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NASA NTRS2019

FUN3D and USM3D Analysis of the Propulsion Aerodynamic Workshop 2018 S-Duct Test Case

This work presents the results of Fun3D and USM3D analyses that were performed for the 4th AIAA Propulsion Aerodynamics Workshop (PAW). The PAW workshop is separated into three sections that focus on internal duct flows, nozzle flows and a special topic. This paper focuses on the internal duct flow section of PAW04 while an accompanying paper discusses the analyses performed for the nozzle portion. For the internal duct flow section, the PAW04 participants were provided with the two configurations consisting of an S-duct with and without aerodynamic interface plane (AIP) rake legs modeled. The participants were asked to perform a grid refinement study as well as a turbulence model study for the configuration with the rake legs. The analyses discussed here were performed on custom grids developed under the guidelines of the workshop. Additionally, the paper discusses the development and use of flow controllers for matching the desired flow characteristics. The results show that both solvers do well for predicting internal flow characteristics of the S-duct based on direct comparison with the experimental data. However, the CFD-to-CFD comparison proved to be more challenging due to the localized occurrence of supersonic flow near the rake legs when using the mass flow controller. A turbulence model study was performed to compare the two-equation SST model to the SA-QCR model. The results show that although the turbulence model does affect the solution, it makes a minimal impact on pressure recovery and inlet distortion intensity for this case. Suggestions for future workshops include gridding guidelines similar to those employed for the Drag Prediction Workshop series for the grid refinement study and a time accuracy study.

Carter, Melissa B.↗

NASA NTRS1993

CFD Analysis of Spray Combustion and Radiation in OMV Thrust Chamber

The Variable Thrust Engine (VTE), developed by TRW, for the Orbit Maneuvering Vehicle (OMV) uses a hypergolic propellant combination of Monomethyl Hydrazine (MMH) and Nitrogen Tetroxide (NTO) as fuel and oxidizer, respectively. The propellants are pressure fed into the combustion chamber through a single pintle injection element. The performance of this engine is dependent on the pintle geometry and a number of complex physical phenomena and their mutual interactions. The most important among these are (1) atomization of the liquid jets into fine droplets; (2) the motion of these droplets in the gas field; (3) vaporization of the droplets (4) turbulent mixing of the fuel and oxidizer; and (5) hypergolic reaction between MMH and NTO. Each of the above phenomena by itself poses a considerable challenge to the technical community. In a reactive flow field of the kind occurring inside the VTE, the mutual interactions between these physical processes tend to further complicate the analysis. The objective of this work is to develop a comprehensive mathematical modeling methodology to analyze the flow field within the VTE. Using this model, the effect of flow parameters on various physical processes such as atomization, spray dynamics, combustion, and radiation is studied. This information can then be used to optimize design parameters and thus improve the performance of the engine. The REFLEQS CFD Code is used for solving the fluid dynamic equations. The spray dynamics is modeled using the Eulerian-Lagrangian approach. The discrete ordinate method with 12 ordinate directions is used to predict the radiative heat transfer in the OMV combustion chamber, nozzle, and the heat shield. The hypergolic reaction between MMH and NTO is predicted using an equilibrium chemistry model with 13 species. The results indicate that mixing and combustion is very sensitive to the droplet size. Smaller droplets evaporate faster than bigger droplets, leading to a well mixed zone in the combustion chamber. The radiative heat flux at combustion chamber and nozzle walls are an order of negligible less than the conductive heat flux. Simulations performed with the heat shield show that a negligible amount of fluid is entrained into the heat shield region. However, the heat shield is shown to be effective in protecting the OMV structure surrounding the engine from the radiated heat.

Giridharan, M. G.↗

NASA NTRSDate not supplied

Mechanical Erosion Modeling of TPS Materials

The goal of this work is to predict the mechanical response of TPS materials, and specifically, to determine if there is additional surface recession in the heat shield’s surface as a result of mechanical erosion due to the mechanical and thermal loads experienced during atmospheric entry. To accomplish this, a solid mechanics module was integrated within the PATO material response code, enabling it to model the potential mechanical erosion in three steps: first, having the effective mechanical properties as function of temperature, the implemented stress analysis solver computes the stress and the displacement fields for the TPS material using the wall shear stress tensor, computed with the DPLR hypersonic CFD code, as boundary conditions; then, regions on the surface where the stress meets the failure criteria are identified; finally, the failed material is removed and the mesh is redistributed accordingly. The outcome is a model capable of predicting the total recession in the TPS material due to surface chemistry and mechanical erosion.

Stress Analysis↗

NASA NTRS2016

Modeling ARRM Xenon Tank Pressurization Using 1D Thermodynamic and Heat Transfer Equations

As a first step in understanding what ground support equipment (GSE) is required to provide external cooling during the loading of 5,000 kg of xenon into 4 aluminum lined composite overwrapped pressure vessels (COPVs), a modeling analysis was performed using Microsoft Excel. The goals of the analysis were to predict xenon temperature and pressure throughout loading at the launch facility, estimate the time required to load one tank, and to get an early estimate of what provisions for cooling xenon might be needed while the tanks are being filled. The model uses the governing thermodynamic and heat transfer equations to achieve these goals. Results indicate that a single tank can be loaded in about 15 hours with reasonable external coolant requirements. The model developed in this study was successfully validated against flight and test data. The first data set is from the Dawn mission which also utilizes solar electric propulsion with xenon propellant, and the second is test data from the rapid loading of a hydrogen cylindrical COPV. The main benefit of this type of model is that the governing physical equations using bulk fluid solid temperatures can provide a quick and accurate estimate of the state of the propellant throughout loading which is much cheaper in terms of computational time and licensing costs than a Computation Fluid Dynamics (CFD) analysis while capturing the majority of the thermodynamics and heat transfer.

Xenon storage↗

NASA NTRSDate not supplied

Simulating Underexpanded Plumes in Martian and Lunar Environments

While the Loci/Chem Computational fluid dynamics (CFD) application has been validated and used extensively for simulating launch environments in atmospheric conditions, use of this tool for simulating supersonic plumes at much lower ambient pressure requires further validation. Simulations of underexpanded plumes have been performed using Loci/Chem at Martian pressure to predict several metrics for laminar, turbulent, and impinging plumes. The CFD results are compared with an experimental data set for low Reynolds number plumes at these conditions in order to evaluate the current capability of the Loci/Chem tool for these types of environments. The CFD validation results to date show reasonable agreement with the experimental data across all the metrics of interest for the configurations considered. The Loci/Chem-Boltzmann tool is a hybrid continuum/rarefied flow solver which extends modeling capabilities to very low-pressure environments such as those on the Moon. The Loci/Chem-Boltzmann solver uses a gradient-based continuum breakdown criterion to restrict solution of the computationally expensive Boltzmann equation to only a subset of the domain, while using the Navier-Stokes equations elsewhere. This CFD application is under active development, and current efforts toward establishing production ready capability for evaluating Lunar plume surface interactions are well under way. Initial simulations of an Apollo Lunar excursion module indicate that several regions of the flow require solving the Boltzmann equations due to extreme rarefaction. Early simulations are promising, indicating reasonable overall computational time for a full 3D human scale lander simulation.

Plume Surface Interaction↗

NASA NTRSDate not supplied

Wall Modeled Large Eddy Simulations for NASA’s Jet Noise Consensus Database of Single-Flow, Round, Convergent Jets

A campaign of wall-modeled large-eddy simulations (WMLES) using structured curvilinear overlapping grids has been performed with the Launch Ascent and Vehicle Aerodynamics(LAVA) computational fluid dynamics (CFD) software to predict jet noise for single-stream axisymmetric round jets. The simulations address the new Prediction Uncertainty Reduction(PUR) technical challenge within the context of NASA’s Commercial Supersonic Technology(CST) project. The goal of PUR is to quantify and reduce uncertainties from scale-resolving simulations to assess noise characteristics of next generation quiet supersonic commercial jets during takeoff and landing conditions where the noise from the exhaust jet dominates. The focus of this effort is to generate a simulation database for single-stream axisymmetric round nozzles at several conditions both for static (no ambient co-flow), which is the focus of this article, and in-flight (flight stream co-flow) conditions, which are beyond the current scope. Nine different flow conditions ranging in jet exit Mach number from 0.38 to 1.0 with nozzle temperature ratios (NTR) from 0.84 to 2.7 have been conducted. Details of the structured overset grids, numerical discretization and wall-model are provided. Near-field comparisons to PIV data show great agreement for both velocity and normal stresses, however a systematic TKE overshoot at the nozzle exit is seen in the lip line shear-layer. A permeable Ffowcs Williams Hawkings (FWH) surface, enclosing the jet, is used to predict far-field noise from the simulated flow-field. Comparison of CFD predictions to microphone array measurements demonstrate excellent agreement within the resolved frequency range. A systematic under-prediction of far-aft observer angles larger than 150 degrees has been observed across all simulations. We achieved a cost reduction of an order of magnitude for these WMLES compared to an earlier study of this configuration due to algorithmic and software improvements. The accuracy of the results and short turnaround time demonstrate that WMLES within the LAVA framework is a cost-effective approach for jet noise predictions that could soon be incorporated into the design cycle of jet noise reduction technologies.

CST↗

NASA NTRS1992

NLS clutching bearing cavity flow analysis

A flow model of the NLS clutching bearing cavity was built for 2-D axisymmetric viscous analysis. From the computational fluid dynamics (CFD) approach, the tangential force exerted on the surfaces of the inner race was integrated to calculate the dividing torque which, in conjunction with the resistance torque, was used to predict the operating speed of the inner race. In order to further reduce the inner race rotation, the swirling flow at the cavity inlet was partially redirected to generate an opposing torque. Thirty six slanted slots were incorporated into the anti-vortex rib to achieve this goal. A 3-D flow analysis performed on this configuration indicates a drastic reduction of the driving torque and inner race RPM.

Tran, Ken↗

NASA NTRS2008

Comparison Between Numerically Simulated and Experimentally Measured Flowfield Quantities Behind a Pulsejet

Pulsed combustion is receiving renewed interest as a potential route to higher performance in air breathing propulsion systems. Pulsejets offer a simple experimental device with which to study unsteady combustion phenomena and validate simulations. Previous computational fluid dynamic (CFD) simulation work focused primarily on the pulsejet combustion and exhaust processes. This paper describes a new inlet sub-model which simulates the fluidic and mechanical operation of a valved pulsejet head. The governing equations for this sub-model are described. Sub-model validation is provided through comparisons of simulated and experimentally measured reed valve motion, and time averaged inlet mass flow rate. The updated pulsejet simulation, with the inlet sub-model implemented, is validated through comparison with experimentally measured combustion chamber pressure, inlet mass flow rate, operational frequency, and thrust. Additionally, the simulated pulsejet exhaust flowfield, which is dominated by a starting vortex ring, is compared with particle imaging velocimetry (PIV) measurements on the bases of velocity, vorticity, and vortex location. The results show good agreement between simulated and experimental data. The inlet sub-model is shown to be critical for the successful modeling of pulsejet operation. This sub-model correctly predicts both the inlet mass flow rate and its phase relationship with the combustion chamber pressure. As a result, the predicted pulsejet thrust agrees very well with experimental data.

Geng, Tao↗

NASA NTRS2010

Wind Tunnel Model Design for the Study of Plume Effects on Sonic Boom for Isolated Exhaust Nozzles

A low cost test capability was developed at the NASA Glenn Research Center 1- by 1-Foot Supersonic Wind Tunnel (SWT), with a goal to reduce the disturbance caused by supersonic aircraft flight over populated areas. This work focused on the shock wave structure caused by the exhaust nozzle plume. Analysis and design was performed on a new rig to test exhaust nozzle plume effects on sonic boom signature. Test capability included a baseline nozzle test article and a wind tunnel model consisting of a strut, a nosecone and an upper plenum. Analysis was performed on the external and internal aerodynamic configuration, including the shock reflections from the wind tunnel walls caused by the presence of the model nosecone. This wind tunnel model was designed to operate from Mach 1.4 to Mach 3.0 with nozzle pressure ratios from 6 to 12 and altitudes from 30,000 ft (4.36 psia) to 50,000 ft (1.68 psia). The model design was based on a 1 in. outer diameter, was 9 in. in overall length, and was mounted in the wind tunnel on a 3/8 in. wide support strut. For test conditions at 50,000 ft the strut was built to supply 90 psia of pressure, and to achieve 20 psia at the nozzle inlet with a maximum nozzle pressure of 52 psia. Instrumentation was developed to measure nozzle pressure ratio, and an external static pressure probe was designed to survey near field static pressure profiles at one nozzle diameter above the rig centerline. Model layout placed test nozzles between two transparent sidewalls in the 1 1 SWT for Schlieren photography and comparison to CFD analysis.

Castner, Raynold S.↗

NASA NTRS2013

NASA Tech Briefs, December 2013

Topics include: Microwave Kinetic Inductance Detector With; Selective Polarization Coupling; Flexible Microstrip Circuits for; Superconducting Electronics; CFD Extraction Tool for TecPlot From DPLR Solutions; RECOVIR Software for Identifying Viruses; Enhanced Contact Graph Routing (ECGR) MACHETE Simulation Model; Orbital Debris Engineering Model (ORDEM) v.3; Scatter-Reducing Sounding Filtration Using a Genetic Algorithm and Mean Monthly Standard Deviation; Thermo-Mechanical Methodology for Stabilizing Shape Memory Alloy Response; Hermetic Seal Designs for Sample Return Sample Tubes; Silicon Alignment Pins: An Easy Way To Realize a Wafer-to-Wafer Alignment; Positive-Buoyancy Rover for Under Ice Mobility; Electric Machine With Boosted Inductance to Stabilize Current Control; International Space Station-Based Electromagnetic Launcher for Space Science Payloads; Advanced Hybrid Spacesuit Concept Featuring Integrated Open Loop and Closed Loop Ventilation Systems; Data Quality Screening Service.

Source record↗

NASA NTRS2017

Application of Sweeping Jet Actuators on the NASA Hump Model and Comparison with CFDVAL2004 Experiments

Flow separation control over a wall-mounted hump model was studied experimentally to assess the performance of sweeping jet actuators. Results were compared to that of the 2004 CFD validation experiment (CFDVAL2004), which examined flow separation control with steady suction and unsteady zero-net-mass-flow actuators. Comparisons were carried out at low and high amplitude excitations. In addition to the active flow control methods, a passive flow control method (i.e., vortex generator) was used to complement the dataset. Steady/unsteady surface pressure measurements and surface oilflow visualization were used in the performance assessment of the actuators. The results indicated that the sweeping jet actuators are more effective than the steady suction and unsteady zero-net-mass-flow actuators. For the same momentum coefficient, the sweeping jet actuators produced more flow acceleration upstream of separation, more pressure recovery downstream, and consistently a smaller separation bubble.

Koklu, Mehti↗

NASA NTRS2016

Predictive Evaluations of Oxygen-Rich Hydrocarbon Combustion Gas-Centered Swirl Coaxial Injectors using a Flamelet-Based 3-D CFD Simulation Approach

NASA Marshall Space Flight Center (MSFC) has embarked upon a joint project with the Air Force to improve the state-of-the-art of space application combustion device design and operational understanding. One goal of the project is to design, build and hot-fire test a 40,000 pound-thrust Oxygen/Rocket Propellant-2 (RP-2) Oxygen-Rich staged engine at MSFC. The overall project goals afford the opportunity to test multiple different injector designs and experimentally evaluate the any effect on the engine performance and combustion dynamics. To maximize the available test resources and benefits, pre-test, combusting flow, Computational Fluid Dynamics (CFD) analysis was performed on the individual injectors to guide the design. The results of the CFD analysis were used to design the injectors for specific, targeted fluid dynamic features and the analysis results also provided some predictive input for acoustic and thermal analysis of the main Thrust Chamber Assembly (TCA). MSFC has developed and demonstrated the ability to utilize a computationally efficient, flamelet-based combustion model to guide the pre-test design of single-element Gas Centered Swirl Coaxial (GCSC) injectors. Previous, Oxygen/RP-2 simulation models utilizing the Loci-STREAM flow solver, were validated using single injector test data from the EC-1 Air Force test facility. The simulation effort herein is an extension of the validated, CFD driven, single-injector design approach applied to single injectors which will be part of a larger engine array. Time-accurate, Three-Dimensional, CFD simulations were performed for five different classes of injector geometries. Simulations were performed to guide the design of the injector to achieve a variety of intended performance goals. For example, two GCSC injectors were designed to achieve stable hydrodynamic behavior of the propellant circuits while providing the largest thermal margin possible within the design envelope. While another injector was designed to purposefully create a hydrodynamic instability in the fuel supply circuit as predicted by the CFD analysis. Future multi-injector analysis and testing will indicate what if any changes occur in the predicted behavior for the single-element injector when the same injector geometry is placed in a multi-element array.

Richardson, Brian R.↗

NASA NTRS2004

NASA Multidimensional Stirling Convertor Code Developed

A high-efficiency Stirling Radioisotope Generator (SRG) for use on potential NASA Space Science missions is being developed by the Department of Energy, Lockheed Martin, Stirling Technology Company, and the NASA Glenn Research Center. These missions may include providing spacecraft onboard electric power for deep space missions or power for unmanned Mars rovers. Glenn is also developing advanced technology for Stirling convertors, aimed at substantially improving the specific power and efficiency of the convertor and the overall power system. Performance and mass improvement goals have been established for second- and third-generation Stirling radioisotope power systems. Multiple efforts are underway to achieve these goals, both in house at Glenn and under various grants and contracts. These efforts include the development of a multidimensional Stirling computational fluid dynamics code, high-temperature materials, advanced controllers, an end-to-end system dynamics model, low-vibration techniques, advanced regenerators, and a lightweight convertor. Under a NASA grant, Cleveland State University (CSU) and its subcontractors, the University of Minnesota (UMN) and Gedeon Associates, have developed a twodimensional computer simulation of a CSUmod Stirling convertor. The CFD-ACE commercial software developed by CFD Research Corp. of Huntsville, Alabama, is being used. The CSUmod is a scaled version of the Stirling Technology Demonstrator Convertor (TDC), which was designed and fabricated by the Stirling Technology Company and is being tested by NASA. The schematic illustrates the structure of this model. Modeled are the fluid-flow and heat-transfer phenomena that occur in the expansion space, the heater, the regenerator, the cooler, the compression space, the surrounding walls, and the moving piston and displacer. In addition, the overall heat transfer, the indicated power, and the efficiency can be calculated. The CSUmod model is being converted to a two-dimensional model of the TDC at NASA Glenn. Validation of the multidimensional Stirling code is an important part of the grant effort. UMN has been generating data in an oscillating-flow test facility using two different test sections: a 90 turn and a cooler/regenerator/heater test section. CSU has created computational fluid dynamics models of both these test sections and has been making comparisons with the data, then improving their models to improve the agreement with the test data. CSU has also been using data available in the literature for code validation. UMN is now preparing to begin fabrication of a new 180 turn test section that will be more representative of certain portions of the Stirling engine geometry. Simulations to almost periodic steady state with the two-dimensional CSUmod model indicate that, to reach periodic steady state on a single 2-GHz desktop computer, 75 to 100 complete simulation cycles would be required and between 1 and 2 months of computer time. Therefore, Glenn has purchased the first 8 computers, of a 64-computer cluster, to be run in parallel to accelerate the simulation. On the basis of CFD Research Corp.'s experience with running the parallelized version of CFD-ACE on their clusters, we estimate that the complete 64-computer cluster will reduce simulation computing time by a factor of about 40. Plans are to continue development of these multidimensional Stirling codes and to use them to study the fluid-flow and heat-transfer phenomena that occur inside Stirling convertors. This is expected to lead to improved thermodynamic loss understanding, onedimensional design and performance codes, and engine performance.

Tew, Roy C.↗

NASA NTRSDate not supplied

Summary of the First AIAA Stability and Control Prediction Workshop

Results from the First AIAA Stability and Control Prediction Workshop are summarized in this paper. The workshop series was developed in support of three primary objectives: (1) to establish best practices for the prediction of stability and control derivatives using industry-standard Computational Fluid Dynamics (CFD) solvers, (2) to provide an impartial forum for evaluating the effectiveness of Reynolds-averaged-Navier-Stokes- and Detached-Eddy-Simulation-based modeling techniques, and (3) to identify areas in need of additional research and development. To address these objectives, the inaugural workshop focused on generating computational aerodynamic predictions for the ONERA version of the NASA/Boeing Common Research Model. The configuration includes the wing, body, horizontal tail, and a vertical tail designed by ONERA. While longitudinal wind tunnel test data for the model had been previously documented, unpublished lateral test data at small sideslip angles provided a unique opportunity for participants to generate blind computational predictions for wind tunnel data comparisons. Additional test cases included assessments of the Mach number effect on static lateral/directional stability and the impact of the wind tunnel sting on longitudinal stability. Participants were invited to generate solutions using two workshop-provided series of structured overset and unstructured grids, in addition to any participant custom grids of interest. Total and component-level breakdowns for the force and moment coefficients for each test case are presented, as well as sectional pressure distribution data on the wing and tail components, to assess the agreement between several different Reynolds-averaged Navier-Stokes CFD solvers.

CFD↗

NASA NTRS2017

Lessons Learned from Inlet Integration Analysis of NASA's Low Boom Flight Demonstrator

In 2016, NASA's Aeronautics Research Mission Directorate announced the New Aviation Horizons Initiative with a goal of designing/building several X-Planes, including a Low Boom Flight Demonstrator (LBFD). That same year, NASA awarded a contract to Lockheed Martin (LM) to advance the LBFD concept through preliminary design. Several configurations of the LBFD aircraft were analyzed by both LM engineers and NASA researchers. This presentation focuses on some of the CFD simulations that were run by NASA Glenn researchers. NASA's FUN3D V13.1 code was used for all adjoint-based grid refinement studies and Spalart-Allmaras turbulence model was used during adaptation. It was found that adjoint-based grid adaptation did not accurately capture inlet performance for high speed top-aft-mounted propulsion.

Adjoint-based Grid Adaptatio↗

NASA NTRSDate not supplied

Comparisons Between NO PLIF Imaging and CFD Simulations of Mixing Flowfields for High-Speed Fuel Injectors

The current work compares experimentally and computationally obtained nitric oxide (NO) planar laser-induced fluorescence (PLIF) images of the mixing flowfields for three types of high-speed fuel injectors: a strut, a ramp, and a rectangular flushwall. These injection devices, which exhibited promising mixing performance at lower flight Mach numbers, are currently being studied as a part of the Enhanced Injection and Mixing Project (EIMP) at the NASA Langley Research Center. The EIMP aims to investigate scramjet fuel injection and mixing physics, and improve the understanding of underlying physical processes relevant to flight Mach numbers greater than eight. In the experiments conducted in the NASA Langley Arc-Heated Scramjet Test Facility (AHSTF), the injectors are placed downstream of a Mach 6 facility nozzle, which simulates the high Mach number air flow at the entrance of a scramjet combustor. Helium is used as an inert substitute for hydrogen fuel. Both schlieren and PLIF techniques are applied to obtain mixing flowfield flow visualizations. The experimental PLIF is obtained by using a UV laser sheet to interrogate a plane of the flow by exciting fluorescence from the NO molecules that are present in the AHSTF air. Consequently, the absence of signal in the resulting PLIF images is an indication of pure helium (fuel). The computational PLIF is obtained by applying a fluorescence model for NO to the results of the Reynolds-averaged simulations (RAS) of the mixing flowfield carried out using the VULCAN-CFD solver. This approach is required because the PLIF signal is a nonlinear function of not only NO concentration, but also pressure, temperature, and the flow velocity. This complexity allows additional flow features to be identified and compared with those obtained from the computational fluid dynamics (CFD) simulations, however, such comparisons are only semiquantitative. Three-dimensional image reconstruction, similar to that used in magnetic resonance imaging, is also used to obtain images in the streamwise and spanwise planes from select cross-stream PLIF plane data. Synthetic schlieren is also computed from the RAS data. Good agreement between the experimental and computational results provides increased confidence in the CFD simulations for investigations of injector performance.

PLIF↗

NASA NTRSDate not supplied

Comparisons Between NO PLIF Imaging and CFD Simulations of Mixing Flowfields for High-Speed Fuel Injectors

PLIF↗

NASA NTRS2013

Supersonic Pitch Damping Predictions of Blunt Entry Vehicles from Static CFD Solutions

A technique for predicting supersonic pitch damping of blunt axisymmetric bodies from static CFD data is presented. The contributions to static pitching moment due to forebody and aftbody pressure distributions are broken out and considered separately. The one-dimension moment equation is cast to model the separate contributions from forebody and aftbody pressures with no traditional damping term included. The aftbody contribution to pitching moment is lagged by a phase angle of the natural oscillation period. This lag represents the time for aftbody wake structures to equilibrate while the body is oscillation. The characteristic equation of this formulation indicates that the lagged backshell moment adds a damping moment equivalent in form to a constant pitch damping term. CFD calculations of the backshell's contribution to the static pitching moment for a range of angles-of-attack is used to predict pitch damping coefficients. These predictions are compared with ballistic range data taken of the Mars Exploration Rover (MER) capsule and forced oscillation data of the Mars Viking capsule. The lag model appears to capture dynamic stability variation due to backshell geometry as well as Mach number.

Schoenenberger, Mark↗