ABSTRACT
DYAKONOV, ARTEM ALEXANDER. Analysis of Aeroheating Augmentation and Control Interference Due to Reaction Control System Jets on Blunt Capsules. (Under the direction of Dr. Fred R. DeJarnette.)
Atmospheric entry capsules are frequently fitted with rocket nozzles as part of a Reaction
Control System (RCS), which is used for attitude control and guidance maneuvers during
en-try. These rocket nozzles are installed on the rear wall of the capsule and the interaction of their exhaust with capsule’s wake causes changes in aeroheating and aerodynamics. Changes
in aeroheating may influence design of Thermal Protection System (TPS) and material
secec-tion, while changes in the surface pressure can cause unbalanced moments on the capsule and interfere with the native RCS control authority. Aerodynamic initerference of RCS must be
understood and bounded for a sound controller design. The method to analyze aerothermal
and aerodynamic effects of RCS on blunt capsules, presented in this dissertation, has been used in analyses of Mars Phoenix, Mars Science Laboratory (MSL) and Crewed Exploration Vehicle
(CEV) RCS. As a result a working RCS design paradigm has been developed. This paradigm
Analysis of Aeroheating Augmentation and Control Interference Due to Reaction Control System Jets on Blunt Capsules
by
Artem Alexander Dyakonov
A dissertation submitted to the Graduate Faculty of North Carolina State University
in partial fulfillment of the requirements for the Degree of
Doctor of Philosophy
Aerospace Engineering
Raleigh, North Carolina
2010
APPROVED BY:
Dr. Hassan A. Hassan Dr. D. Scott McRae
Dr. Jack R. Edwards Dr. Pierre A. Gremaud
DEDICATION
BIOGRAPHY
The author was born on February 26th, 1976, in Moscow, modern Russia. His middle school
years were largely spent at the school number 179, and he finished high school number 1182 (current number 1550). After high school he got accepted to Moscow Institute of Automobiles
and Roads, in the curriculum of ”wheel and caterpillar - based vehicles” due to interest in
mechanical engineering. There he finished first year of study before coming to USA with his family at age 17 in the Summer of 1993. He lived in Wichita, KS, in Greensboro, Durham and
Raleigh in NC, and presently living in Newport News, VA. Since coming to the US he attended
Wichita Area Vocational Technical School, where learned auto-repair and English language and various aspects of American culture, attended Wichita State University, North Carolina
A&T State University in Greensboro (received BS in mechanical engineering), North Carolina
State University in Raleigh NC (received MS in mechanical engineering). While at NC State he began working on doctoral degree in aerospace engineering, but began his job at NASA
Langley. He continued to work toward his degree while working at NASA, and completed this
ACKNOWLEDGEMENTS
I would like to thank my grandfather, Arkadiy E. Mikirov, for having been a defining influence
for me, encouraging my early curiosity, interest in science and engineering. I think I owe him my intuition and desire to seek out and solve challenging problems. He left us early, I wish I
got to know him more. I would like to thank my advisor for his mentorship and help, and for
his patience with a working student. I would like to thank my committee for having shaped my understanding of the field of hypersonics, and for helping me explore my own ability. I’d
like to thank my family for their encouragement, understanding and support. I would like to
TABLE OF CONTENTS
List of Tables . . . vi
List of Figures . . . vii
Chapter 1 Introduction . . . 1
1.1 Introduction . . . 1
1.2 Literature . . . 5
1.3 Data from past missions . . . 7
1.3.1 Apollo Program . . . 7
1.3.2 Viking Program . . . 8
1.3.3 Winged Vehicles, Space Shuttle Orbiter . . . 9
Chapter 2 Description of the Problem . . . 10
2.1 Summary . . . 10
2.1.1 Shocklayer . . . 10
2.1.2 Shoulder Expansion . . . 11
2.1.3 Mixing layer and the recirculating zone . . . 11
2.1.4 Thruster nozzle internal flow . . . 23
2.1.5 Thruster plume . . . 29
2.2 Plume and Nozzle Scaling . . . 35
Chapter 3 Analysis . . . 39
3.1 CFD Modeling . . . 39
3.2 Analysis of Recent Flight Vehicles . . . 40
3.2.1 Mars Phoenix Capsule Aero-RCS Analysis . . . 40
3.2.2 Mars Science Laboratory RCS-Aerodynamics and RCS-Aeroheating Anal-ysis . . . 57
3.2.3 Analysis of Orion CEV RCS aeroheating . . . 82
3.2.4 Flight CFD Model . . . 84
3.3 Summary and Conclusions . . . 94
LIST OF TABLES
Table 2.1 MSL hypersonic conditions . . . 14 Table 2.2 Product moles as function of NH3 dissociation . . . 25 Table 2.3 Combustion product as function of NH3 dissociation, assuming 0.25%
water by mass . . . 25 Table 2.4 Values of γ at different stations within the nozzle for a frozen mixture of
LIST OF FIGURES
Figure 1.1 Computed(LAURA) MSL capsule flowfield at Mach 18 hypersonic
con-dition, streamlines, contours of pressure . . . 2
Figure 1.2 Layout of Apollo CM RCS, borrowed from [2] . . . 3
Figure 1.3 View of Apollo 8 capsule showing effects of aeroheating due to RCS, source - JSC photoarchives . . . 8
Figure 2.1 Variance in shock stand-off and shape at Mars, U=2km/sec, density=3.483E-3 kg/mdensity=3.483E-3 (LAURA) . . . 12
Figure 2.2 MSL trajectory profile . . . 14
Figure 2.3 Properties above the wake shear layer for hypersonic conditions . . . 15
Figure 2.4 Flowfield at Mach 6 . . . 16
Figure 2.5 Flowfield at Mach 10 . . . 16
Figure 2.6 Flowfield at Mach 14 . . . 16
Figure 2.7 Flowfield at Mach 18 . . . 16
Figure 2.8 Flowfield at Mach 22 . . . 17
Figure 2.9 Flowfield at Mach 26 . . . 17
Figure 2.10 Re at Mach 6 . . . 17
Figure 2.11 Re at Mach 10 . . . 17
Figure 2.12 Re at Mach 14 . . . 17
Figure 2.13 Re at Mach 18 . . . 17
Figure 2.14 Re at Mach 22 . . . 18
Figure 2.15 Re at Mach 26 . . . 18
Figure 2.16 Predicted flowfield for Apollo free-flying model, Mach 10 Helium,α=0 . 19 Figure 2.17 Effect of grid size on predicted aftbody pressure, Mach 10 Helium,α=0 20 Figure 2.18 Comparison of predictions with measured pressures, Mach 10 Helium . . 21
Figure 2.19 Variation of base pressure coefficient with Mach number for blunt base capsule at Mars . . . 23
Figure 2.20 Variation of free-stream, dynamic and base pressure (base pressure con-structed using curve in previous figure . . . 24
Figure 2.21 Representative nozzle flow, Mach countours (LAURA) . . . 27
Figure 2.22 Effect of scarf on predicted performance . . . 29
Figure 2.23 Nozzle shape used for calculations at 65 degree scarf angle (showing complimentary 25 degree angle labeled) . . . 29
Figure 2.24 Fine (.84M points) grid used for nozzle calculations. Unscarfed grid is shown. . . 30
Figure 2.25 Representative pressure along the nozzle wall . . . 30
Figure 2.26 Regular (top) and Mach (bottom) reflections within the under-expanded jet . . . 32
Figure 2.27 Plume at Mach 6 . . . 32
Figure 2.28 Plume at Mach 10 . . . 32
Figure 2.30 Plume at Mach 18 . . . 33
Figure 2.31 Plume at Mach 22 . . . 33
Figure 2.32 Partial schematic of dual thruster flow field . . . 34
Figure 2.33 Flight Enthalpies, red line - jet enthalpy, black - free-stream . . . 36
Figure 2.34 Predicted effect of enthalpy ratio on heating due to roll thruster . . . 37
Figure 2.35 Predicted effect of enthalpy ratio on heating due to yaw thruster . . . 37
Figure 2.36 Predicted effect of enthalpy ratio on heating due to yaw thruster, local effects . . . 38
Figure 3.1 Phoenix capsule geometry . . . 42
Figure 3.2 Illustration of the flowfield around Phoenix capsule . . . 43
Figure 3.3 Phoenix capsule features, image borrowed from project material. . . 44
Figure 3.4 Phoenix RCS layout, image borrowed from project material. . . 45
Figure 3.5 Pitch firing configuration . . . 46
Figure 3.6 Yaw firing configuration . . . 47
Figure 3.7 Moments about X-axis . . . 47
Figure 3.8 Moments about Y-axis . . . 48
Figure 3.9 Investigated conditions . . . 48
Figure 3.10 Variation of dynamic pressure and basecover pressure . . . 49
Figure 3.11 Iteration history of aftshell moment . . . 50
Figure 3.12 Iteration history of control gain . . . 50
Figure 3.13 Mach 27.2 and 6 deg sideslip without the thruster . . . 51
Figure 3.14 Mach 27.2 and 6 deg sideslip with the thruster . . . 52
Figure 3.15 Mach 27.2 and 6 deg sideslip without the thruster . . . 52
Figure 3.16 Mach 27.2 and 10 deg sideslip with the thruster . . . 53
Figure 3.17 Yaw interaction at Mach 27.2 for 6, 10 deg sideslip . . . 53
Figure 3.18 Pitch control and aerodynamics at Mach 18.8 . . . 54
Figure 3.19 Yaw control and aerodynamics at Mach 18.8 . . . 54
Figure 3.20 Pitch interference at Mach 18.8 . . . 55
Figure 3.21 Yaw interference at Mach 18.8 . . . 55
Figure 3.22 Flow around MSL capsule at Mach 18.1 . . . 57
Figure 3.23 Jet-wake interaction . . . 58
Figure 3.24 Layout of OML 6 RCS model showing roll and pitch-yaw jets . . . 60
Figure 3.25 Detail of the grid near nozzle (every other gridpoint shown) . . . 60
Figure 3.26 Mach 2.5 comparison of LAURA predictions with data . . . 61
Figure 3.27 Mach 3.5 moment coefficient with and without jets over a range of angles of attack . . . 61
Figure 3.28 Mach 3.5 flowfield with the sting . . . 62
Figure 3.29 Mach 3.5 flowfield without the sting . . . 63
Figure 3.30 Mach 3.5 flowfield pressure with the sting . . . 63
Figure 3.31 Mach 3.5 flowfield pressure without the sting . . . 64
Figure 3.32 Mach 3.5 comparison of moments, effects of support sting . . . 64
Figure 3.33 Slice of flowfield showing structure at range of nozzle pressures . . . 65
Figure 3.34 Surface pressures from solutions with different nozzle pressures . . . 66
Figure 3.36 Viking RCS[35] . . . 67
Figure 3.37 Second iteration of RCS . . . 68
Figure 3.38 Third iteration of RCS . . . 68
Figure 3.39 Flow environment . . . 69
Figure 3.40 RCS cover heating, qualitative. . . 69
Figure 3.41 Thruster effluent mixing with the capsule’s wake . . . 70
Figure 3.42 Final thruster arrangement of MSL RCS . . . 71
Figure 3.43 MSL aftbody pressure, yaw jets, candidate RCS layout, computed for Mach 18.1 . . . 72
Figure 3.44 Aftshell surface yaw-moment arm distribution . . . 72
Figure 3.45 MSL aftbody pressure, yaw jets, computed for Mach 18.1 . . . 73
Figure 3.46 MSL aftbody pressure, yaw jets, computed for Mach 5 . . . 74
Figure 3.47 Nozzles in grid, configuration 3 . . . 75
Figure 3.48 Nozzles in grid, final configuration . . . 75
Figure 3.49 Mach 18 high incidence baseline solution . . . 75
Figure 3.50 Mach 18 high incidence yaw solution . . . 76
Figure 3.51 Mach 18 LAURA-DPLR comparisons with and without RCS, from [33] . 77 Figure 3.52 X-moment arm lengths for each point on the MSL backshell w.r.t. the CG 78 Figure 3.53 X-moment arm lengths for each point on the MSL backshell w.r.t. the CG . . . 79
Figure 3.54 Thrust direction options . . . 79
Figure 3.55 Predicted surface pressures before redesign . . . 80
Figure 3.56 Predicted surface pressures after redesign . . . 80
Figure 3.57 Layout of Orion RCS. . . 83
Figure 3.58 Schematic of Orion hypersonic flowfield. . . 84
Figure 3.59 Representative laminar aftbody heating distribution, Run 18 condition . 86 Figure 3.60 Windside aftbody comparison, run 18, from [40] . . . 86
Figure 3.61 Single yaw jet, TSP . . . 87
Figure 3.62 Single yaw jet, LAURA . . . 87
Figure 3.63 Dual yaw jet, TSP . . . 88
Figure 3.64 Dual yaw jet, LAURA . . . 88
Figure 3.65 Entry trajectory profiles . . . 89
Figure 3.66 9.8 km/s heatrate (roll RCS) . . . 90
Figure 3.67 5 km/s heatrate (roll RCS) . . . 90
Figure 3.68 4 km/s heatrate (roll RCS) . . . 91
Figure 3.69 2 km/s heatrate (roll RCS) . . . 91
Chapter 1
Introduction
1.1
Introduction
As a capsule enters an atmosphere, it interacts with the surrounding gas. This interaction produces aerodynamic forces and moments that act on the capsule during entry, and in the
process, reduce its kinetic energy to an acceptable level for the deployment of a decelerator
or to start the powered descent. Interactions between the vehicle and the surrounding flow, which are of importance to this paper, occur during hypersonic and supersonic flight. In these
regimes, flow around the capsule is characterized by the presence of a bow shock ahead of the
capsule, multiple expansion waves around the forebody shoulder, a massively separated wake flow field, and a complex recompression shock system behind the vehicle as shown in Figure
1.1.
Depending on the capsule shape and size and the free stream conditions, the flow around it may be laminar, transitional, or turbulent. Because of a large amount of energy that must be
dissipated during entry, capsules are shaped to produce large amounts of drag for their volume. Typically a small amount of lift is required for aeroassist maneuvers, therefore low lift-to-drag
ratios are used. While drag, experienced by the vehicle during entry reduces the vehicles total
energy, lift can be used to alter its course through the atmosphere. Lift can be obtained by flying an axisymmetrically-shaped capsule at an angle-of-attack, either by CG offset or by using
a hypersonic trim tab. Use of lift for guidance during entry can help reduce peak deceleration
loads and aeroheating as compared to a ballistic entry, all other things being equal. Reduction of the landing ellipse and a greater altitude at parachute deployment are typically sited as
additional benefits of guided lifting entry. Viking landers flew lifting unguided entry with the
lift vector pointed straight up to maximize the altitude at parachute deployment for safety, because of concerns over very high uncertainty in Mars atmosphere.
Figure 1.1: Computed(LAURA) MSL capsule flowfield at Mach 18 hypersonic condition, streamlines, contours of pressure
Science Laboratory entry vehicle has hypersonic L/D of .24 and will perform bank reversals
during entry to mitigate heating, minimize landing dispersion and to achieve required altitude
at parachute deployment [1]. Orion entry vehicle will carry a human crew, so the use of guided lifting entry is especially critical to reduce deceleration loads to acceptable levels. Mars Phoenix
lander, conceived as a low L/D vehicle, has abandoned lifting entry partly because of the limited
resources, in lieu of a three-axis stabilized controlled ballistic entry. Phoenix will use its control system to dampen out attitude rates, but not for guidance during entry. Concept vehicles,
including future Mars architectures to deliver large payloads (>20 metric tons) to surface, all
employ various guided entry technologies.
Reaction Control System (RCS) is an enabling technology for entry vehicle guidance and
control. RCS is composed of rocket nozzles typically installed on the back wall of a capsule, some form of fuel storage and supply and valves that are operated through some electronic
interface by the flight control program. In the course of atmospheric entry these rocket nozzles
Guidance maneuvers may be commanded at any time during entry.
Figure 1.2: Layout of Apollo CM RCS, borrowed from [2]
Properties of the local flow in the proximity of the nozzle depend on the free-stream
pa-rameters, atmospheric composition, capsule size, shape and attitude and the location of the
nozzle. Local flow can be attached and supersonic, or it can be separated. Generally, attached flow is more energetic, and interactions between it and the nozzle effluent can produce shock
structures, sometimes referred to as horse-shoe shocks. Such structures develop a
quazi-nozzle-like flow directed toward the surface, essentially creating a high energy stagnation flow at the surface of the capsule upstream of the rocket nozzle exit. This type of an interaction can
re-sult in a significant increase over baseline surface heating, pressure and shear. Irrespectively
of the character of the local flow, any interaction between the rocket nozzle effluent and the local flow will result in changes to the wake flow. This is due to the fact that much of wake
is subsonic, and any changes in a given location affect any other location that is within the
elliptic boundary. The result of this kind of dependence is that changes in surface environments can occur over most of the rear wall of the capsule when an RCS nozzle is fired. Most of the
environmental changes, that occur within the separated part of the wake are low in magnitude,
however any interaction with energetic flow outside of the wake shear layer, like the kind that will happen if the jet from the rocket nozzle punches through the separated zone and into the
more energetic flow, can result in significant changes in surface environments. In addition to
the changes in aeroheating environment which influences TPS response, a change in surface pressure distribution will produce moments on the capsule, which can interfere with the native
authority of RCS. Possible effects of RCS jets on gasdynamic environments should be
in these analyses, however it has several important limitations. It is impossible to test a live
size capsule at conditions, representing flight. Because of this a scaled model must be tested at the conditions, approximating flight. Flowfield past the model, installed in a wind tunnel is not
similar, strictly speaking, to that around the flight vehicle at hypersonic speed for a number of
reasons. These reasons include the support interference, lack of real gas effects in most facilities and a frequent lack of availability of relevant gas compositions (for example, Mars) specific to
the given mission. Because most hypersonic facilities operate at temperatures, where real gas
effects are not present, the tunnel simulation has an additional handicap. These limitations aside, scaling of nozzles presents another challenge. When designing a test to look for effects of
RCS interference the nozzles must be scaled appropriately to ensure relevance of the jet - flow
interference phenomena. Current thinking on the subject of scaling is to duplicate flight jet exit pressure ratio and momentum ratio expected in flight. These parameters have been successfully
used to perform Shuttle and MSL analyses. Their adoption is based on empirical evidence of
ap-plicability, and not on any rigorous analyses. Even if all of these limitations and challenges can be overcome there remains a question of measurement technique. Heatfluxes on the back cover
of a blunt body model in the test are frequently so small that the measurement uncertainty and
variability of the signal (noise) may outweigh the signal itself. Similar difficulty exists in the force-moment testing for aero-RCS interference effects: a balance, sized to handle forces and
moments, developed on the forebody is typically too insensitive to measure small moments on the back cover due to unbalanced pressure forces. Measurement of forces and moments can not,
strictly speaking, be viewed as a validation of an RCS-aero interference numerical model. The
reason is simple: an infinite number of pressure distributions may achieve the same total torque. From this point of view the agreement between computed and measured moments is not all
that is required. It is beneficial to have test data on a model, whose back cover is instrumented
with multiple pressure ports, so that a direct comparison of computed pressures and pressures measured in the test can be made. Current approach to analysis of RCS-induced aeroheating
augmentation and control interference is to use state of the art numerical techniques for flight
predictions at supersonic and hypersonic speeds, and to use ground test facilities to validate these numerical methods at flight-like conditions, achievable in those facilities. Ground testing
is typically limited to perfect gas air supersonic and hypersonic facilities, in which a cold gas
(N2) is used as working fluid to produce jets. To capture aeroheating augmentation tempera-ture sensitive paint (TSP) has been used so far, some researchers are developing plans to use
thin film gauges along with TSP. RCS aerodynamic interference has been measured using a
force-moment balance with mixed success, and plans are being developed to test a model with a large number of aftbody pressure ports.
In this dissertation analysis of experimental, computational and engineering data sources
conclusions:
1. Effect of attitude control thruster firings on aftbody forces and aftbody aeroheating can
be significant for blunt capsules; the aftbody is an aerodynamic surface and the forces and moments, generated on it can compete with RCS authority
2. In order to minimize RCS interaction with aerodynamics and aeroheating it is best to use smallest thrusters with largest moment arm; thrusters should be pointed as close to
external flow (free-stream) as feasible; this design approach allows to minimize strong
interactions
3. CFD is generally uncertain in predicting RCS interactions; requiring that experimental techniques be used whenever possible;
4. RCS design cycle must consider aerodynamics
1.2
Literature
This section contains an overview of available relevant literature on the subject of supersonic jets, their interaction with exterior flow, and the existing ideas on the simulation of these
processes, both analytically, and with ground test facilities. The analysis of the interaction of
an under-expanded jet and exterior flow underwent significant development over much of the last century to present. Experimental facilities can now do unsteady heat flux and pressure
measurements, high speed flow visualization, hot wire techniques to determine unsteady content of the flowfield. Analysis tools went from something as simple as fitting a constant radius arc
as an approximate plume boundary, to the method of characteristics, to the CFD techniques
in use today.
Spaid and Cassel [3] report on aerodynamic interference due to RCS jets. This report is
particularly useful for high performance vehicles. The report is a compilation of experiments
with sonic and supersonic jets in mainly a supersonic cross-flow. Some attempts are made to develop analysis methods for a general jet in a cross-flow problem by constructing correlations
between various parameters of the flowfield. These parameters include combinations of jet
and ambient flow pressures, jet thrust, ambient flow dynamic pressure, jet exit Mach number, cross-flow Mach number among others. The report is published in 1974 before the widespread
acceptance of discretized numerical methods, and the authors make an effort to realistically
assess validity of the developed correlational models to predict other data. Authors underscore the complexity of the flowfield and the inadequacy of the simplified models for general analysis.
flowfields. Authors treat what is a relatively generic problem of interaction of a jet with
cross-flow. They make no attempt to investigate the interaction of jets in flows of mixed character (separated flows) where a jet may penetrate a shear layer. This type of a situation occurs in
the case of blunt capsules, and is not typical for high performance vehicles that appear to be
the focus of the report. In general most jet-crossflow environments result in flow separation some distance upstream of the jet, however this is not the same as the jet exhausting into the
separated flow and intersecting a supersonic shear layer.
A report on simulation of jets in ground test facilities by Pindzola [4] treats the problem of ground facility simulation of under-expanded jets in either quiescent medium or in supersonic
flow aligned with the jet. This situation arises when a nozzle flow exits from the base of a
rocket. Pindzola starts by describing in detail the flowfield, associated with the under-expanded plume in quiescent and moving streams. The assumption is made that the internal flow is
well characterized, and directs effort to the plumes. Detailed discussion of pertinent physics
and experimental observations allows to make determination of applicable analysis techniques. Initial inclination of the jet boundary and the shape of the jet boundary are discussed at length,
and experimental correlation are shown. Through the paper an assertion is made that plume
boundary shape is of paramount importance to jet simulations. To simplify simulation and analysis the initial turn is treated as a two-dimensional expansion, governed by Prandtl-Meyer
equations. As the distance from nozzle lip increases the 3D flow aspects become important, and author references the method of characteristics and other inviscid techniques to define
the shape of plume boundary. Further from nozzle, the transition to turbulence within the
plume boundary is possible. Transition to turbulence makes inviscid techniques less relevant, and instead experimental data is required. For some jet pressure ratios a Mach reflection on
the axis, frequently referred to as the termination shock, will develop, and its positioning and
strength is of significance to ground simulation, which requires a match of static pressure ratio and the Kawamura parameter. Systems with multiple disk shocks are discussed in the context
of the ”length of the periodic structure” but are of little relevance to the present topic of
plume-wake interaction for blunt capsules. It should be pointed out that most of the report appears focused on the type of the flow that exists in case of a rocket motor installed in a base of a
slender body that moves axially at some velocity, spanning subsonic to hypersonic regimes.
This flow has different scales then the present problem. For example, the size of the plume is comparable if not greater then the size of the undisturbed wake, whereas this isn’t usually the
1.3
Data from past missions
There is a significant generation gap in NASA’s use of blunt capsules for space exploration.
Capsules of the 60’s and 70’s (Mercury/Gemini, Apollo and Viking) have flown successful controlled unguided and guided entries into Earth and Mars atmospheres. In the early 80’s the
Space Shuttle took over the task of flying people and cargo into Earth’s orbit and it was viewed
as more versatile and capable, thus ending the use by NASA of capsules for manned flights near Earth. Crew Exploration Vehicle (CEV) is slated to be a replacement for the Space Shuttle
orbiter and will return a capsule - based architecture to human flights near Earth and to the
Moon.
Since the two successful landings of Viking 1 and 2 in 1976, landings on Mars have seized for
twenty years. A small and a comparatively simple mission, Mars Pathfinder, landed on Mars in 1997 and marked the renewed interest in Mars surface exploration. MPF was followed by
larger and more complex MER Spirit and Opportunity in 2004 which are operational today.
Capsules of these relatively recent missions were spin-stabilized and did not use controlled entry. Two other recent missions to Mars (Mars Polar Lander and Mars Phoenix) have used RCS
for attitude rate control and azimuth alignment. It is unclear what happened to Mars Polar
Lander which was due to land in December of 1999, but its sister ship Phoenix underwent significant system-wide changes, as compared to MPL, and has been launched in 2007 for a
successful landing in 2008. For the purposes of this report Phenix is viewed as a current
mission and not a prior mission. Analysis of Phoenix RCS is presented in this dissertation along with respective analyses for other current missions. Because none of the recently flown
3-axis stabilized spacecraft (MPL and Phoenix) had any instrumentation to help measure RCS
effects in flight, and all other recent flights were not controlled, any inquiry into heritage data on RCS aeroheating and control interference for blunt capsules has to be addressed to prior
missions, such as Apollo and Viking, which used RCS during entry and do have some data.
1.3.1 Apollo Program
Apollo program carried out ground testing of aeroheating augmentation due to RCS jets using
the then-new phase change coating technique. Results of that work are summarized by Jones
and Hunt [5]. Authors found that interference heating on the Apollo shape was significant for yaw and roll jets. Augmentation factor of 4 due to yaw jet, factor of 11 due to forward-firing roll
jets and a factor of 3 due to aft-firing roll jets. No appreciable augmentation was found due to
pitch jets, which are located on the lee-side of the aftshell, and interact with separated subsonic flow. Interference heating in the case of the yaw and roll jets covered significant acreage of
the backshell. In particular, forward-firing roll jets produced the most energetic interaction
augmentation over the largest area.
Figure 1.3: View of Apollo 8 capsule showing effects of aeroheating due to RCS, source - JSC photoarchives
Apollo entry capsules were instrumented to measure surface heating. Heating rate spikes
on the lee-side of the spacecraft during entry were found to correspond to RCS jet firings and
amounted to about a factor of 5 times the nominal measurement [6].
While nominally there was no tests to look at the effect of RCS jets on aerodynamics of
Apollo capsules, the flight of Apollo 7 saw ”considerable pitch and yaw control activity in the
transonic region during the final 2 min before drogue deployment”, which was attributed to winds and thruster-flow interference [2].
1.3.2 Viking Program
Viking program has made an attempt to measure experimentally the magnitude of jet-aerodynamic interference. A test was conducted in Mach 20 wind tunnel, where thruster plumes were
simu-lated as solid bodies. This test did not net any significant insight into the jet-wake interference
repeated with a balance, designed to measure smaller moments, but this was never carried out.
No attempts were made by Viking Project to measure aeroheating augmentation due to jets because aftbody heating was not expected to be significant [8]. Viking was entered into Mars
atmosphere from circular orbit at a relative velocity of about 4.6 km/sec [9]. Low speed entry
of a capsule with a relatively low ballistic coefficient (m/CDA=63.7) resulted in very low heat
fluxes on the aft-cover. Because these heatfluxes were low, on the order of 1 Watt/cm2, it was
possible to make the aft-cover of aluminum, and not cover it with thermal protection material.
Use of the small 8lbf thrusters for rate damping and for lift vector alignment would not produce the heat fluxes and heat loads much beyond the baseline. Therefore, it was not essential for
Viking to test RCS aeroheating augmentation.
1.3.3 Winged Vehicles, Space Shuttle Orbiter
Space Shuttle Orbiter is a lifting body winged vehicle and does not share aerodynamic
char-acteristics with blunt entry capsules. Aerothermodynamics and aerodynamics programs have
conducted experimental and computational investigations to investigate some effects of nozzles, but only aerodynamic effects of blowing nozzles were investigated, see for example, Scallion
Chapter 2
Description of the Problem
2.1
Summary
This section describes in detail the relevant phenomena and outlines the basic analysis tools and the state of knowledge with respect to these phenomena. By very nature of RCS-gasdynamic
interaction, the process of interest occurs in the aft portion of the capsule flowfield. Because
of this, the fidelity of the analysis depends on the fidelity of capture of individual processes, which occurr upstream of the interaction. While analysis of uncertainty is not in the scope of
this dissertation (largely due to insufficient existing data) it is important to recognize the role
of uncertainty in capture of various areas of the flowfield to the problem at hand. Because of the diversity of flow environment this section is separated by type of flow process:
1. Shocklayer
2. Shoulder expansion
3. Separation
4. Recirculated air zone
5. Thruster nozzle-internal flow
6. Thruster plume
7. Shear layer
2.1.1 Shocklayer
Shocklayer on the forebody of the capsule is composed of a chemically reacting and sometimes
flow becoming low-supersonic. The current state of the art numerical tools LAURA [11] and
DPLR [14] have been shown to accurately capture the bow shock shape and distance from a blunt body at hypervelocity in perfect gas (see, for example Horvath[15]), pressure and heating
on the surface for both laminar and turbulent boundary layers (Hollis [16]). While both codes
are capable of treating non-equilibrium dissociated mixtures, this capability is not entirely validated. Specific questions exist about modeling of thermal energy modes of polyatomic
molecules, ex.: CO2. The author of this dissertation found an unexpected sensitivity to the
two temperature model currently in use in the CO2 environment at Mars. Because of the low atmospheric density there, the shocklayer is in non-equilibrium through much of entry, and the
shock stand-off can vary dramatically as a function of the model that’s used, as illustrated by
figure 2.1. This figure is generated by use of CAMAC and Millican-White CO2 vibrational relaxation models. Stand-off and shape has a first order effect on shocklayer pressure, and
can impact accuracy of analysis of any area downstream. This issue is of main concern in
the low-density atmospheres made up of polyatomic gases (i.e. Mars), and is generally not a driver for flights into Earth atmosphere, where the pressures are sufficiently high to keep the
shocklayer gas in thermal equilibrium. It is, therefore, reasonable to rely on LAURA and DPLR
to solve this segment of the flowfield and to expect accurate results, keeping in mind possible uncertainty at Mars.
2.1.2 Shoulder Expansion
The expansion fan at the blunt capsule’s shoulder is formed as flow turns to align with the windside aftshell on the windside and with the lee-side mixing layer on the leeside. Generally
the expanded flow reaches Mach number around 4 for much of hypersonic flight. Fidelity of
computations through the expansion is difficult to quantify. The more practical parameter to consider is the heat flux, predicted on the windside aftbody surface. Comparisons between
computation and wind tunnel measurements, carried out for that area by Hollis [16] show that
the heat flux predictions in both laminar and turbulent flowfields are simulated accurately on the Orion shape with the use of aforementioned numerical tools. This provides some level of
confidence that the parameters of the flow immediately after the expansion are correct.
2.1.3 Mixing layer and the recirculating zone
The mixing layer divides the supersonic high energy flow from the recirculating zone of low
energy air near capsule’s leeside aftbody. The mixing layer determines the balance of mass,
momentum and energy transport between these two highly dissimilar regions. Accurate predic-tion of the transport across the mixing layer and its geometry is vital to pressure and enthalpy
Figure 2.1: Variance in shock stand-off and shape at Mars, U=2km/sec, density=3.483E-3 kg/m3 (LAURA)
lee-side external flow, as it is influenced by the wake angle. Nominal operation of tools, such as LAURA and DPLR results in inadequate grid density in the wake and incorrect grid alignment
with respect to the mixing layer. Significant additional grid density is required, together with some suitable grid alignment procedure, to provide the solution domain for the mixing layer
(see, for example, Hollis [17]).
Discussion of the simulation of transport phenomena across the mixing layer must include a discussion of turbulence. The mechanism, postulated by Chapman [18] required that the mass
of recirculating air that is evacuated by the mixing layer is replaced through the layer itself
near the trailing end of the recirculating zone. If all or part of the layer is turbulent - this balance will be affected, resulting in a different shape of the mixing layer and a new pressure
of the recirculating air. Because of the extent to which turbulent transition in the mixing layer
can affect the outcome of the wake analysis, it should be determined if turbulence in the layer is likely.
It has been shown (for example, see von Doenhoff [19]) that low speed free shear layers are
the same Reynolds number, free shear layers transition earlier than attached boundary layers.
However, at high Mach numbers, mixing layers have been shown to exhibit remarkable stability [18]. For example, the laminar limit of about Re=1.E6 was shown for Mach 4 flows for a
wide range of flowfield geometries. This is particularly significant in the context of the present
discussion involving a hypersonic free shear layer. As will be discussed later, in some cases of hypersonic capsules there appears to be a good reason to expect a laminar shear layer, which
might transition only toward the end of the recirculating region.
The mixing layer establishes the interface between the external flow and the recirculating zone. The recirculating zone contains a mass of air, whose total enthalpy is between 15-50
percent of that in free-stream. The enthalpy and momentum of the recirculating air mass is
provided from the exterior flow through diffusion across the mixing layer, and is, therefore, directly affected by whether the layer is laminar or turbulent. The state of the mixing layer is
therefore a critical player in the pressure and enthalpy of the recirculating air. The above
assess-ment of 15-50 percent is based on the author’s experience through numerous CFD calculations using a laminar model over a broad range of Mach numbers.
The state of the flow inside the recirculating region is not necessarily coupled to the state of
the mixing layer. Inside the recirculating zone, the predicted local Reynolds number is generally low due to low pressure there, and the flow scale length there is of the order of a meter. It
appears unlikely that such a flow will develop and sustain turbulence, instead it should remain laminar, even if unsteady and vortical. Existing leeside aftbody heating data for CEV [16]
suggests that the laminar models adequately capture heat rates in the separated area even
when the attached flow elsewhere on the capsule is turbulent. Convective heating predicted by both laminar and turbulent models is also shown to be very close in this low density separated
area. This is, however, not an indication of completeness of these models.
MSL Entry Trajectory, Free Stream Profile and Flow Predictions
Figure 2.2 shows variation of conditions along MSL design trajectory. Data in this plot is generated by POST[20], and is used here as a source of conditions for relevant analysis. The plot
shows the free-stream Mach number, Reynolds number and the free-stream dynamic pressure
along the trajectory. This plot is going to be a backdrop to following discussion of MSL wake environment. Table 2.1 shows free-stream conditions selected for analysis from figure
2.2. Preceding discussion of likelihood of turbulence is relevant here, and examining figures
2.4 through 2.9 and 2.10 through 2.15 shows why. The first set demonstrates the scale of the recirculating region predicted using laminar model at Mach 26, 22, 18, 14, 10 and 6 along the
trajectory shown in the figure 2.2. The latter set of figures shows the predicted Reynolds number
show that the lee-side shear layer Mach number at these hypersonic conditions falls between 3
and 6. Reynolds number above the shear layer does not exceed 45000, as shown in the figure 2.3. Error bars on Mach and Reynolds numbers indicate variance within the relevant portion
of the flowfield, and are plotted simply to give a better indication of the flow parameters. For
a recirculating region of the order of capsule diameter (here 4.5 meters), this mixing layer is likely to stay laminar for much of hypersonic entry, making laminar analysis appropriate. This
doesn’t necessarily mean that the flow should be expected to be steady, and at some of these
conditions (particularly near maximum dynamic pressure) unsteadfy flow is predicted by the model, requiring time-consistent integration.
Figure 2.2: MSL trajectory profile
Table 2.1: MSL hypersonic conditions
M∞ ρ∞, kg/m3 V∞, m/sec T∞, K
26 2.44E-4 5325 164.2
22 9.85E-4 4677 173.2
18 1.93E-3 3861 185.4
14 2.83E-3 3057 191.8
10 3.67E-3 2212 194.2
Figure 2.4: Flowfield at Mach 6 Figure 2.5: Flowfield at Mach 10
Figure 2.8: Flowfield at Mach 22 Figure 2.9: Flowfield at Mach 26
Figure 2.10: Re at Mach 6 Figure 2.11: Re at Mach 10
CFD comparison with Free-flying Model Pressure Data
Accurate prediction of pressure in the recirculating zone of a blunt capsule at hypervelocity
remains a challenge. Validation of CFD codes for this task is held back for a number of reasons:
It is difficult to provide good quality wind tunnel measurement in the wake of a capsule model, in part due to low pressure, that’s being measured, and in part due to presence of the support and
uncertain interaction between the support and the wake. Presence of the support complicates
the CFD model by introducing shear layer impingement mechanics, that would not be as severe for a flight vehicle. Kemp [21] conducted a number of experiments on free-flying tunnel models
with precise intent to avoid support interference while measuring aftbody pressure. Models were
tested in NASA Ames hypersonic helium tunnels and used FM signal telemetry to communicate with their data acquisition system. Models were launched by a pneumatic launcher into the
test section, such that the model velocity relative to the facility was a negligible fraction of the total free-stream velocity. Pressure was measured half-way down the aftbody cone, and it was
done on the wind-side of the aftbody in those cases where a high angle of attack test was being
conducted. Data in the report is sufficient to reconstruct all relevant conditions and scales and to set up a CFD simulation to approximate the experiment.
Figure 2.16: Predicted flowfield for Apollo free-flying model, Mach 10 Helium,α=0
LAURA calculations were set up in an attempt to match experimental predictions of Kemp.
Laminar LAURA simulations with no symmetry plane and with a time-consistent integration were used. Grids had sizes from 3.1M elements to 9.5 M elements. Perfect gas Helium model
used molecular weight 4.003, Prandtl number 0.667 and specific heats ratio 1.667. LAURA
Com-puted flowfield at zero angle of attack is shown in the figure 2.16. No symmetry is assumed in
the solution, and at these conditions wake computation is steady and non-oscillating. Figure 2.17 shows the variation of base pressure predictions as a function of the volume grid size for a
a model at Mach 10 in helium, again assuming zero angle of attack. The figure indicates that as
the grid is refined to the upper limit, explored here, the aftbody pressure prediction is continu-ing to change. There is a practical limit to grid refinement, and while it is not reached in these
perfect gas calculations, the present grids are past that point should a real gas non-equilibrium
entry environment be analyzed on them. The purpose of the last comment is to illustrate that the CFD grid-independence is not always practical, nor it is reachable in some circumstances.
Example of such a circumstance would be a wake simulation, in which successive refinement
picks up finer flow scales, thus slightly changing the flow. Comparisons of predictions with
Figure 2.17: Effect of grid size on predicted aftbody pressure, Mach 10 Helium,α=0
measured data at Mach 10 are shown in the figure 2.18. CFD overpredicts data for very low
angle of attack. At small non-zero angle of attack predicted pressure drops to a level, more
Figure 2.18: Comparison of predictions with measured pressures, Mach 10 Helium
dataset from the same source), and at higher angles of attack where the flow becomes attached
the CFD and data match very well. One possible explanation of the disagreement at zero
de-gree angle of attack is that the physical model, with its pitching motion may never develop a truly axisymmetric wake when going through zero incidence, unlike the CFD model, where the
capsule is held at a static angle to the stream, allowing the wake to settle into an axisymmetric
configuration. Wether the disagreement is in fact a local phenomena and is centered at local angles of attack, thus traceable to the lack of symmetry in the flow, can not be answered with
the present data, as little of it is collected at low angles of attack. The general outcome of this
and other comparisons [17] of CFD against experimental hypersonic wake data is that lack of relevant physics models is in the way of widespread use of CFD for such problems. Credible
turbulence modeling and time accuracy are some of the essential requirements.
Aftbody Pressure on Blunt Capsules at Mars
During most of the atmospheric entry the pressure on the aftbody of the capsule is significantly
smaller then the forebody stagnation pressure. At hypersonic speeds aftbody pressure coefficient
is essentially independent of the free-stream Mach number. The influence may come in due to vehicle passing through regions of equilbrium and non-equilibrium flow and due to change in
ratio of specific heats in shocklayer, which can affect shocklayer geometry, and, consequently,
Because of the uncertainty, associated with the CFD prediction of the wake of a blunt
cap-sule, Mitcheltree (see, for example, [22]) reconstructed aftbody pressure from Viking flight data and arrived at the base pressure coefficient for use for Mars Pathfinder. He fit a polynomial of
the form
CA,base=Cp,base=a0+ a1
M∞
+ a2
M2
∞
+ a3
M3
∞
(2.1)
wherea0 = 8.325E−03, a1 = 1.129E−01, a2 =−1.801E+ 00 anda3= 1.289E−00.
Figure 2.19 shows the form of the Cp curve in the above equation. The curve indicates
two regions of distinct wake behavior. At hypersonic speed, wake pressure coefficient is nearly constant with respect to Mach number. The two mechanisms that could influence Cp in that
region (and, thus, possibly conflict with the shape of the curve in the figure 2.19) are shear
layer turbulence and shocklayer non-equiolibrium. The former would change transport across the layer, thus influence pressure, the latter would change conditions within the ”external” part
of the flowfield, which will in tern drive separation line and angle. At hypersonic conditions the pressure on the base of the capsule at Mars will track dynamic pressure, and will exceed
free-stream static pressure during part of the entry. At supersonic conditions, as the dynamic
pressure drops, the pressure in the wake will drop below the free-stream static pressure and form what’s typically thought as a low pressure wake. As the velocity further decreases the
mo-mentum deficit in the wake becomes less noticeable, and wake pressure will tend to free-stream
static pressure. Velocities, at which this occurs are not interesting to the present work, because capsules typically deploy a parachute at low supersonic velocities, and control interaction under
parachute is a mute point. Figure 2.20 shows the free-stream pressure, dynamic pressure, and
aftbody, or base pressure, reconstructed from it and the Cp, shown in the figure 2.19.
This relation is currently applied to all Mars entry capsules to determine base pressure for
aerodynamics. Its applicability across a range of entry system designs needs further research,
Figure 2.19: Variation of base pressure coefficient with Mach number for blunt base capsule at Mars
2.1.4 Thruster nozzle internal flow
Typical RCS thruster is a mono-propellant hydrazine thruster where catalyst is used to start
and maintain combustion. Because of the complexity of the interaction of thruster flow with the wake, it is important to understand operation of these thrusters. Hydrazine combustion is
composed of two main processes:
1. 3N2H4⇔ 4NH3 + N2 +Q
2. 4NH3 + Q ⇔2N2+6H2
Breakup of ammonia occurring in the second reaction takes the heat out of the system, reducing
thruster performance. The existing test data indicates that about 50% of ammonia is consumed
by the time flow exits the thruster. It can also be shown that the composition changes very little after the nozzle throat, and it is common to assume frozen flow through the diverging
part of the nozzle. There are a number of ways to obtain the properties at the exit plane of
Figure 2.20: Variation of free-stream, dynamic and base pressure (base pressure constructed using curve in previous figure
and McBride [23] [24]. The included rocket problem allows a rough assessment of exit state and
performance parameters. CEA is not able to account for non-equilibrium aspect of the hydrazine combustion, however it is possible to freeze the composition within some bounds. Generally,
because freezing is only possible starting at throat, the properties at nozzle exit will not capture
effect of non-equilibrium accurately. A better approach is to calculate gas properties based on assumed dissociation of ammonia. Because experimental data on composition of effluent
exists this shouldn’t be very difficult to do. A most rigorous approach is to develop a CFD
simulation to include the above species, and reverse-engineer the composition in the chamber based on the relevant measurements of the composition at exit. In other words, several sets
of chamber compositions should be used, and the exit of each simulation compared to the
desired. Composition changes very little between subsonic chamber and exit plane for this type of thruster. This means that the iteration process can be bypassed in the interest of time. Table
2.2 shows mole fractions of ammonia, nitrogen and hydrogen as a function of completeness of
Table 2.2: Product moles as function of NH3 dissociation
dissociation,% N H3 N2 H2
0 4 1 0
10 3.6 1.2 0.6
20 3.2 1.4 1.2
30 2.8 1.6 1.8
40 2.4 1.8 2.4
50 2.0 2.0 3.0
60 1.6 2.2 3.6
70 1.2 2.4 4.2
80 0.8 2.6 4.8
90 0.4 2.8 5.4
100 0.0 3 6
0.25% water is assumed to be in fuel because N2H4 is a hygroscopic substance. In addition to that, most original development of these thrusters was done with traces of water in fuel, and
it is believed that the removal of water might have unintended consequences [25]. Mole fractions
of the products can be computed with correction for the presence of water as shown in the table 2.3. Values ofγ are based on the ideal gas degrees of freedom for respective substances.
Table 2.3: Combustion product as function of NH3 dissociation, assuming 0.25% water by mass
dissociation,% N H3 N2 H2 H2O Mmixture γmixture,ideal
0 0.798 0.200 0.000 0.0025 19.22 1.347 10 0.665 0.222 0.111 0.0025 17.80 1.356 20 0.550 0.241 0.206 0.0025 16.58 1.363 30 0.450 0.257 0.290 0.0025 15.51 1.370 40 0.363 0.272 0.363 0.0025 14.58 1.376 50 0.285 0.285 0.428 0.0025 13.74 1.381 60 0.216 0.297 0.485 0.0025 13.00 1.385 70 0.153 0.307 0.537 0.0025 12.34 1.390 80 0.097 0.316 0.584 0.0025 11.74 1.393 90 0.046 0.325 0.626 0.0025 11.20 1.397 100 0.000 0.333 0.665 0.0025 10.70 1.400
along the nozzle for the same mixture of gases. The following example demonstrates.
Calcula-tions using CEA code were carried out for hydrazine fuel for the exit area ratio 26.2, chamber pressure 11.12 bar and temperature 1364K. Unfortunately CEA doesn’t allow composition at
the chamber to be frozen (freezing possible only after the throat) so the resultant composition
has very low content of NH3, though the example in the table 2.4 is still illustrative. It should
Table 2.4: Values of γ at different stations within the nozzle for a frozen mixture of 87.11% N2, 12.54% H2 and .3% NH3 by mass
location T,K p,bar γ
chamber 1364 11.12 1.342 throat 1120 5.2 1.358 exit 438.5 0.175 1.397
be noted that the computer programs that exist to determine thruster performance have a
slightly different objective, from what’s needed for the present analysis. Here, the main interest is in the gas properties and composition. The fact that the properties of the effluent will have
some uncertainty associated with them, and that this uncertainty isn’t directly related to the
Performance of the thruster for scaling purposes can be assessed in a number of ways. Figure
2.21 shows a representative nozzle flow, calculated using LAURA code for this analysis. To circumvent lack of characteristic inflow boundary condition in LAURA the author employed a
technique of artificially freezing part of the domain to create an upstream boundary condition.
This technique may result in around a 10% error in pressure, but the error can be easily quantified by integrating across the inlet, and corrected. Because there are no provisions in
LAURA for subsonic inflow, this approach was developed and used in most of simulations in
this dissertation. Thrust in vacuum can be found by integrating over the exit plane
Tvac=
Z
exit
( ˙mu)dA+ Z
exit
P dA (2.2)
which is the same as
Tvac=−
Z
inlet
( ˙mu)dA+ Z
inlet
P dA+ Z
surf0,1
FsurfdA (2.3)
For many thrusters
Z
surf1
FsurfdA∼= 0.25Tvac (2.4)
which sets the practical upper limit on effects of nozzle scarfing on thrust.
Figure 2.21: Representative nozzle flow, Mach countours (LAURA)
The term ”scarfing” refers to a nozzle exit, such that the exit plane is not perpendicular to the nozzle axis. Scarfing is done frequently to accommodate installation with non-orthogonal
intersection between thruster axis and capsule’s outer surface. Scarfing is done by one of three
methods. Simplest and least effective is the addition of a cylindrical extension to the bell nozzle, and cutting the cylinder at an angle. Simple as it is, this approach generates internal shocks and
to the wall angle of the bell nozzle near exit. This approach removes internal shocks, but yet
a better approach is to extend the nozzle and to cut the bell at an angle. While this produces a more complex intersection with the capsule surface, possibly increasing the difficulty on the
mechanical side, the overall best nozzle performance is achieved. For purposes of scaling flight
nozzles to tunnel conditions it is sometimes important to know the nozzle’s area ratio. While a very simple task for an axisymmetric nozzle, a case of a scarfed nozzle presents a challenge.
Several approaches have been used to determine the ”effective” area ratio. One approach is
to determine the ratio as an average of the ”long side” and ”short side” area ratios. The long and short side refer to the longest and shortest distances along the nozzle to exit lip. Another
approach is to determine area ratio based on the projection of the nozzle’s exit plane onto the
plane, orthogonal to thruster axis. This can be tedious, and fundamentally doesn’t add any real value. Namely, while the estimate of the axial flow area is slightly better then the first approach,
the relationship between the effective area ratio, effective exit Mach and real distribution of
Mach is still the question. Either approach works, as long as its clearly understood which one is being used. Because RCS thruster flows are under-expanded in most applications, the exit
Mach is not the most important parameter in of itself, instead the relation of nozzle geometry,
exit and ambient conditions and resultant plume geometry are desired.
Practical scarfing angles have moderate effect on thrust magnitude and direction. As figure
2.22 indicates there’s a range of scarf angles for which axial thrust degradation is on the order of a couple of percent. The figure represents LAURA simulations set up for the thruster
configuration shown in the figure 2.21. Nozzle scarfing was performed as shown in the figure
2.23. Several grids were used, the finest had .84M points, and its unscarfed version is shown in the figure 2.24. There is a practical reason why even the large scarf angles result in moderate
thrust penalty. As the figure 2.25 indicates, pressure in the divergent section of the nozzle drops
very quickly, so that alterations of the nozzle, made far enough from throat do not change the integral in equation 2.4 significantly, which is reflected in the figure 2.22. Another way to think
of effect of scarfing is that its effect on thrust direction is mainly through the pressure term in
the equation 2.2, as the direction of velocity doesn’t change, but the pressure integral acquires a side projection. Notably, the scarf angle and the scarf location shown in the figure 2.23 are
Figure 2.22: Effect of scarf on predicted performance
Figure 2.23: Nozzle shape used for calculations at 65 degree scarf angle (showing complimentary 25 degree angle labeled)
2.1.5 Thruster plume
Geometry of the thruster plume is cited by Pindzola as one of the most important parameters
Figure 2.24: Fine (.84M points) grid used for nozzle calculations. Unscarfed grid is shown.
Figure 2.25: Representative pressure along the nozzle wall
application he appears to be considering. In a general case of a plume interacting with a wake of a blunt capsule the plume shape may not be as critical a parameter, as it is for a rocket.
Analysis of plume geometry is not a new field. Manuel Salas [26] developed an inviscid method
the plume. The method can capture lip shocks, termination shocks, as well as treat periodic
structures when they occur. This method doesn’t answer the question of turbulent transition of the plume boundary, and effects that might have on downstream plume development, but its
a quick and accurate tool for comparison of plume/wake scale between the flight vehicle and a
wind tunnel model.
Plumes of RCS thrusters are under-expanded for all trajectory conditions during entry due
to comparatively low backpressure that’s created in the capsule’s wake. Geometry and the
physics of an undisturbed thruster plume are explored in this section on the example of MSL thruster in as-built configuration. As the capsule decelerates through the atmosphere, pressure
in the wake is changing continuously as was shown in the figure 2.20. From near vacuum at the
entry interface, the base pressure will build up to its maximum at near peak dynamic pressure, which is followed by a decrease to the ambient pressure at low speeds.
Physics of the supersonic jet in an inviscid fluid are discussed in great detail in a classical
work of Pai [27]. As the flow exits the thruster it undergoes a 2D initial turn, where the turn angle and properties immediately downstream are governed by a Prandtl-Meyer function. As
the distance from nozzle lip increases, the 3D effects become important to the shape of the
plume and an axisymmetric correction must be introduced to the inviscid technique used. Pai discusses the method of characteristics as a tool to determine some aspects of the jet flowfield,
a method popular at the time of the work. Figure 2.26 shows possible plume structures, produced by under-expanded jets. The difference between the upper and lower schematic is the
transition from the regular to the Mach reflection. Jet shock can undergo a regular reflection
at the centerline, or it can transition to Mach reflection, where the oblique shock is connected to the centerline with a normal shock (also called termination shock, or Mach disk). The area
behind this normal shock is a high pressure and high temperature zone, that forms a
convergent-divergent nozzle flow further downstream (see, for example, [26]). The jet pressure ratio, gas properties (γ) and nozzle exit wall angle are some of the differentiators between the regular and
Mach reflection. Generally, as the jet shock strength increases, Mach reflection is more likely.
Figures 2.27 through 2.31 show the relative scale of RCS thruster plumes and the computed wake structure for MSL entry at Mach 22, 18, 14, 10 and 6. As the figures indicate the
undisturbed plume dimensions follow aftshell pressure (figure 2.20) inversely, with the smallest
plume occurring near maximum trajectory dynamic pressure. Large plume occurs at high altitude condition, where aftbody pressure is low, and at a supersonic condition, where pressure
drops again. In the early hypersonic regime the aftbody pressure is low enough to not expect
significant RCS-aero interaction. This will be demonstrated on the example of Phoenix capsule in the section on Phoenix analysis. Regardless of the conditions it is clear from the figures 2.27
through 2.31 that a thruster of adequate power produces a plume that will interfere with the
Figure 2.26: Regular (top) and Mach (bottom) reflections within the under-expanded jet
Figure 2.29: Plume at Mach 14 Figure 2.30: Plume at Mach 18
Figure 2.31: Plume at Mach 22
A particular challenge to analysis is presented by the dual thruster arrangement. It is not
uncommon to have a dual-string thruster arrangement, where pairs of thrusters are installed
such that the nozzles are parallel, and are placed very close to each other. The plume flowfield that is produced by such a system is characterized by a high pressure turbulent mixing zone,
and pair of shocks that traverse the inviscid part of each plume. Figure 2.32 shows the partial schematic of such a flow. Part of the flow to the right of the shown structure is usually turbulent
due to natural transition in the plume boundary and due to transition in the compression zone
2.2
Plume and Nozzle Scaling
Testing of RCS in ground facilities requires duplication of a number of relevant physical scales.
External flow would typically require to some degree replication of the free-stream Mach, Reynolds numbers, enthalpy, momentum thickness Reynolds number, especially if this is an
aeroheating test. Comparable properties of the gas mixture are also desired. In addition to
that, the nozzles and nozzle flow should be scaled appropriately. Scaling parameters, presented by Pindzola [4] for this problem result in the attempt to match pressure, momentum and
en-thalpy ratio. Pressure ratio is defined as the ratio of the jet exit to local ambient 2.5. Here,
some ambiguity exists in determining what the local ambient is, and whether it should include the dynamic component of pressure, in the case of strong crossflow. The former concern results
in a appropriate uncertainty that’s placed on the left and right hand side of the equation 2.5, while the latter concern leads to the equation 2.6.
Plocalf low
Pjet,exit
T est
=
Plocalf low
Pjet,exit
F light
(2.5)
Spaid and Cassel [3] indicate jet penetration into a supersonic stream related to a momentum ratio-type term. For the purposes of the RCS-gasdynamic interaction this quantity, as defined
in the equation 2.6 should use momentum outside the capsule’s shear layer. Flight-to-test
scal-ing change the relation between that local momentum and free-stream momentum. Specifically, free-stream enthalpy, dissociation in the shocklayer, surface roughness and effect of wake
tur-bulence on the separation location and wake closure angle all can influence the difference in the
momentum ratio.
QexitAexit
Q∞Aref
T est
=
QexitAexit
Q∞Aref
F light
(2.6)
HT∞−Hw
Hjet−Hw
T est
=
HT∞−Hw
Hjet−Hw
F light
(2.7)
Equation 2.7 formulates scaling to enthalpy. Enthalpy ratio between free stream and the jet
influences characteristics of RCS-induced aeroheating. This ratio can assume very high values at entry and low values at the end of the deceleration. For example, the enthalpy of the jet of a
hydrazine thruster is of the order of 3MJ/kg. Lunar return free-stream enthalpy at entry is of
the order 63 MJ/kg. By the time capsule’s deceleration is over the free-stream enthalpy is of the order of 0.3 MJ/kg. Clearly, the ratio of jet and free-stream enthalpies can assume a range of
values, and enthalpy potentials, referenced to the wall can be further altered due to variations
of wall temperature in flight. Figure 2.33 shows the relevant enthalpies graphically. As the capsule slows down free-stream enthalpy departs from being a square of free-stream velocity,
during flight. Two types of interactions are likely: the first type is interaction of the jet with
Figure 2.33: Flight Enthalpies, red line - jet enthalpy, black - free-stream
a nominally separated flow, where mixing of the jet with exterior flow will produce a complex
flow structure, and the aeroheating augmentation will be driven by some average of jet and
free-stream enthalpy. The second case is when the jet interacts with a nominally attached flow. In this second case the aeroheating horseshoe will be driven solely by the free-stream enthalpy,
and near-nozzle heating will be driven by the jet enthalpy. An example of the first type of
interaction is shown in the figure 2.34 where roll thrusters of Orion, nominally in separated zone, are simulated in LAURA at simulated wind tunnel conditions. In this case enthalpy ratio
is changed through the jet temperature. Evident effect on the horseshoe heating with increase
in jet temperature. The second type of an interaction is shown in figures 2.35 and 2.36. This example is of Orion yaw thrusters, which are nominally in attached supersonic crossflow. The
exterior interaction (horseshoe) shows little if any sensitivity to the enthalpy of the jet, but near nozzle phenomena are driven by it, for example the compression heating along the line splitting
the nozzles. The negative value of enthalpy ratio in one case is simply the manifestation of
indeterminance in the equation 2.7 at near-equal values of jet and wall enthalpies.
Generally, because of low free-stream enthalpies in ground facilities it is impossible to make
meaningful use of this parameter for blunt capsules. Testing for wake environments is generally
Figure 2.34: Predicted effect of enthalpy ratio on heating due to roll thruster
Figure 2.35: Predicted effect of enthalpy ratio on heating due to yaw thruster
due to wake establishment considerations), so the driving enthalpy on the separated aftbody is disproportionally low. It is possible to get the ratio itself to be close to flight, but at that
point the wall enthalpy and jet enthalpy may be very close in magnitude, making measurement
challenging. Relevance of enthalpy matching is, therefore, a questionable proposition for RCS testing of blunt capsules in low enthalpy flows. Given the above relations the parameters of
interest can be computed as shown in 2.8 and 2.9.
Pjet,exit T est=
Plocalf low T est·Pjetexit F light
Plocalf low F light
(2.8)
QexitAexit T est =
(Q∞Aref)test·(QexitAexit) F light
(Q∞Aref)F light
(2.9)
The exit diameter doesn’t strictly have to be identically scaled to the flight vehicle. It can be
Figure 2.36: Predicted effect of enthalpy ratio on heating due to yaw thruster, local effects
Additional challenges to RCS scaling include, for example, the duplication of chemical com-position of the flowfield. It is usually not possible to duplicate external flow (take, for
exam-ple,the CO2 atmosphere), nor the RCS effluent (non-equilibrium flow of combustion products). Matching molecular weights will only partly fill the requirement, as in most reacting
environ-ments the composition changes with location in the flowfield. It is possible to compensate for
Chapter 3
Analysis
3.1
CFD Modeling
Development of RCS modeling capability in LAURA and RCS modeling capability for blunt capsules in general was driven by the intent to assess aerodynamic-RCS interactions at
super-sonic speeds for MSL entry capsule. Aerothermal augmentation was not expected, nor was
there any expectation of the significant aero-RCS interaction at hypersonic speeds, the latter partly due to a misunderstanding of aftbody pressure and aftbody contribution to
aerodynam-ics at hypersonic speeds, in the context of the RCS authority. It was thought, that since the
forces and moments on a hypersonic capsule are dominated by the forebody, no reasonable amount of change of aftbody environment can be significant. Later relating aftbody changes
to the nominal thruster authority exposed the flaw in thinking, as for some capsules, thruster
activity can trigger changes in aftbody flow that will generate moments comparable to the thruster authority. this last point was later supported with the idea, that the aftbody
pres-sure can significantly exceed free-stream static prespres-sure during hypersonic flight. Effect of RCS thrusters on the aerothermal environment was found later to be significant for MSL, as will be
shown later. Analysis methodology developed over several years, and it benefited greatly from
the increase in computer availability. Initially the method involved the basic LAURA code, where several cells on the surface were set up to allow the outflow to be specified (this was put
into LAURA by Cheatwood [28]). Velocity, density and temperature were set consistent with
expected thruster values, and the number of cells was set to mimic the exit area of the thruster. This approach allowed (crudely) to develop a very coarse plume as essentially a protuberance
to the surrounding flow. This approach worked well enough to illustrate that aeroheating
con-cerns may be warranted at hypersonic speeds, once a plume is introduced into the flowfield. The slightly more complex approach involved the use of MORPH tool [29] to modify the flight
