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NASA NTRS2009

Device for Measuring Low Flow Speed in a Duct

A multiple-throat venturi system has been invented for measuring laminar flow of air or other gas at low speed (1 to 30 cm/s) in a duct while preserving the laminar nature of the flow and keeping the velocity profile across the duct as nearly flat as possible. While means for measuring flows at higher speeds are well established, heretofore, there have been no reliable means for making consistent, accurate measurements in this speed range. In the original application for which this system was invented, the duct leads into the test section of a low-speed wind tunnel wherein uniform, low-speed, laminar flow is required for scientific experiments. The system could also be used to monitor a slow flow of gas in an industrial process like chemical vapor deposition. In the original application, the multiple- throat venturi system is mounted at the inlet end of the duct having a rectangular cross section of 19 by 14 cm, just upstream of an assembly of inlet screens and flow straighteners that help to suppress undesired flow fluctuations (see Figure 1). The basic venturi measurement principle is well established: One measures the difference in pressure between (1) a point just outside the inlet, where the pressure is highest and the kinetic energy lowest; and (2) the narrowest part (the throat) of the venturi passage, where the kinetic energy is highest and the pressure is lowest. Then by use of Bernoulli s equation for the relationship between pressure and kinetic energy, the volumetric flow speed in the duct can be calculated from the pressure difference and the inlet and throat widths. The design of this system represents a compromise among length, pressure recovery, uniformity of flow, and complexity of assembly. Traditionally, venturis are used to measure faster flows in narrower cross sections, with longer upstream and downstream passages to maintain accuracy. The dimensions of the passages of the present venturi system are sized to provide a readily measurable pressure drop. Multiple throats are used to minimize the length needed to recover internal energy and enable the velocity profile to recover to near flatness.

Quinn, Frank↗

NASA NTRS2009

Measuring Thermal Conductivity of a Small Insulation Sample

Miller, Robert A.↗

NASA NTRS2004

Algorithm Determines Wind Speed and Direction from Venturi-Sensor Data

An algorithm computes the velocity of wind from the readings of an instrument like the one described in another Tech Brief. To recapitulate: The sensor has no moving parts and is a compact, rugged means of measuring wind vectors having magnitudes of as much as 300 mph (134 m/s). The sensor includes a Venturi gap bounded by a curved upper and a curved lower surface that are axisymmetric with respect to a vertical axis and mirror-symmetric with respect to a horizontal midplane. One of the curved surfaces is instrumented with multiple ports for measuring dynamic pressures. The sensor also incorporates auxiliary sensors for measuring temperature, relative humidity, and static atmospheric pressure. The design and operation of the sensor are based on the concepts of (1) using Bernoulli's equation (which expresses the relationship among variations of speed, density, and pressure along a streamline) to calculate the speed of the wind from differences among the pressure readings at the various ports; and (2) calculating the direction of the wind from the angular positions of ports selected according to comparisons among their pressure readings. The present algorithm performs these calculations.

Zysko, Jan A.↗

NASA NTRS2003

Three-Dimensional Venturi Sensor for Measuring Extreme Winds

A three-dimensional (3D) Venturi sensor is being developed as a compact, rugged means of measuring wind vectors having magnitudes of as much as 300 mph (134 m/s). This sensor also incorporates auxiliary sensors for measuring temperature from -40 to +120 F (-40 to +49 C), relative humidity from 0 to 100 percent, and atmospheric pressure from 846 to 1,084 millibar (85 to 108 kPa). Conventional cup-and-vane anemometers are highly susceptible to damage by both high wind forces and debris, due to their moving parts and large profiles. In addition, they exhibit slow recovery times contributing to an inaccurately high average-speed reading. Ultrasonic and hot-wire anemometers overcome some of the disadvantages of the cup and-vane anemometers, but they have other disadvantageous features, including limited dynamic range and susceptibility to errors caused by external acoustic noise and rain. In contrast, the novel 3D Venturi sensor is less vulnerable to wind damage because of its smaller profile and ruggedness. Since the sensor has no moving parts, it provides increased reliability and lower maintenance costs. It has faster response and recovery times to changing wind conditions than traditional systems. In addition, it offers wide dynamic range and is expected to be relatively insensitive to rain and acoustic energy. The Venturi effect in this sensor is achieved by the mirrored double-inflection curve, which is then rotated 360 to create the desired detection surfaces. The curve is optimized to provide a good balance of pressure difference between sensor ports and overall maximum fluid velocity while in the shape. Four posts are used to separate the two shapes, and their size and location were chosen to minimize effects on the pressure measurements. The 3D Venturi sensor has smart software algorithms to map the wind pressure exerted on the surfaces of the design. Using Bernoulli's equation, the speed of the wind is calculated from the differences among the pressure readings at the various ports. The direction of the wind is calculated from the spatial distribution and magnitude of the pressure readings. All of the pressure port sizes and locations have been optimized to minimize measurement errors and to reside in areas demonstrating a stable pressure reading proportional to the velocity range.

Zysko, Jan A.↗

NASA NTRS2013

Developing a Model Component

The Spaceport Command and Control System (SCCS) Simulation Computer Software Configuration Item (CSCI) is responsible for providing simulations to support test and verification of SCCS hardware and software. The Universal Coolant Transporter System (UCTS) was a Space Shuttle Orbiter support piece of the Ground Servicing Equipment (GSE). The initial purpose of the UCTS was to provide two support services to the Space Shuttle Orbiter immediately after landing at the Shuttle Landing Facility. The UCTS is designed with the capability of servicing future space vehicles; including all Space Station Requirements necessary for the MPLM Modules. The Simulation uses GSE Models to stand in for the actual systems to support testing of SCCS systems during their development. As an intern at Kennedy Space Center (KSC), my assignment was to develop a model component for the UCTS. I was given a fluid component (dryer) to model in Simulink. I completed training for UNIX and Simulink. The dryer is a Catch All replaceable core type filter-dryer. The filter-dryer provides maximum protection for the thermostatic expansion valve and solenoid valve from dirt that may be in the system. The filter-dryer also protects the valves from freezing up. I researched fluid dynamics to understand the function of my component. The filter-dryer was modeled by determining affects it has on the pressure and velocity of the system. I used Bernoulli's Equation to calculate the pressure and velocity differential through the dryer. I created my filter-dryer model in Simulink and wrote the test script to test the component. I completed component testing and captured test data. The finalized model was sent for peer review for any improvements. I participated in Simulation meetings and was involved in the subsystem design process and team collaborations. I gained valuable work experience and insight into a career path as an engineer.

Fields, Christina M.↗

NASA NTRS2013

Developing a Model Component

The Spaceport Command and Control System (SCCS) Simulation Computer Software Configuration Item (CSCI) is,. responsible for providing simulations to support test and verification of SCCS hardware and software. The Universal Coolant Transporter System (UCTS) is a Space Shuttle Orbiter support piece of the Ground Servicing Equipment (GSE). The purpose of the UCTS is to provide two support services to the Space Shuttle Orbiter immediately after landing at the Shuttle Landing Facility. The Simulation uses GSE Models to stand in for the actual systems to support testing of SCCS systems s:luring their development. As an intern at KSC, my assignment was to develop a model component for the UCTS. I was given a fluid component (drier) to model in Matlab. The drier was a Catch All replaceable core type filter-drier. The filter-drier provides maximum protection for the thermostatic expansion valve and solenoid valve from dirt that may be in the system. The filter-drier also protects the valves from freezing up. I researched fluid dynamics to understand the function of my component. I completed training for UNIX and Simulink to help aid in my assignment. The filter-drier was modeled by determining affects it has on the pressure, velocity and temperature of the system. I used Bernoulli's Equation to calculate the pressure and velocity differential through the dryer. I created my model filter-drier in Simulink and wrote the test script to test the component. I completed component testing and captured test data. The finalized model was sent for peer review for any improvements.

Fields, Christina M.↗

NASA NTRS1966

Analysis of fluid conditions in the discharge line of a cryogenic container undergoing self- pressurized draining.

Discharge line fluid conditions in cryogenic container with self-pressurized draining, using Bernoulli, continuity and general energy equations and fluid properties

ENERGY EQUATION↗

NASA NTRS1982

A composite velocity procedure for the compressible Navier-Stokes equations

A new boundary-layer relaxation procedure is presented. In the spirit of the theory of matched asymptotic expansions, a multiplicative composite of the appropriate velocity representations for the inviscid and viscous regions is prescribed. The resulting equations are structured so that far from the surface of the body the momentum equations lead to the Bernoulli relation for the pressure, while the continuity equation reduces to the familiar compressible potential equation. Close to the body surface, the governing equations and solution techniques are characteristic of those describing interacting boundary-layers; although, the full Navier-Stokes equations are considered here. Laminar flow calculations for the subsonic flow over an axisymmetric boattail simulator geometry are presented for a variety of Reynolds and Mach numbers. A strongly implicit solution method is applied for the coupled velocity components.

Khosla, P. K.↗

NASA NTRS1985

ISAAC (integrated Structural Analysis and Control) via Continuum Modeling and Distributed Frequency Domain Design Techniques

A methodology is proposed for the integrated design of structures and their controls. The integration of design is accomplished through simultaneous selection, via optimization, of designer-specified parameters governing the structure and its controller. The cost function is chosen to address the primary structural and control goals. Inequality constraints are added to insure that additional design requirements are met. The methodology is illustrated through development of an example involving a cantilever beam. A distributed transfer function is derived from the Bernoulli-Euler beam equation. A controller parameterization is then chosen, and performance requirements specified. A controller is then obtained via optimization, which is shown to give good performance.

Gustafson, C. L.↗

NASA NTRS1993

Acoustic radiation damping of flat rectangular plates subjected to subsonic flows

The acoustic radiation damping for various isotropic and laminated composite plates and semi-infinite strips subjected to a uniform, subsonic and steady flow has been predicted. The predictions are based on the linear vibration of a flat plate. The fluid loading is characterized as the perturbation pressure derived from the linearized Bernoulli and continuity equations. Parameters varied in the analysis include Mach number, mode number and plate size, aspect ratio and mass. The predictions are compared with existing theoretical results and experimental data. The analytical results show that the fluid loading can significantly affect realistic plate responses. Generally, graphite/epoxy and carbon/carbon plates have higher acoustic radiation damping values than similar aluminum plates, except near plate divergence conditions resulting from aeroelastic instability. Universal curves are presented where the acoustic radiation damping normalized by the mass ratio is a linear function of the reduced frequency. A separate curve is required for each Mach number and plate aspect ratio. In addition, acoustic radiation damping values can be greater than or equal to the structural component of the modal critical damping ratio (assumed as 0.01) for the higher subsonic Mach numbers. New experimental data were acquired for comparison with the analytical results.

Lyle, Karen Heitman↗

NASA NTRS1985

Error caused by using a constant extinction/backscattering ratio in the lidar solution

The Bernoulli solution of the lidar equation with the assumption of a constant extinction/backscattering ratio can lead to errors in the derived aerosol extinction and backscattering profiles. This paper presents a general theoretical analysis of the errors that result from differences between the assumed and actual extinction/backscattering ratio profiles. Examples of the influence of the constant extinction/backscattering ratio assumption on the lidar derived aerosol extinction profile are presented for various laser wavelengths.

Sasano, Y.↗

NASA NTRS1991

Distributed parameter estimation for NASA Mini-Mast truss through displacement measurements

Most methods of system identification of large flexible structures by far are based on the lumped parameter approach. Because of the considerable computational burden due to the large number of unknown parameters, distributed parameter approach, which greatly decreases the number of unknowns, has being investigated. In this paper a distributed parameter model for the estimation of modal characteristics of NASA Mini-Mast truss has been formulated. Both Bernoulli-Euler beam and Timoshenko beam equations are used to characterize the lateral bending vibrations of the truss. The measurement of the lateral displacement at the tip of the truss is provided to the maximum likelihood estimator. Closed-form solutions of the partial differential equations and closed-form expressions of the sensitivity functions are derived so that the estimation algorithm is highly efficient. The resulting estimates from test data by using Timoshenko beam model are found to be comparable to those derived from finite element analysis.

Huang, Jen-Kuang↗

NASA NTRS2005

Study of a 30-M Boom For Solar Sail-Craft: Model Extendibility and Control Strategy

Space travel propelled by solar sails is motivated by the fact that the momentum exchange that occurs when photons are reflected and/or absorbed by a large solar sail generates a small but constant acceleration. This acceleration can induce a constant thrust in very large sails that is sufficient to maintain a polar observing satellite in a constant position relative to the Sun or Earth. For long distance propulsion, square sails (with side length greater than 150 meters) can reach Jupiter in two years and Pluto in less than ten years. Converting such design concepts to real-world systems will require accurate analytical models and model parameters. This requires extensive structural dynamics tests. However, the low mass and high flexibility of large and light weight structures such as solar sails makes them unsuitable for ground testing. As a result, validating analytical models is an extremely difficult problem. On the other hand, a fundamental question can be asked. That is whether an analytical model that represents a small-scale version of a solar-sail boom can be extended to much larger versions of the same boom. To answer this question, we considered a long deployable boom that will be used to support the solar sails of the sail-craft. The length of fully deployed booms of the actual solar sail-craft will exceed 100 meters. However, the test-bed we used in our study is a 30 meter retractable boom at MSFC. We first develop analytical models based on Lagrange s equations and the standard Euler-Bernoulli beam. Then the response of the models will be compared with test data of the 30 meter boom at various deployed lengths. For this stage of study, our analysis was limited to experimental data obtained at 12ft and 18ft deployment lengths. The comparison results are positive but speculative. To observe properly validate the analytic model, experiments at longer deployment lengths, up to the full 30 meter, have been requested. We expect the study to answer the extendibility question of the analytical models. In operation, rapid temperature changes can be induced in solar sails as they transition from day to night and vice versa. This generates time dependent thermally induced forces, which may in turn create oscillation in structural members such as booms. Such oscillations have an adverse effect on system operations, precise pointing of instruments and antennas and can lead to self excited vibrations of increasing amplitude. The latter phenomenon is known as thermal flutter and can lead to the catastrophic failure of structural systems. To remedy this problem, an active vibration suppression system has been developed. It was shown that piezoelectric actuators used in conjunction with a Proportional Feedback Control (PFC) law (or Velocity Feedback Control (VFC) law) can induce moments that can suppress structural vibrations and prevent flutter instability in spacecraft booms. In this study, we will investigate control strategies using piezoelectric transducers in active, passive, and/or hybrid control configurations. Advantages and disadvantages of each configuration will be studied and experiments to determine their capabilities and limitations will be planned. In particular, special attention will be given to the hybrid control, also known as energy recycling, configuration due to its unique characteristics.

Keel, Leehyun↗

NASA NTRS1988

Creep rupture analysis of a beam resting on high temperature foundation

A simplified uniaxial strain controlled creep damage law is deduced with the use of experimental observation from a more complex strain dependent law. This creep damage law correlates the creep damage, which is interpreted as the density variation in the material, directly with the accumulated creep strain. Based on the deduced uniaxial strain controlled creep damage law, a continuum mechanical creep rupture analysis is carried out for a beam resting on a high temperature elastic (Winkler) foundation. The analysis includes the determination of the nondimensional time for initial rupture, the propagation of the rupture front with the associated thinning of the beam, and the influence of creep damage on the deflection of the beam. Creep damage starts accumulating in the beam as soon as the load is applied, and a creep rupture front develops at and propagates from the point at which the creep damage first reaches its critical value. By introducing a series of fundamental assumptions within the framework of technical Euler-Bernoulli type beam theory, a governing set of integro-differential equations is derived in terms of the nondimensional bending moment and the deflection. These governing equations are subjected to a set of interface conditions at the propagating rupture front. A numerical technique is developed to solve the governing equations together with the interface equations, and the computed results are presented and discussed in detail.

Gu, Randy J.↗

NASA NTRS1983

Modeling of steady, rotational, transonic winds from rotating stars and galaxies

The theory of steady transonic winds from condensed bodies is extended to general, two-dimensional, axisymmetric systems. A stream function is used to reduce the gasdynamics equations to a single, second-order differential equation plus an algebraic equation for the density. The approach extends Parker's (1958) quasi-one-dimensional theory, which uses Bernoulli's theorem, to a complete two-dimensional calculation which includes vorticity and rotation. The conceptual basis of the stream function approach is described in detail, and a numerical method for solving the resulting equations is presented. The applications illustrate solutions for stellar (spherical source surface) and galactic (oblate spheroidal source surface) models. Among other things, it is found that for rapidly rotating stellar models the Coriolis force dominates the centrifugal terms and the streamlines bend toward the rotation axis as a consequence of the axisymmetry. For both the rotating and nonrotating galaxy models, the streamlines bend toward the equator.

Kopriva, D. A.↗

NASA NTRS1973

The solution of transcendental equations

Some of the existing methods to globally approximate the roots of transcendental equations namely, Graeffe's method, are studied. Summation of the reciprocated roots, Whittaker-Bernoulli method, and the extension of Bernoulli's method via Koenig's theorem are presented. The Aitken's delta squared process is used to accelerate the convergence. Finally, the suitability of these methods is discussed in various cases.

Agrawal, K. M.↗

NASA NTRS1988

A novel approach to the modelling and control of flexible robot arms

A general dynamic model of a two-link Euler-Bernoulli beam flexible robot arm is presented in the form of partial-differential-integral equations. Observations are made on important properties of the dynamic model. The resulting infinite-dimensional system is then input-output decoupled and partially linearized by a diffeomorphic state transformation and nonlinear state feedback. The local stability issue is addressed for a one-link flexible robot arm.

Ding, Xuru↗

NASA NTRS1990

A fully Sinc-Galerkin method for Euler-Bernoulli beam models

A fully Sinc-Galerkin method in both space and time is presented for fourth-order time-dependent partial differential equations with fixed and cantilever boundary conditions. The Sinc discretizations for the second-order temporal problem and the fourth-order spatial problems are presented. Alternate formulations for variable parameter fourth-order problems are given which prove to be especially useful when applying the forward techniques to parameter recovery problems. The discrete system which corresponds to the time-dependent partial differential equations of interest are then formulated. Computational issues are discussed and a robust and efficient algorithm for solving the resulting matrix system is outlined. Numerical results which highlight the method are given for problems with both analytic and singular solutions as well as fixed and cantilever boundary conditions.

Smith, R. C.↗