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Composite structures can be laminated to have very low coefficients of thermal expansion. Such structures are light and strong and have many uses where expansion or contraction with temperature change is undesirable. One application is with instruments that measure thermal expansion.
A theoretical and experimental investigation of the kinetics of CO2 dimer formation in the adiabatically expanding core of a free jet expansion has been carried out. The theoretical analysis is based on dimer formation by an efficient termolecular process and dimer destruction by bimolecular collisions. Account is taken of the expected variation of the specific heat ratio during the expansion and of the effective increase in the termolecular collision rate at low temperatures due to the presence of loosely bound orbiting pairs. Experimental dimer concentrations were measured mass spectrometrically by forming a molecular beam from the expanded gas mixture after the onset of molecular flow. Observed dimer concentrations, for a range of pre-expansion conditions of 400 to 900 torr pressure and room temperature, are in good agreement with the theoretical analysis, provided that account is taken of the effect of loosely bound orbiting pairs at low temperatures.
Free-stream flow velocity measurements were made in the Langley pilot model expansion tube during the test flow interval. During this interval, an anomalous dip in pitot pressure occurs for the expansion tube operating conditions employed. Within the test flow interval, the main conclusions reached from comparison of the measured flow velocity, pitot pressure, and tube wall pressure are: the variations which occur in velocity and wall pressure are small compared with the variations in pitot pressure; a corresponding dip in the derived flow density is associated with the dip in pitot pressure; and the value of the average density over the interval, which results from the expansion from the shocked intermediate chamber condition, is approximately one-half of the value that can result from only an isentropic process.
An analytical study of the unsteady wave interaction of a shock wave overtaking a previously initiated shock tube flow has been conducted for a real gas by solving a finite-difference representation of the one-dimensional Navier-Stokes equations. This analysis has been used to determine the effect on the available test time of opening the secondary diaphragm in the expansion-tube operating cycle prior to the arrival of the incident shock wave. Special emphasis is placed on determining expansion-tube test-time limitations resulting from a nonuniform entropy distribution occurring during the early test-gas flow due to the varying Mach number of the incident shock wave as it traverses the expansion fan caused by the preopening process. Time distributions of velocity, temperature, pressure, and entropy at various distances from the diaphragm are presented as a function of the time required to open the diaphragm.
This paper presents a technique for the partial-fraction expansion of functions which are ratios of polynomials with real coefficients. The expansion coefficients are determined by writing the polynomials as Taylor's series and obtaining the Laurent series expansion of the function. The general formula for the inverse Laplace transform is also derived.
The design requirements of the aerospace and high-temperature nuclear reactor industries necessitate reliable thermal expansion data for graphite and other carbonaceous materials. The feasibility of an acceptable reference for calibration of expansion measuring systems that operate in carbon-rich atmospheres at temperatures ranging to 2500 C is the prime subject of this work. Present-day graphite technology provides acceptable materials for stable, reproducible references, as reflected by some of the candidate materials. The repeatability for a single specimen in a given expansion measuring system was found to be plus or minus 1%, while the combined results of several tests made on a number of samples fell within a plus or minus 2.5% band.
The thermal expansion of GeSe has been studied above room temperature up to the melting point of 670 plus or minus 5 C by X-ray diffraction techniques using a 190 mm Unicam high temperature camera. The thermal expansion of the crystallographic axes is linear with a distinct change in the expansion coefficients for all axes above 400 C. The relative changes in the axes indicate a rearrangement of the structure towards cubic symmetry with increasing temperature. The transformation of GeSe from the orthorhombic to a normal NaCl-type structure is observed at 651 plus or minus 5 C. The lattice parameter of the cubic form of GeSe is a 0 ? 5.730 plus or minus 0.003 A at 656 C. The GeSe lattice remains cubic up to the melting point.
The exhaust plumes of the space shuttle solid rocket motors can have a significant effect on the base pressure and base drag of the shuttle vehicle. A parametric analysis was conducted to assess the sensitivity of the initial plume expansion angle of analytical solid rocket motor flow fields to various analytical input parameters and operating conditions. The results of the analysis are presented and conclusions reached regarding the sensitivity of the initial plume expansion angle to each parameter investigated. Operating conditions parametrically varied were chamber pressure, nozzle inlet angle, nozzle throat radius of curvature ratio and propellant particle loading. Empirical particle parameters investigated were mean size, local drag coefficient and local heat transfer coefficient. Sensitivity of the initial plume expansion angle to gas thermochemistry model and local drag coefficient model assumptions were determined.
The introductory sections of the work are devoted to the theory of thermal expansion of solids and to methods for the measurement of the linear thermal expansion of solids (X-ray methods, high speed methods, interferometry, push-rod dilatometry, etc.). The bulk of the work is devoted to numerical data on the thermal linear expansion of all the metallic elements, a large number of intermetallics, and a large number of binary alloy systems and multiple alloy systems. A comprehensive bibliography is provided along with an index to the materials examined.
A study was conducted to examine the effect of synchronization of an electromagnetically opened tertiary diaphragm with flow arrival at the diaphragm on the pitot pressure measured at the test section of an expansion tunnel. The effect of tertiary diaphragm pressure ratio (ratio of initial nozzle pressure to quiescent acceleration section pressure) on the pitot pressure time history is also determined. The inadequacy of a pressure transducer protection arrangement used in previous expansion tube and expansion tunnel tests was revealed.
The thermal expansion of a composite of epoxy (diglycidyl ether of bisphenol A) and solid glass microspheres was investigated. The microspheres had surfaces which were either untreated or treated with a silicone release agent, an epoxy coupling agent, or a general purpose silane coupling agent. Both room temperature (about 300 K) and elevated temperature (about 475 K) cures were used for the epoxy. Two microsphere size ranges were used, about 50 microns, which is applicable in filled moldings, and about 125 microns, which is applicable as bond line spacers. The thermal expansion of the composites was measured from 300 to 350 K or from 300 to 500 K, depending on the epoxy cure temperature. Measurements were made on composites containing up to .6 volume fraction microspheres. Two predictive models, which required only the values of thermal expansion of the polymer and glass and their specific gravities, were tested against the experimental data. A finite element analysis was made of the thermal strain of a composite cell containing a single microsphere surrounded by a finite-thickness interface.
Fourier expansions based on both the true anomaly and the mean anomaly are obtained for the functions of velocity in the two-body problem; the series of coefficients is written from classical formulae involving associated Legendre polynomials, Gegenbauer polynomials, or Bessel functions. The Fourier expansions are compared with the expansions in powers of eccentricity developed by Broucke (1974) through use of computerized Poisson series manipulation.
Cooling is one of the critical technologies for efficient design of exhaust nozzles, especially for the developing technology of nonaxisymmetric (2D) nozzles for future aircraft applications. Several promising 2D nozzle designs have external expansion surfaces which need to be cooled. Engine data are scarce, however, on nozzle cooling effectiveness in the supersonic flow environment (with shocks) that exists along external expansion surfaces. This paper will present experimental film cooling data obtained during exploratory testing with an axisymmetric plug nozzle having external expansion and installed on an afterburning turbojet engine in an altitude test facility. The data obtained shows that the shocks and local hot gas stream conditions have a marked effect on film cooling effectiveness. An existing film cooling correlation is adequate at some operating conditions but inadequate at other conditions such as in separated flow regions resulting from shock-boundary-layer interactions.
The saturated equilibrium expansion approximation for two phase flow often involves ideal-gas and latent-heat assumptions to simplify the solution procedure. This approach is well documented by Wegener and Mack and works best at low pressures where deviations from ideal-gas behavior are small. A thermodynamic expression for liquid mass fraction that is decoupled from the equations of fluid mechanics is used to compare the effects of the various assumptions on nitrogen-gas saturated equilibrium expansion flow starting at 8.81 atm, 2.99 atm, and 0.45 atm, which are conditions representative of transonic cryogenic wind tunnels. For the highest pressure case, the entire set of ideal-gas and latent-heat assumptions are shown to be in error by 62 percent for the values of heat capacity and latent heat. An approximation of the exact, real-gas expression is also developed using a constant, two phase isentropic expansion coefficient which results in an error of only 2 percent for the high pressure case.
The effect of static tensile load on the thermal expansion of Gr/PI composite material was measured for seven different laminate configurations. A computer program was developed which implements laminate theory in a piecewise linear fashion to predict the coupled nonlinear thermomechanical behavior. Static tensile load significantly affected the thermal expansion characteristics of the laminates tested. This effect is attributed to a fiber instability micromechanical behavior of the constituent materials. Analytical results correlated reasonably well with free thermal expansion tests (no load applied to the specimen). However, correlation was poor for tests with an applied load.
Thermal expansion data for several composite materials, including generic epoxy resins, various graphite, boron, and glass fibers, and unidirectional and woven fabric composites in an epoxy matrix, were compiled. A discussion of the design, material, environmental, and fabrication properties affecting thermal expansion behavior is presented. Test methods and their accuracy are discussed. Analytical approaches to predict laminate coefficients of thermal expansion (CTE) based on lamination theory and micromechanics are also included. A discussion is included of methods of tuning a laminate to obtain a near-zero CTE for space applications.
Silicon has interesting harmonic and anharmonic properties such as the low lying transverse acoustic modes at the X and L points of the Brillouin zone, negative Gruneisen parameters, negative thermal expansion and anomalous acoustic attenuation. In an attempt to understand these properties, a lattice dynamical model employing long range, nonlocal, dipole-dipole interactions was developed. Analytic expression for the Gruneisen parameters of several modes are presented. These expressions explain how the negative Gruneisen parameters arise. This model is applied to the calculation of the thermal expansion of silicon from 5K to 1700K. The thermoelastic contribution to the acoustic attenuation of silicon is computed from 1 to 300 K. Strong attenuation anomalies associated with negative thermal expansion are found in the vicinity of 17K and 125K.
Cyclic furnace and cyclic natural gas-oxygen torch rig tests were conducted to (1) identify a thermal-barrier system for a nickel-aluminum-molybdenum alloy, (2) study the oxidation of the bond coating, and (3) study the effect of the substrate coefficient of thermal expansion on thermal barrier system life. It is found that the latter is affected by the composition of the bond coating, yttria concentration in zirconia, and the coefficient of thermal expansion of the substrate material. In addition, small compositional changes in the bond and thermal barrier coatings have greater effect on thermal barrier system life than the 40% increase in the coefficient of thermal expansion of the substrate material. No simple relation exists between the weight gain caused by bond-coating oxidation with increasing yttria concentration in zirconia and increasing bond coating thickness on the one hand, and thermal barrier system life on the other.