compared- tot eh case without
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American Institute of Aeronautics and Asxronautics
Fig. 13 Pressure rise on the cylindrical after- Fig. 14 Difference in pressure on the cylin-
body of the ogive at iblm = 0.9 with and without drical after-body of the ogive at Mm = 0.9 with
the strut (Pressure ratio=88) and without conical nozzle (Pressure ratio=88)
the strut as shown in fig. 13 for a pressure ratio highly complex configurations such as the space
of 88.0. shuttle in ascent configuration in a very short
The present tool makes it possible for a user time. This capabiiity is combined with the high-
to specify the boundary conditions at one of sev- energy boundary conditions to obtain a solution
eral locations. One approach may be to specif>- of the aerodynamics on the shuttle with the plume
the conditions at the exit plane. The advantage on. Figure 15 shows the Mach number contours
of this approach is that the details of a nozzle on the surface of the Space shuttle as well as
duct do not need to be modeled making the ge- in selected cutting planes in the vicinity of the
ometry much simpler. However, in the course of plumes. Though all three Space shuttle main en-
the implementation of this tool it is observed that gines(SSME) are active, only two are shown to
the geometry of the nozzle is an important aspect be active in order to keep the third engine frorn
of the flow modeling as the flow leaving the exit blocking the view of the plumes.
plane can not be assuxed to be a constant prcl-
Concluding remarks
file across the plane. To illustrate this point, fig.
14 shows the comparison between the pressure on A high-energy boundary condition is imple-
the after-body with and without the modeling of mented in a Cartesian method to model inlet flows
the nozzle. Also shown is the modeling when only and exhaust plumes on aircraft, spacecraft and
a part of the nozzle (from throat to exit plane) is missiles. Their proper modeling and the result-
modeled. When the nozzle is not modeled or par- ing effect on vehicle aerodynamics is needed to
tially modeled, isentropic flow relations are used accurately predict the forces and moments on the
to obtain the conditions at the throat and sub- vehicle.
sequently at the exit plane. It can be concluded Two supersonic inlet designs that have subsonic
that the modeling of the nozzle geometry is essen- flow in the inlet duct are used to validate the
tial to accurately predicting the pressure on the method for inlet flows. A pitot inlet and a two-
surface of the vehicle. shock wedge shaped inlet show that the method
accurately predicts the location and stregth of the
Space shuttle
shocks. Two exhaust plume cases are compared
The Space Shuttle simulation is performed to to experiment to validate the exhaust capability
show the ultimate usefulness of the capability. of the method. The first case shows that the size
Similar simulations have been performed in the and shape of the plume as well as its effect on
past using structured overset meshes [9,1 01. Like the flow field are well predicted. The second test
the overset method, the Cartesian methd of- case is a numerical comparison of the pressures on
fers complex geometry capability. The CART3D the after-body as a function of a changing plume.
code makes it possible to generate meshes on It is comcluded that the modelling of the nozzle.
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