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NASA NTRS1995

Aperture Shield Materials Characterized and Selected for Solar Dynamic Space Power System

The aperture shield in a solar dynamic space power system is necessary to prevent thermal damage to the heat receiver should the concentrated solar radiation be accidentally or intentionally focused outside of the heat receiver aperture opening and onto the aperture shield itself. Characterization of the optical and thermal properties of candidate aperture shield materials was needed to support the joint U.S./Russian solar dynamic space power effort for Mir. The specific objective of testing performed at the NASA Lewis Research Center was to identify a high-temperature material with a low specular reflectance, a low solar absorptance, and a high spectral emittance so that during an off-pointing event, the amount of solar energy reflecting off the aperture shield would be small, the ratio of solar absorptance to spectral emittance would provide the lowest possible equilibrium temperature, and the integrity of the aperture shield would remain intact.

Source record↗

NASA NTRS2015

Unsteady Three-Dimensional Simulation of a Shear Coaxial GO2/GH2 Rocket Injector with RANS and Hybrid-RAN-LES/DES Using Flamelet Models

Historically, the analysis and design of liquid rocket engines (LREs) has relied on full‐scale testing and one‐dimensional empirical tools. The testing is extremely expensive and the one‐dimensional tools are not designed to capture the highly complex, and multi‐dimensional features that are inherent to LREs. Recent advances in computational fluid dynamics (CFD) tools have made it possible to predict liquid rocket engine performance, stability, to assess the effect of complex flow features, and to evaluate injector‐driven thermal environments, to mitigate the cost of testing. Extensive efforts to verify and validate these CFD tools have been conducted, to provide confidence for using them during the design cycle. Previous validation efforts have documented comparisons of predicted heat flux thermal environments with test data for a single element gaseous oxygen (GO2) and gaseous hydrogen (GH2) injector. The most notable validation effort was a comprehensive validation effort conducted by Tucker et al. [1], in which a number of different groups modeled a GO2/GH2 single element configuration by Pal et al [2]. The tools used for this validation comparison employed a range of algorithms, from both steady and unsteady Reynolds Averaged Navier‐Stokes (U/RANS) calculations, large‐eddy simulations (LES), detached eddy simulations (DES), and various combinations. A more recent effort by Thakur et al. [3] focused on using a state‐of‐the‐art CFD simulation tool, Loci/STREAM, on a two‐dimensional grid. Loci/STREAM was chosen because it has a unique, very efficient flamelet parameterization of combustion reactions that are too computationally expensive to simulate with conventional finite‐rate chemistry calculations. The current effort focuses on further advancement of validation efforts, again using the Loci/STREAM tool with the flamelet parameterization, but this time with a three‐dimensional grid. Comparisons to the Pal et al. heat flux data will be made for both RANS and Hybrid RANSLES/ Detached Eddy simulations (DES). Computation costs will be reported, along with comparison of accuracy and cost to much less expensive two‐dimensional RANS simulations of the same geometry.

Westra, Doug G.↗

NASA NTRS2016

Simulation of an Electromechanical Spin Motor System of a Control Moment Gyroscope

A two-phase brushless DC motor (BDCM) with pulse-width modulated (PWM) voltage drive is simulated to control the flywheel speed of a control moment gyroscope (CMG). An overview of a double-gimballed control moment gyroscope (DGCMG) assembly is presented along with the CMG torque effects on the spacecraft. The operating principles of a two-phase brushless DC motor are presented and the system's electro-mechanical equations of motion are developed for the root-mean-square (RMS) currents and wheel speed. It is shown that the system is an extremely "stiff" set of first-order equations for which an implicit Euler integrator is required for a stable solution. An adaptive proportional voltage controller is presented which adjusts the PWM voltages depending on several control modes for speed, current, and torque. The simulation results illustrate the interaction between the electrical system and the load dynamics and how these influence the overall performance of the system. As will be shown, the CMG spin motor model can directly provide electrical power use and thermal power output to spacecraft subsystems for effective (average) calculations of CMG power consumption.

Inampudi, Ravi↗

NASA NTRS1995

Experimental Results from the Thermal Energy Storage-1 (TES-1) Flight Experiment

The Thermal Energy Storage-1 (TES-1) is a flight experiment that flew on the Space Shuttle Columbia (STS-62), in March 1994, as part of the OAST-2 mission. TES-1 is the first experiment in a four experiment suite designed to provide data for understanding the long duration microgravity behavior of thermal energy storage fluoride salts that undergo repeated melting and freezing. Such data have never been obtained before and have direct application for the development of space-based solar dynamic (SD) power systems. These power systems will store solar energy in a thermal energy salt such as lithium fluoride or calcium fluoride. The stored energy is extracted during the shade portion of the orbit. This enables the solar dynamic power system to provide constant electrical power over the entire orbit. Analytical computer codes have been developed for predicting performance of a spaced-based solar dynamic power system. Experimental verification of the analytical predictions is needed prior to using the analytical results for future space power design applications. The four TES flight experiments will be used to obtain the needed experimental data. This paper will focus on the flight results from the first experiment, TES-1, in comparison to the predicted results from the Thermal Energy Storage Simulation (TESSIM) analytical computer code. The TES-1 conceptual development, hardware design, final development, and system verification testing were accomplished at the NASA lewis Research Center (LeRC). TES-1 was developed under the In-Space Technology Experiment Program (IN-STEP), which sponsors NASA, industry, and university flight experiments designed to enable and enhance space flight technology. The IN-STEP Program is sponsored by the Office of Space Access and Technology (OSAT).

Wald, Lawrence W.↗

NASA NTRS1991

Advanced development receiver thermal vacuum tests with cold wall

The first ever testing of a full size solar dynamic heat receiver using high temperature thermal energy storage was completed. The heat receiver was designed to meet the requirements for operation on the Space Station Freedom. The purpose of the test program was to quantify the receiver thermodynamic performance, its operating temperatures, and thermal response to changes in environmental and power module interface boundary conditions. The heat receiver was tested in a vacuum chamber with liquid nitrogen cold shrouds and an aperture cold plate to partially simulate a low Earth orbit environment. The cavity of the receiver was heated by an infrared quartz lamp heater with 30 independently controllable zones to produce flux distributions typical of candidate concentrators. A closed Brayton cycle engine simulator conditioned a helium xenon gas mixture to specific interface conditions to simulate various operational modes of the solar dynamic power module. Inlet gas temperature, pressure, and flow rate were independently varied. A total of 58 simulated orbital cycles were completed during the test conduct period. The test hardware, execution of testing, test data, and post test inspections are described.

Sedgwick, Leigh M.↗

NASA NTRS2007

Thermal Analysis on Plume Heating of the Main Engine on the Crew Exploration Vehicle Service Module

The crew exploration vehicle (CEV) service module (SM) main engine plume heating is analyzed using multiple numerical tools. The chemical equilibrium compositions and applications (CEA) code is used to compute the flow field inside the engine nozzle. The plume expansion into ambient atmosphere is simulated using an axisymmetric space-time conservation element and solution element (CE/SE) Euler code, a computational fluid dynamics (CFD) software. The thermal analysis including both convection and radiation heat transfers from the hot gas inside the engine nozzle and gas radiation from the plume is performed using Thermal Desktop. Three SM configurations, Lockheed Martin (LM) designed 604, 605, and 606 configurations, are considered. Design of multilayer insulation (MLI) for the stowed solar arrays, which is subject to plume heating from the main engine, among the passive thermal control system (PTCS), are proposed and validated.

Wang, Xiao-Yen J.↗

NASA NTRS2011

Space Shuttle Main Engine - The Relentless Pursuit of Improvement

The Space Shuttle Main Engine (SSME) is the only reusable large liquid rocket engine ever developed. The specific impulse delivered by the staged combustion cycle, substantially higher than previous rocket engines, minimized volume and weight for the integrated vehicle. The dual pre-burner configuration permitted precise mixture ratio and thrust control while the fully redundant controller and avionics provided a very high degree of system reliability and health diagnosis. The main engine controller design was the first rocket engine application to incorporate digital processing. The engine was required to operate at a high chamber pressure to minimize engine volume and weight. Power level throttling was required to minimize structural loads on the vehicle early in flight and acceleration levels on the crew late in ascent. Fatigue capability, strength, ease of assembly and disassembly, inspectability, and materials compatibility were all major considerations in achieving a fully reusable design. During the multi-decade program the design evolved substantially using a series of block upgrades. A number of materials and manufacturing challenges were encountered throughout SSME s history. Significant development was required for the final configuration of the high pressure turbopumps. Fracture control was implemented to assess life limits of critical materials and components. Survival in the hydrogen environment required assessment of hydrogen embrittlement. Instrumentation systems were a challenge due to the harsh thermal and dynamic environments within the engine. Extensive inspection procedures were developed to assess the engine components between flights. The Space Shuttle Main Engine achieved a remarkable flight performance record. All flights were successful with only one mission requiring an ascent abort condition, which still resulted in an acceptable orbit and mission. This was achieved in large part via extensive ground testing to fully characterize performance and to establish acceptable life limits. During the program over a million seconds of accumulated test and flight time was achieved. Post flight inspection and assessment was a key part of assuring proper performance of the flight hardware. By the end of the program the predicted reliability had improved by a factor of four. These unique challenges, evolution of the design, and the resulting reliability will be discussed in this paper.

VanHooser, Katherine P.↗

NASA NTRSDate not supplied

RST Optical Telescope Integration and Test Preparation

The OTA for the Nancy Grace Roman Space Telescope includes the primary mirror, secondary mirror, and aft optics for guiding light into the Wide Field Instrument and the Coronagraph Instrument. The telescope is taking shape as the tested optical mirror assemblies are integrated. The assemblies have been thermal cycled to the cold temperatures for infrared operation, load tested to launch loads, vibration tested, and optically tested. Testing included launch-level vibration testing of the 2.4-meter light-weighted primary mirror assembly. In addition, the telescope control electronics (TCE) box has been fully assembled and the environmental testing of the TCE is progressing. Pictures and descriptions of the integration and test progress are provided, along with performance results measured at these levels of assemblies. Planning and test equipment preparation for the telescope thermal vacuum testing continues including plans to take advantage of the large dynamic range available with focus diversity phase retrieval and a Shack-Hartmann wavefront sensor for the gravity-sagged primary mirror.

Tony L Whitman↗

NASA NTRS2017

Dynamic Testbed Demonstration of WFIRST Coronagraph Low Order Wavefront Sensing and Control (LOWFS/C)

To maintain the required performance of WFIRST Coronagraph in a realistic space environment, a Low Order Wavefront Sensing and Control (LOWFS/C) subsystem is necessary. The LOWFS/C uses a Zernike wavefront sensor (ZWFS) with the phase shifting disk combined with the starlight rejecting occulting mask. For wavefront error corrections, WFIRST LOWFS/C uses a fast steering mirror (FSM) for line-of-sight (LoS) correction, a focusing mirror for focus drift correction, and one of the two deformable mirrors (DM) for other low order wavefront error (WFE) correction. As a part of technology development and demonstration for WFIRST Coronagraph, a dedicated Occulting Mask Coronagraph (OMC) testbed has been built and commissioned. With its configuration similar to the WFIRST flight coronagraph instrument the OMC testbed consists of two coronagraph modes, Shaped Pupil Coronagraph (SPC) and Hybrid Lyot Coronagraph (HLC), a low order wavefront sensor (LOWFS), and an optical telescope assembly (OTA) simulator which can generate realistic LoS drift and jitter as well as low order wavefront error that would be induced by the WFIRST telescope’s vibration and thermal changes. In this paper, we will introduce the concept of WFIRST LOWFS/C, describe the OMC testbed, and present the testbed results of LOWFS sensor performance. We will also present our recent results from the dynamic coronagraph tests in which we have demonstrated of using LOWFS/C to maintain the coronagraph contrast with the presence of WFIRST-like line-of-sight and low order wavefront disturbances.

Zhou, Hanying↗

NASA NTRS1991

Mechanical and thermal disturbances of the PSR Moderate Focus-Mission Structure

The primary objective of this paper is to evaluate the optical pointing performance of the PSR Moderate Focus-Mission Structure when subjected to both mechanical and thermal disturbances. The mechanical disturbances are based on secondary mirror chopping. Results indicate that dynamic responses of the primary reflector and the secondary reflector subjected to chopping disturbances of the secondary reflector about its center of mass are within the figure maintenance control capabilities. The effects of modal damping, truss-type secondary support, interface boundary constraints, and alternate configurations, are also evaluated in the analysis. Thermal distortions of the structure were also evaluated based on the on-orbit temperature profiles derived from the submillimeter telescope missions. Results from thermal deformation analysis indicate that figure initialization control is needed for the PSR Moderate Focus-Mission. However, a figure maintenance system may not be required if adequate thermal isolation is incorporated into the support truss design for the PSR Moderate Focus-Mission Structure.

Shih, Choon-Foo↗

NASA NTRS1998

Detailed Experimental Data for CFD Code Validation

Recent interest in low cost, reliable access to space has generated increased interest in advanced technology approaches to space transportation systems. A key to the success of such programs lies in the development of advanced propulsion systems capable of achieving the performance and operations goals required for the next generation of space vehicles. One extremely promising approach involves the combination of rocket and air-breathing engines into a rocket-based combined-cycle engine (RBCC). A key element of that engine is the rocket ejector that is utilized in the zero to Mach two operating regime. Studies of RBCC engine concepts are not new and studies dating back thirty years are well documented in the literature. However, studies focused on the rocket ejector mode of the RBCC cycle are lacking. The present investigation utilizes an integrated experimental and computation fluid dynamics (CFD) approach to examine critical rocket ejector performance issues. In particular, the development of a predictive methodology capable of performance prediction is a key objective in order to analyze thermal choking and its control, primary/secondary pressure matching considerations, and effects of nozzle expansion ratio. To achieve this objective, the present study emphasizes obtaining new data using advanced optical diagnostics such as Schlieren photography and Raman spectroscopy, and CFD techniques to investigate mixing in the rocket ejector mode. A new research facility for the study of the rocket ejector mode has been developed. In the last milestone report, the operational capabilities of this research facility were described. In this milestone report, the experimentally obtained measurements for CFD code validation are presented and discussed.

Santoro, Robert J.↗

NASA NTRS1997

Rocket Ejector Studies for Application to RBCC Engines: An Integrated Experimental/CFD Approach

Recent interest in low cost, reliable access to space has generated increased interest in advanced technology approaches to space transportation systems. A key to the success of such programs lies in the development of advanced propulsion systems capable of achieving the performance and operations goals required for the next generation of space vehicles. One extremely promising approach involves the combination of rocket and air- breathing engines into a rocket-based combined-cycle engine (RBCC). A key element of that engine is the rocket ejector which is utilized in the zero to Mach two operating regime. Studies of RBCC engine concepts are not new and studies dating back thirty years are well documented in the literature. However, studies focused on the rocket ejector mode of the RBCC cycle are lacking. The present investigation utilizes an integrated experimental and computation fluid dynamics (CFD) approach to examine critical rocket ejector performance issues. In particular, the development of a predictive methodology capable of performance prediction is a key objective in order to analyze thermal choking and its control, primary/secondary pressure matching considerations, and effects of nozzle expansion ratio. To achieve this objective, the present study emphasizes obtaining new data using advanced optical diagnostics such as Raman spectroscopy and CFD techniques to investigate mixing in the rocket ejector mode. A new research facility for the study of the rocket ejector mode is described along with the diagnostic approaches to be used. The CFD modeling approach is also described along with preliminary CFD predictions obtained to date.

Pal, S.↗

NASA NTRS2003

Relative Motion of Two Spacecraft Near the Sun-Earth L2 Point

Over the next two decades international space agencies including the National Aeronautics and Space Administration and the European Space Agency are proposing space missions which employ distributed spacecraft technologies to enable vast improvements in remote sensing performance as compared to fundamental performance limitations associated with fairing sizes of even the largest launch vehicles. These missions will require numerous advanced technologies to enable some extreme scientific goals. However, on the critical path to developing many of those technologies, understanding realistic achievable performance, and formulating such missions involving formation flying spacecraft, is the detailed understanding of the vehicle relative motion in the appropriate dynamic environment. Due to the appealing gravitational and thermal environment, the Sun-Earth L(sub 2) point is a strong candidate for placement of many of these missions. Henceforth, this paper begins to unravel the dynamics of relative motion near L(sub 2), with particular consideration given to the ultimate requirements for flying space- craft in precise formation. This work is meant to be a predecessor to detailed formation flying mission analysis efforts in the areas of formation design, formation control, and relative navigation.

Collange, Guillaume↗

NASA NTRS2020

Mars Ascent Vehicle Hybrid Propulsion Configuration

As part of a Mars Sample Return (MSR) campaign, two Mars Ascent Vehicle (MAV) configurations have been designed in parallel. Each ascent vehicle configuration has a different propulsion system which ultimately leads to two unique vehicle designs. As part of a Preliminary Architecture Assessment (PAA), these vehicle designs were developed to the same level of maturity in order to inform the selection of one of the vehicles as the point of departure design for the campaign. The selection will be made in November 2019. The initial MSR architecture called for a hybrid-based propulsion MAV. This type of propulsion system calls for a solid wax motor that would utilize liquid MON-25 as an oxidizer. Hybrid rocket propulsion allows for more flexibility than traditional solid or liquid propulsion options, and typically benefits from the advantages of both. A hybrid motor can be throttled and shut down easily, and avoids significant risk in manufacturing and handling. On a theoretical level, hybrid motors perform at a higher specific impulse (Isp) than solid motors. The primary disadvantage of hybrid motors comes from additional complexity and significantly less flight heritage and low Technology Readiness Level (TRL). This paper describes the design of the hybrid propulsion configuration. An additional paper will be published describing the design of the solid propulsion configuration1. The hybrid propulsion configuration MAV was developed in 2019 by NASA Marshall Space Flight Center (MSFC) in association with NASA Jet Propulsion Laboratory (JPL). It features a Single Stage to Orbit (SSTO) design with an SP7A solid wax fuel and MON-25 liquid oxidizer. The liquid portion of the vehicle allows for a Liquid Injection Thrust Vector Controller (LITVC) as well as hypergolic propellant additives for ignition. The vehicle was designed to deliver approximately 0.31kg of Martian geological samples to a circular orbit at Mars of 343km at a 25o inclination. Although hybrid propulsion in general has been used on launch vehicles in the past, the integrated vehicle subsystems that operate in conjunction with these propulsion elements do not typically operate in a Martian environment, which in this application can get as cold as -40oC. The PAA advanced the maturity of these subsystems by performing detailed design and analysis on the vehicle with respect to structures and mechanisms, Guidance/Navigation/Control (GNC) systems, avionics, Reaction Control System (RCS), LITVC, thermal environments, and advanced Computational Fluid Dynamics (CFD). This paper will summarize the results of these studies.

Yaghoubi, Darius↗

NASA NTRS2020

Mars Ascent Vehicle Solid Propulsion Configuration

As part of a Mars Sample Return (MSR) campaign, two Mars Ascent Vehicle (MAV) configurations have been designed in parallel. Each ascent vehicle configuration has a different propulsion system, which ultimately leads to two unique vehicle designs. As part of a Preliminary Architecture Assessment (PAA), these vehicle designs were developed to the same level of maturity in order to inform the selection of one of the vehicles as the point of departure design for the campaign. The selection will be made in November 2019. Although the initial MSR architecture called for a hybrid-based propulsion MAV featuring solid wax fuel with liquid oxidizer, a configuration using more traditional solid propulsion was developed as an additional risk mitigation option. Though lacking in the single stage to orbit (SSTO) and throttle flexibility of a hybrid configuration, a solid configuration vehicle allows a simpler design with significantly longer flight heritage and higher Technology Readiness Level (TRL). This paper describes the design of the solid propulsion configuration. An additional paper will be published describing the design of the hybrid propulsion configuration. The solid propulsion configuration MAV was developed in 2019 by NASA Marshall Space Flight Center (MSFC) in association with NASA Jet Propulsion Laboratory (JPL). It features two stages with a modified STAR-17 motor for the second stage and a traditional electromechanical actuator Thrust Vector Controller (TVC). The vehicle was designed to deliver approximately 0.47kg of Martian geological samples to a circular orbit at Mars of 343km at a 25° inclination. Although solid motor designs in general are at a relatively high TRL, the integrated vehicle subsystems that operate in conjunction with these propulsion elements do not typically operate in a Martian environment, which in this application can get as cold as -40°C. The PAA advanced the maturity of these subsystems by performing detailed design and analysis on the vehicle with respect to structures and mechanisms, Guidance/Navigation/Control (GNC) systems, avionics, Reaction Control System (RCS), TVC, thermal environments, and advanced Computational Fluid Dynamics (CFD). This paper will summarize the results of these studies.

Yaghoubi, Darius↗

NASA NTRS2020

Mars Ascent Vehicle Solid Propulsion Configuration

As part of a Mars Sample Return (MSR) campaign, two Mars Ascent Vehicle (MAV) configurations have been designed in parallel. Each ascent vehicle configuration has a different propulsion system, which ultimately leads to two unique vehicle designs. As part of a Preliminary Architecture Assessment (PAA), these vehicle designs were developed to the same level of maturity in order to inform the selection of one of the vehicles as the point of departure design for the campaign. The selection will be made in November 2019. Although the initial MSR architecture called for a hybrid-based propulsion MAV featuring solid wax fuel with liquid oxidizer, a configuration using more traditional solid propulsion was developed as an additional risk mitigation option. Though lacking in the single stage to orbit (SSTO) and throttle flexibility of a hybrid configuration, a solid configuration vehicle allows a simpler design with significantly longer flight heritage and higher Technology Readiness Level (TRL). This paper describes the design of the solid propulsion configuration. An additional paper will be published describing the design of the hybrid propulsion configuration. The solid propulsion configuration MAV was developed in 2019 by NASA Marshall Space Flight Center (MSFC) in association with NASA Jet Propulsion Laboratory (JPL). It features two stages with a modified STAR-17 motor for the second stage and a traditional electromechanical actuator Thrust Vector Controller (TVC). The vehicle was designed to deliver approximately 0.47kg of Martian geological samples to a circular orbit at Mars of 343km at a 25° inclination. Although solid motor designs in general are at a relatively high TRL, the integrated vehicle subsystems that operate in conjunction with these propulsion elements do not typically operate in a Martian environment, which in this application can get as cold as -40°C. The PAA advanced the maturity of these subsystems by performing detailed design and analysis on the vehicle with respect to structures and mechanisms, Guidance/Navigation/Control (GNC) systems, avionics, Reaction Control System (RCS), TVC, thermal environments, and advanced Computational Fluid Dynamics (CFD). This paper will summarize the results of these studies.

Yaghoubi, Darius↗

NASA NTRS1999

Shock Wave Dynamics in Weakly Ionized Plasmas

An investigation of the dynamics of shock waves in weakly ionized argon plasmas has been performed using a pressure ruptured shock tube. The velocity of the shock is observed to increase when the shock traverses the plasma. The observed increases cannot be accounted for by thermal effects alone. Possible mechanisms that could explain the anomalous behavior include a vibrational/translational relaxation in the nonequilibrium plasma, electron diffusion across the shock front resulting from high electron mobility, and the propagation of ion-acoustic waves generated at the shock front. Using a turbulence model based on reduced kinetic theory, analysis of the observed results suggest a role for turbulence in anomalous shock dynamics in weakly ionized media and plasma-induced hypersonic drag reduction.

Johnson, Joseph A., III↗

NASA NTRS1989

The transient performance of a two-phase fluid reservoir

Thermal control of future large, high power spacecraft will require a two-phase fluid central bus. The two-phase fluid reservoir is a critical component in the two-phase fluid bus. It both controls the saturation temperature and provides a space for volumetric changes. A dynamic reservoir simulation model does not currently exist, but it is needed to expedite efforts and reduce risk. During 1989 an effort was made to develop a simulation model of the transient performance of a two-phase fluid reservoir. As a beginning, a preliminary model was developed. It is based upon component mathematical models in lumped parametric form and build upon five component mathematical models for calculating dynamic responses of two-phase fluid reservoirs, primary feedback elements, controller commands, heater actuators, and reservoir heaters. As much as possible, the model took advantage of the available SINDA'85/FLUINT thermal/fluid integrator. Additional calculation logic and computer subroutines were developed to complete implementation of the model. The model is capable of simulating dynamic response of an equilibrium two-phase fluid reservoir. Modification of the model to include the liquid/vapor nonequilibrium is required for applications of the model to simulate performance of reservoir in which the liquid and vapor phases of the reservoir fluid are not in equilibrium. In addition, the model in its present form, needs to be refined in several respects. More empirical data are needed to guide the model development. The model may then be used to conduct a full parametric study of two-phase fluid reservoirs. More complexities in two-phaes flow regions in laboratory and flight conditions may have to be considered eventually if empirical data cannot be simulated satisfactorily. System with other components arrangement also need to be simulated if optimization is ever to be attained. The present model does, however, preliminarily demonstrates that such analyses are quite possible and offers a far less expensive method to understand the transient of a two-phase fluid reservoir system than a totally headware approach.

Chi, Joseph↗