Dynamic similitude between a model and a full-scale body for model investigation at full-scale Mach number
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Dynamic similitude in internal-combustion engines
In this report it will be seen that the piston speed - as, moreover, any other speed, such as bearing velocity - must be independent of the quantity dimensions and must be a representative quantity similar to the high speed and the specific weight per horsepower.
Lutz, O↗
Matters of simulation of the semicircular canal system
A scale model of the human semicircular canal system was developed based on the theory of dynamic similitude. This enlarged model makes it convenient to conduct tests on the vestibular processes and dynamics in the semicircular canals. Tests revealed hydromechanical interaction between canals, with asymmetry of the conditions of movement of the endolymph in the canals in opposite directions. A type of vestibular reactions, occurring with angular oscillations of the head, was predicted and demonstrated using this model and human test subjects.
Gurfinkel, V. S.↗
Similitude in hydrodynamic tests involving planing
The problems of using models in planing tests are addressed. If one passes from the model to a hull of linear dimensions n times greater, the speeds are connected by the law of mechanical similitude. The normal forces given by the hydrodynamic equations (perfect fluid) also follow the law of dynamic similitude (Reech's method) and are multiplied by n(exp 3). A series of tests were performed and the actual results were compared to theoretical results.
Gruson, M F↗
Unique Testing Capabilities of the NASA Langley Transonic Dynamics Tunnel, an Exercise in Aeroelastic Scaling
NASA Langley Research Center's Transonic Dynamics Tunnel (TDT) is the world's most capable aeroelastic test facility. Its large size, transonic speed range, variable pressure capability, and use of either air or R-134a heavy gas as a test medium enable unparalleled manipulation of flow-dependent scaling quantities. Matching these scaling quantities enables dynamic similitude of a full-scale vehicle with a sub-scale model, a requirement for proper characterization of any dynamic phenomenon, and many static elastic phenomena. Select scaling parameters are presented in order to quantify the scaling advantages of TDT and the consequence of testing in other facilities. In addition to dynamic testing, the TDT is uniquely well-suited for high risk testing or for those tests that require unusual model mount or support systems. Examples of recently conducted dynamic tests requiring unusual model support are presented. In addition to its unique dynamic test capabilities, the TDT is also evaluated in its capability to conduct aerodynamic performance tests as a result of its flow quality. Results of flow quality studies and a comparison to a many other transonic facilities are presented. Finally, the ability of the TDT to support future NASA research thrusts and likely vehicle designs is discussed.
Ivanco, Thomas G.↗
Supersonic Free-Flight Dynamics Testing in the Stratosphere
A new technique for obtaining stratospheric free-flight dynamics data for atmospheric entry capsules is described. The Stratospheric Projectile Experiment of Entry Dynamics (SPEED) represents a new approach to characterizing the free-flight dynamics of vehicles in the supersonic and transonic regime of flight. The SPEED test architecture leverages a stratospheric balloon and 3D-printed flight system in a novel two-stage configuration to deliver test articles to supersonic conditions in the atmosphere which achieve dynamic similitude with a full-scale vehicle. Designed to address the limitations of existing test facilities, SPEED captures the complete time evolution of a vehicle’s dynamic state while producing a statistically significant number of observed flight trajectories to address the stochastic nature of the wake-driven dynamic stability phenomenon. SPEED was developed over two years at NASA Ames Research Center. The inaugural flight of the SPEED test platform was conducted in the summer of 2024 where scaled capsules of the Mars Sample Return Earth Entry System and Dragonfly entry vehicle were tested. This paper describes the motivation for a new test architecture, operational constraints and achievable flight test envelopes, the design and development of the SPEED concept, and results from the demonstration flight. Techniques for estimating the dynamic aerodynamic characteristics and atmospheric conditions for each test article individually and as a collective are also discussed.
Entry Vehicle↗
Design and Technology Maturation of the Stratospheric Projectile Experiment of Entry Dynamics
A new technique for obtaining stratospheric free-flight dynamics data for atmospheric entry capsules is described. The Stratospheric Projectile Experiment of Entry Dynamics (SPEED) represents a new approach to characterizing the free-flight dynamics of vehicles in the supersonic and transonic regime of flight. The SPEED test architecture leverages a stratospheric balloon and 3D-printed flight system in a novel two-stage configuration to deliver test articles to supersonic conditions in the atmosphere which achieve dynamic similitude with a full-scale vehicle. Designed to address the limitations of existing test facilities, SPEED captures the complete time evolution of a vehicle’s dynamic state while producing a statistically significant number of observed flight trajectories to address the stochastic nature of the wake-driven dynamic stability phenomenon. SPEED was developed over two years at NASA Ames Research Center. This presentation describes the motivation for a new test architecture, operational constraints and achievable flight test envelopes, the design, and development of the SPEED concept.
Dynamic Stability↗
Determination of Longitudinal Stability and Control Characteristics from Free-Flight Model Tests with Results at Transonic Speeds for Three Airplane Configurations
A test technique and data analysis method has been developed for determining the longitudinal aerodynamic characteristics from free-flight tests of rocket-propelled models. The technique makes use of accelerometers and an angle-of-attack indicator to permit instantaneous measurements of lift, drag, and pitching moments. The data, obtained during transient oscillations resulting from control-surface disturbances, are analyzed by essentially nonlinear direct methods (such as cross plots of the variation of lift coefficient with angle of attack) and by linear indirect methods by using the equations of motion for a transient oscillation. The analysis procedure has been set forth in some detail and the feasibility of the method has been demonstrated by data measured through the transonic speed range on several airplane configurations. It was shown that the flight conditions and dynamic similitude factors for the tests described were reasonably close to typical full-scale airplane conditions.
Gillis, Clarence L↗
A Tabletop Tool for Modeling Life Support Systems
This paper describes the development plan for a comprehensive research and diagnostic tool for aspects of advanced life support systems in space-based laboratories. Specifically it aims to build a high fidelity tabletop model that can be used for the purpose of risk mitigation, failure mode analysis, contamination tracking, and testing reliability. We envision a comprehensive approach involving experimental work coupled with numerical simulation to develop this diagnostic tool. It envisions a 10% scale transparent model of a space platform such as the International Space Station that operates with water or a specific matched index of refraction liquid as the working fluid. This allows the scaling of a 10 ft x 10 ft x 10 ft room with air flow to 1 ft x 1 ft x 1 ft tabletop model with water/liquid flow. Dynamic similitude for this length scale dictates model velocities to be 67% of full-scale and thereby the time scale of the model to represent 15% of the full- scale system; meaning identical processes in the model are completed in 15% of the full- scale time. The use of an index matching fluid (fluid that matches the refractive index of cast acrylic, the model material) allows making the entire model (with complex internal geometry) transparent and hence conducive to non-intrusive optical diagnostics. So using such a system one can test environment control parameters such as core flows (axial flows), cross flows (from registers and diffusers), potential problem areas such as flow short circuits, inadequate oxygen content, build up of other gases beyond desirable levels, test mixing processes within the system at local nodes or compartments and assess the overall system performance. The system allows quantitative measurements of contaminants introduced in the system and allows testing and optimizing the tracking process and removal of contaminants. The envisaged system will be modular and hence flexible for quick configuration change and subsequent testing. The data and inferences from the tests will allow for improvements in the development and design of next generation life support systems and configurations.
Ramachandran, N.↗
Space Laboratory on a Table Top: A Next Generative ECLSS design and diagnostic tool
This paper describes the development plan for a comprehensive research and diagnostic tool for aspects of advanced life support systems in space-based laboratories. Specifically it aims to build a high fidelity tabletop model that can be used for the purpose of risk mitigation, failure mode analysis, contamination tracking, and testing reliability. We envision a comprehensive approach involving experimental work coupled with numerical simulation to develop this diagnostic tool. It envisions a 10% scale transparent model of a space platform such as the International Space Station that operates with water or a specific matched index of refraction liquid as the working fluid. This allows the scaling of a 10 ft x 10 ft x 10 ft room with air flow to 1 ft x 1 ft x 1 ft tabletop model with water/liquid flow. Dynamic similitude for this length scale dictates model velocities to be 67% of full-scale and thereby the time scale of the model to represent 15% of the full- scale system; meaning identical processes in the model are completed in 15% of the full- scale-time. The use of an index matching fluid (fluid that matches the refractive index of cast acrylic, the model material) allows making the entire model (with complex internal geometry) transparent and hence conducive to non-intrusive optical diagnostics. So using such a system one can test environment control parameters such as core flows (axial flows), cross flows (from registers and diffusers), potential problem areas such as flow short circuits, inadequate oxygen content, build up of other gases beyond desirable levels, test mixing processes within the system at local nodes or compartments and assess the overall system performance. The system allows quantitative measurements of contaminants introduced in the system and allows testing and optimizing the tracking process and removal of contaminants. The envisaged system will be modular and hence flexible for quick configuration change and subsequent testing. The data and inferences from the tests will allow for improvements in the development and design of next generation life support systems and configurations. Preliminary experimental and modeling work in this area will be presented. This involves testing of a single inlet-exit model with detailed 3-D flow visualization and quantitative diagnostics and computational modeling of the system.
Ramachandran, N.↗
Aeroelastic Stability Assessment Methodology and Application to Slat Noise Treatments on the High-Lift Common Research Model
This work supports a larger effort at NASA to reduce airframe noise and, thus, environmental noise around airports. The leading-edge slat of conventional high-lift systems is a prominent source of airframe noise, and two technologies were previously identified as promising for noise reduction without significant aerodynamic or weight penalty: the slat cove filler (SCF) and the slat gap filler (SGF). NASA fabricated a 10%-scale semispan aircraft model for wind tunnel testing based upon the High-Lift Common Research Model (CRM-HL). NASA embarked on a test campaign with the 10% CRM-HL to determine the noise reduction effectiveness and other performance metrics of 3D SCF and SGF treatments in flow conditions representative of flight. The highly flexible SCF and SGF treatments posed a risk to the model and aeroelastic instability would compromise research integrity, so aeroelastic stability assessment was required. This work briefly describes the 10% CRM-HL, design of the SCF and SGF treatments to the model, and supporting fluid structure interaction (FSI) research. Relations for static and dynamic aeroelastic similitude are then developed for convenience of reference, and simplifications are introduced of particular utility to the cases considered in this study. The similitude relations are employed to assess the stability of the treatments under wind tunnel flow conditions based upon known behaviors from the supporting research. It is shown that the treatments are safe for test under the anticipated wind tunnel flow conditions with significant margins/factors of safety. It is furthermore demonstrated that the SCF is more susceptible to aeroelastic instability than the SGF, which has implications for flight feasibility.
Similitude↗
Dynamic stability of space vehicles. Structural dynamics model testing
Dimensional analysis, and similitude and scaling laws for structural dynamics model testing of spacecraft dynamic stability
Wissmann, J. W.↗
Application of similitude principle to the numerical simulation of solar atmospheric dynamics
Numerical simulation has become an essential part of solar physics because the complex nonlinear characteristics of solar phenomena makes analytical solutions difficult to obtain. Realistic simulation of the birth and decay of an active region still is not possible because of the wide range of spatial and time scales that must be considered. Therefore, proper scaling rules must be recognized for the development of appropriate models. In this paper, the similitude principle is applied to develop scaling rules. It is found that these rules are highly dependent on the physical nature of the specific problem under consideration. A set of 'similitude critiques' is presented for some specific physical conditions. Numerical examples of coronal dynamic response and active region dynamics are used to demonstrate these ideas.
Wu, S. T.↗
Overview of Dynamic Test Techniques for Flight Dynamics Research at NASA LaRC (Invited)
An overview of dynamic test techniques used at NASA Langley Research Center on scale models to obtain a comprehensive flight dynamics characterization of aerospace vehicles is presented. Dynamic test techniques have been used at Langley Research Center since the 1920s. This paper will provide a partial overview of the current techniques available at Langley Research Center. The paper will discuss the dynamic scaling necessary to address the often hard-to-achieve similitude requirements for these techniques. Dynamic test techniques are categorized as captive, wind tunnel single degree-of-freedom and free-flying, and outside free-flying. The test facilities, technique specifications, data reduction, issues and future work are presented for each technique. The battery of tests conducted using the Blended Wing Body aircraft serves to illustrate how the techniques, when used together, are capable of characterizing the flight dynamics of a vehicle over a large range of critical flight conditions.
Owens, D. Bruce↗
Theories of flow similitude
The laws of comparison of dynamically similar fluid motions are derived by three different methods based on the same principle and yielding the same or equivalent formulas. This report outlines the three current methods of comparing dynamically similar motions, more especially of fluids, initiated respectively by Newton, Stokes (or Helmholtz), and Rayleigh. These three methods, viz., the integral, the differential, and the dimensional, are enough alike to be studied profitably together. They are treated in succession then compared. (author)
Zahm, A F↗
Fluid Dynamics and Solidification of Molten Solder Droplets Impacting on a Substrate in Microgravity
This program investigates the fluid dynamics and simultaneous solidification of molten solder droplets impacting on a flat substrate. The problem of interest is directly relevant to the printing of microscopic solder droplets in surface mounting of microelectronic devices. The study consists of a theoretical and an experimental component. The theoretical work uses axisymmetric Navier-Stokes models based on finite element techniques. The experimental work is performed in microgravity to allow for the use of larger solder droplets that make feasible the performance of accurate measurements while maintaining similitude of the relevant fluid dynamics groups (Re, We) and keeping the effect of gravity negligible.
Poulikakos, Dimos↗
Fluid Dynamics and Solidification of Molten Solder Droplets Impacting on a Substrate in Microgravity
This program investigates the fluid dynamics and simultaneous solidification of molten solder droplets impacting on a flat smooth substrate. The problem of interest is directly relevant to the printing of microscopic solder droplets in surface mounting of microelectronic devices. The study consists of a theoretical and an experimental component. The theoretical work uses axisymmetric Navier-Stokes models based on finite element techniques. The experimental work will be ultimately performed in microgravity in order to allow for the use of larger solder droplets which make feasible the performance of accurate measurements, while maintaining similitude of the relevant fluid dynamics groups (Re, We).
Megardis, C. M.↗
Molten-Metal Droplet Deposition on a Moving Substrate in Microgravity: Aiding the Development of Novel Technologies for Microelectronic Assembly
Driven by advancements in microelectronics manufacturing, this research investigates the oblique (non-axisymmetric) impact of liquid-metal droplets on flat substrates. The problem of interest is relevant to the development of the novel technology of on-demand dispension (printing) of microscopic solder deposits for the surface mounting of microelectronic devices. The technology, known as solder jetting, features on-demand deposition of miniature solder droplets (30 to 120 microns in diameter) in very fine, very accurate patterns using techniques analogous to those developed for the ink-jet printing industry. Despite its promise, severe limitations exist currently with regards to the throughput rates of the technology; some of these limitations are largely due to the lack of the capability for reliable prediction of solder bump positioning and shapes, especially under ballistic deposition conditions where the droplet impact phenomena are inherently three-dimensional. The study consists of a theoretical and an experimental component. The theoretical work uses a finite element formulation to simulate numerically the non-axisymmetric (3-D) fluid mechanics and heat transfer phenomena of a liquid solder droplet impacting at an angle alpha on a flat substrate. The work focuses on the pre-solidification regime. The modeling of the most challenging fluid mechanics part of the process has been completed successfully. It is based upon the full laminar Navier-Stokes equations employing a Lagrangian frame of reference. Due to the large droplet deformation, the surface (skin) as well as the volumetric mesh have to be regenerated during the calculations in order to maintain the high accuracy of the numerical scheme. The pressure and velocity fields are then interpolated on the newly created mesh. The numerical predictions are being tested against experiments, for cases where wetting phenomena are not important. For the impact parameters used in the example shown (We = 2.38, Fr = 16300, Re = 157), the droplet rolls along the substrate, but its shape remains practically axisymmetric for all impact angles within the range from 0 to 60 deg. Interestingly, the substrate/droplet contact area during the recoiling phase of the impact is not a monotonically decreasing function of time. The experimental component of the research tests the numerical predictions and provides necessary input data (contact angles) for the theoretical model. The experiments are performed in microgravity (2.2s drop tower of the NASA GRC) in order to allow for the use of mm-size solder droplets, which make feasible the performance of accurate measurements, while maintaining similitude of the relevant fluid dynamic groups (Re, Fr, We, Ste). Preliminary oblique impact experiments have been performed using water droplets in normal gravity.
Megaridis, C. M.↗