Liquid Sloshing in a Spherical Tank Filled to an Arbitrary Depth
Dynamic analysis of liquid in a spherical tank with applications to trajectory failure and loss of control in missile and rocket flight
ROCKET FLIGHT↗
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Liquid propellant sloshing in mobile tanks of arbitrary shape
Equations for dynamic behavior of liquid propellants sloshing in mobile tanks of arbitrary shape
LIQUID PROPELLANT↗
Fluid Dynamic and Stability Analysis of a Thin Liquid Sheet
Interest in thin sheet flows has recently been renewed due to their potential application in space radiators. Theoretical and experimental studies of the fluid dynamics and stability of thin liquid sheet flows have been carried out in this thesis. A computer program was developed to determine the cross-sectional shape of the edge cylinder given the cross-sectional area of the edge cylinder. A stability analysis was performed on a non-planer liquid sheet. A study was conducted to determine the effects of air resistance on the sheet.
McMaster, Matthew S.↗
Colorimetric qualification of shear sensitive liquid crystal coatings
The work that has been done to date on the Shear Sensitive Liquid Crystal Project demonstrated that cholesteric liquid crystal coatings respond to both the direction and magnitude of a shearing force. The response of the coating is to selectively scatter incident white light into a spectrum of colors. Discernible color changes at a fixed angle of observation and illumination are the result of an applied shear stress. The intention was to be able to convert these observable color patterns from a flow visualization technique into a quantitative tool. One of the earlier intentions was to be able to use liquid crystals in dynamic flow fields. This was assumed possible because liquid crystals had made it possible to visualize transients in surface shear forces. Although the transients were visualized by color changes to an order one micro second, the time response of a coating to align to a shearing force is dependent on the magnitude of the change between its initial and final states. Unfortunately, the response is not instantaneous. It is for this reason any future attempt at quantifying the magnitude and directions of a shearing force are limited to surface shear stress vector fields in three dimensional steady state flows. This limitation does not significantly detract from the utility of liquid crystal coatings. The measurement of skin friction in the study of transition on wings, prediction of drag forces, performance assessment, and the investigation of boundary layer behavior is of great importance in aerodynamics. There exist numerous examples of techniques for the measurement of surface shear stress. Most techniques require arduous calibrations and necessitate extensive preparation of the receiving surfaces. However, the main draw back of instruments such as Preston tubes, hot films, buried wire gages, and floating element balances is that they only provide a point measurement. The advantages of capturing global shear data would be appreciable when compared with conventional point measurement sensors. It has yet to be determined if a repeatable correlation exists between the measured color of a liquid crystal coating and the magnitude/directional components of a shear vector imposed onto it.
Muratore, Joseph J., Jr.↗
Modeling the Effects of Liquid-to-Gas Density Ratio on Slosh Dynamics
Mechanical models are commonly used in Guidance, Navigation and Controls (GN&C) system-level models to represent propellant slosh forces on launch vehicles and spacecraft. The slosh model parameters are typically predicted using semi-empirical analytical methods that are based on experimental data for high liquid-to-gas density ratios (such as water and air at standard sea level conditions). Model parameter calculations typically neglect any contribution to slosh dynamics from the gas phase. However, some cryogenic propellant systems operate in conditions where the density ratio can be orders of magnitude smaller. Analytical and computational modeling was used in this effort to investigate the effects of liquid-to-gas density ratio on slosh dynamics. No experimental data nor previous studies are available at this time that quantify the effect of liquid-to-gas density ratio on slosh dynamics. However, in a recent CFD study, results showed that density ratio can have a significant effect on slosh model parameters. In this study, a dual pendulum slosh model was created that distinctly represents both liquid and gas phase dynamics. Solution of the model, which invokes the Euler-Lagrange equations of motion, demonstrates that slosh frequency is a combination of liquid slosh frequency and gas phase slosh frequency. Additionally, it shows that slosh mass is reduced due to the opposing motion of the gas phase with respect to that of the liquid phase. The slosh model parameter trends were verified using Computational Fluid Dynamics (CFD) analysis results for various liquid-to-gas density ratios, tanks, and fill levels.
Christopher D Moore↗
Experimental observations relating the inception of liquid rocket engine popping and resonant combustion to the stagnation dynamics of injection impingement
Characteristics of unsteady liquid rocket propellant combustion processes
Clayton, R. M.↗
Natural and thermocapillary convection in multiple liquid layers
A numerical and experimental investigation is conducted of the fluid dynamics of immiscible liquid layers, as encountered in the liquid encapsulation of electronic melts. Attention is given to the convective flow in multiple liquid layers that are driven by temperature gradients that are either parallel or perpendicular to the liquid/liquid interfaces. The experimental and theoretical results obtained are noted not to be in agreement for differential side-heating of a three-layer system.
Prakash, A.↗
Dynamic Mechanical Properties and Fracture Surface Morphologies of Core-Shell Rubber (CSR) Toughened Epoxy at Liquid Nitrogen (Ln2) Temperatures
The dynamic mechanical properties and fracture surface morphologies were evaluated for a commercial epoxy resin toughened with two types of core-shell rubber (CSR) toughening agents (Kane Ace(Registered TradeMark) MX130 and MX960). The impact resistance (R) was evaluated by the resulting breaking energy measured in Charpy impact tests conducted on an instrumented drop tower. The resulting fracture surface morphologies were examined using Scanning Electron Microscopy (SEM). Fractographic observations of the CSR toughened epoxy tested at ambient temperature, showed a fracture as characterized by slender dendrite textures with large voids. The increasing number of dendrites and decreasing size of scale-like texture with more CSR particles corresponded with increased R. As the temperature decreased to Liquid Nitrogen (LN 2), the fracture surfaces showed a fracture characterized by a rough, torn texture containing many river markings and deep furrows.
Wang, J.↗
An investigation of the response of a scaled model of a liquid-propellant multistage launch vehicle to longitudinal excitation
Longitudinal vibration characteristics of scaled dynamic model of liquid propellant multistage launch vehicle
MULTISTAGE ROCKET VEHICLE↗
Numerical studies of the surface tension effect of cryogenic liquid helium
The generalized mathematical formulation of sloshing dynamics for partially filled liquid of cryogenic superfluid helium II in dewar containers driven by both the gravity gradient and jitter accelerations applicable to scientific spacecraft which is eligible to carry out spinning motion and/or slew motion for the purpose of performing scientific observation during the normal spacecraft operation is investigated. An example is given with Gravity Probe-B (GP-B) spacecraft which is responsible for the sloshing dynamics. The jitter accelerations include slew motion, spinning motion, atmospheric drag on the spacecraft, spacecraft attitude motions arising from machinery vibrations, thruster firing, pointing control of spacecraft, crew motion, etc. Explicit mathematical expressions to cover these forces acting on the spacecraft fluid systems are derived. The numerical computation of sloshing dynamics has been based on the non-inertia frame spacecraft bound coordinate, and solve time-dependent, three-dimensional formulations of partial differential equations subject to initial and boundary conditions. The explicit mathematical expressions of boundary conditions to cover capillary force effect on the liquid vapor interface in microgravity environments are also derived. The formulations of fluid moment and angular moment fluctuations in fluid profiles induced by the sloshing dynamics, together with fluid stress and moment fluctuations exerted on the spacecraft dewar containers, have been derived.
Hung, R. J.↗
Validation of Computational Fluid Dynamics Model for Pressurized Expulsion of Liquid Methane using Non-Condensable Pressurant
An important aspect of cryogenic fluid management is the design of the pressurization systems used to maintain and regulate the tank pressure as propellant is expelled from the tanks. To design these systems efficiently and effectively it is important to be able to predict the amount pressurant gas needed and how the pressurant gas affects the propellant as it is added in the tank. Computational fluid dynamics (CFD) modeling is a common tool that is used to help with these predictions, so it is crucial to have CFD models that are validated by comparing numerical results to experimental data. In the 1970’s extensive testing was done at NASA Plum Brook K-Site Facility exploring the pressurant gas requirements needed to maintain tank pressure while liquid methane is discharged from a spherical tank. These tests explored using different pressurant gases (methane, helium, hydrogen, and nitrogen) under static and sloshing conditions. The data gathered from the experiments includes the gas and wall temperatures at the end of the expulsion, the gas concentrations, and the total amount of pressurant added. This study presents a CFD model that accurately predicts similar results to the experimental data specifically for the tests in which helium, a non-condensable gas, was used. This comparison anchors the commercial CFD code Flow3D model and gives confidence for future use in design and analysis of pressurization systems for cryogenic propellant tanks
computational fluid dynamics↗
Enhanced simulation software for rocket turbopump, turbulent, annular liquid seals
One of the main objectives of this work is to develop a new dynamic analysis for liquid annular seals with arbitrary profile and to analyze a general distorted interstage seal of the space shuttle main engine high pressure oxygen turbopump (SSME-ATD-HPOTP). The dynamic analysis developed is based on a method originally proposed by Nelson and Nguyen. A simpler scheme based on cubic splines is found to be computationally more efficient and has better convergence properties at higher eccentricities. The first order solution of the original analysis is modified by including a more exact solution that takes into account the variation of perturbed variables along the circumference. A new set of equations for dynamic analysis are derived based on this more general model. A unified solution procedure that is valid for both Moody's and Hirs' friction models is presented. Dynamic analysis is developed for three different models: constant properties, variable properties, and thermal effects with variable properties. Arbitrarily varying seal profiles in both axial and circumferential directions are considered. An example case of an elliptical seal with varying degrees of axial curvature is analyzed in detail. A case study based on predicted clearances of an interstage seal of the SSME-ATD-HPOTP is presented. Dynamic coefficients based on external specified load are introduced to analyze seals that support a preload. The other objective of this work is to study the effect of large rotor displacements of SSME-ATD-HPOTP on the dynamics of the annular seal and the resulting transient motion. One task is to identify the magnitude of motion of the rotor about the centered position and establish limits of effectiveness of using current linear models. This task is accomplished by solving the bulk flow model seal governing equations directly for transient seal forces for any given type of motion, including motion with large eccentricities. Based on the above study, an equivalence is established between linearized coefficients based transient motion and the same motion as predicted by the original governing equations. An innovative method is developed to model nonlinearities in an annular seal based on dynamic coefficients computed at various static eccentricities. This method is thoroughly tested for various types of transient motion using bulk flow model results as a benchmark.
Padavala, Satya↗
Analysis of Flow-System Starting Dynamics of Turbopump-Fed Liquid-Propellant Rocket
Two rocket configurations with turbopump drive were investigated analytically. In one configuration the inlet pressure to the turbine was fixed at the design value. The second configuration employed a "bootstrap" technique for supplying energy to the turbine. An injector was the chief resistance between the pump and the rocket combustion chamber. From the analysis two parameters were developed from which the speed response time of the turbopump, the flow response time, and the maximum dynamic line loss could be evaluated. These parameters were functions of turbopump moment of inertia, design performance of the turbine, and flow-system geometry. The moment of inertia of the turbopump and the ratio of turbine torque at zero speed to design torque had the most influence on the starting dynamics of the flow system. These parameters were also applicable to the bootstrap configuration as long as the inlet pressure to the turbine exceeded half the design value.
Krebs, Richard P.↗
Uniform hydrogen fuel layers for inertial fusion targets by microgravity
A critical concern in the fabrication of targets for inertial confinement fusion (ICF) is ensuring that the hydrogenic (D(sub 2) or DT) fuel layer maintains spherical symmetry. Solid layered targets have structural integrity, but lack the needed surface smoothness. Liquid targets are inherently smooth, but suffer from gravitationally induced sagging. One method to reduce the effective gravitational field environment is freefall insertion into the target chamber. Another method to counterbalance field gravitational force is to use an applied magnetic field combined with a gradient field to induce a magnetic dipole force on the liquid fuel layer. Based on time dependent calculations of the dynamics of the liquid fuel layer in microgravity environments, we show that it may be possible to produce a liquid layered ICF target that satisfies both smoothness and symmetry requirements.
Parks, P. B.↗
Interaction of a sodium ion with the water liquid-vapor interface
Molecular dynamics results are presented for the density profile of a sodium ion near the water liquid-vapor interface at 320 K. These results are compared with the predictions of a simple dielectric model for the interaction of a monovalent ion with this interface. The interfacial region described by the model profile is too narrow and the profile decreases too abruptly near the solution interface. Thus, the simple model does not provide a satisfactory description of the molecular dynamics results for ion positions within two molecular diameters from the solution interface where appreciable ion concentrations are observed. These results suggest that surfaces associated with dielectric models of ionic processes at aqueous solution interfaces should be located at least two molecular diameters inside the liquid phase. A free energy expense of about 2 kcal/mol is required to move the ion within two molecular layers of the free water liquid-vapor interface.
NASA Center ARC↗
Aspects of model-based rocket engine condition monitoring and control
A rigorous propulsion system modelling method suitable for control and condition monitoring purposes is developed. Previously developed control oriented methods yielding nominal models for gaseous medium propulsion systems are extended to include both nominal and anomalous models for liquid mediums in the following two ways. First, thermodynamic and fluid dynamic properties for liquids such as liquid hydrogen are incorporated into the governing equations. Second, anomalous conditions are captured in ways compatible with existing system theoretic design tools so that anomalous models can be constructed. Control and condition monitoring based methods are seen as an improvement over some existing modelling methods because such methods typically do not rigorously lead to low order models nor do they provide a means for capturing anomalous conditions. Applications to the nominal SSME HPFP and degraded HPFP serve to illustrate the approach.
Karr, Gerald R.↗
Combustion Dynamics and Stability Modeling of a Liquid Oxygen/RP-2 Oxygen-Rich Staged Combustion Preburner and Thrust Chamber Assembly with Gas-Centered Swirl Coaxial Injector Elements
The Combustion Stability Tool Development (CSTD) project, funded by the Air Force Space and Missile Systems Center, began in March 2015 supporting a renewed interest in the development of a liquid oxygen/hydrocarbon, oxygen-rich combustion engine. The project encompasses the design, assembly, and hot-fire testing of the NASA Marshall Space Flight Center 40-klbf Integrated Test Rig (MITR). The test rig models a staged-combustion configuration by combining an oxygen-rich preburner (ORPB), to generate hot gas, with a thrust chamber assembly (TCA) using gas-centered swirl coaxial injector elements. There are five separately designed interchangeable injectors in the TCA that each contain 19- or 27- injector elements. A companion paper in this JANNAF conference describes the design characteristics, rationale, and fabrication issues for all the injectors. The data acquired from a heavily instrumented rig encompasses several injectors, several operating points, and stability bomb tests. Another companion paper in this JANNAF conference describes this test program in detail. In this paper, dynamic data from the hot-fire testing is characterized and used to identify the responses in the ORPB and TCA. A brief review of damping metrics are discussed and applied as a measure of stability margin for damped acoustic modes. Chug and longitudinal combustion stability models and predictions are described which includes new dynamic models for compressible flow through an orifice and a modification to incorporate a third feed line for inclusion of the fuel-film coolant. Flow-acoustics finite element modeling is used to investigate the anticipated TCA acoustics, the effects of injector element length on stability margin, and the potential use of an ORPB orifice trip ring for improving longitudinal stability margin.
Casiano, M. J.↗
How Does a Liquid Wet a Solid? Hydrodynamics of Dynamic Contact Angles
A contact line is defined at the intersection of a solid surface with the interface between two immiscible fluids. When one fluid displaces another immiscible fluid along a solid surface, the process is called dynamic wetting and a "moving" contact line (one whose position relative to the solid changes in time) often appears. The physics of dynamic wetting controls such natural and industrial processes as spraying of paints and insecticides, dishwashing, film formation and rupture in the eye and in the alveoli, application of coatings, printing, drying and imbibition of fibrous materials, oil recovery from porous rocks, and microfluidics.
Rame, Enrique↗