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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 343 records · Page 19
All sourcesNASA NTRSDOE OSTI
NASA NTRS1994

Micromechanical Modeling of the Thermal Expansion of Graphite/copper Composites with Nonuniform Microstructure

Two micromechanical models were developed to investigate the thermal expansion of graphite/copper (Gr/Cu) composites. The models incorporate the effects of temperature-dependent material properties, matrix inelasticity, initial residual stresses due to processing history, and nonuniform fiber distribution. The first model is based on the multiple concentric cylinder geometry, with each cylinder treated as a two-phase composite with a characteristic fiber volume fractions. By altering the fiber volume fraction of the individual cylinders, unidirectional composites with radially nonuniform fiber distributions can be investigated using this model. The second model is based on the inelastic lamination theory. By varying the fiber content in the individual laminae, composites with nonuniform fiber distribution in the thickness direction can be investigated. In both models, the properties of the individual regions (cylinders or laminae) are calculated using the method of cells micromechanical model. Classical incremental plasticity theory is used to model the inelastic response of the copper matrix at the microlevel. The models were used to characterize the effects of nonuniform fiber distribution on the thermal expansion of Gr/Cu. These effects were compared to the effects of matrix plasticity, choice of stress-free temperature, and slight fiber misalignment. It was found that the radially nonuniform fiber distribution has little effect on the thermal expansion of Gr/Cu but could become significant for composites with large fiber-matrix transverse CTE and Young's modulus mismatch. The effect of nonuniform fiber distribution in the through-thickness direction of a laminate was more significant, but only approached that of the stress-free temperature for the most extreme cases that include large amounts of bending. Subsequent comparison with experimental thermal expansion data indicated the need for more accurate characterization of the graphite fiber thermomechanical properties. Correlation with cyclic data revealed the presence of a mechanism not considered in the developed models. The predicted response did, however, exhibit ratcheting behavior that has been observed experimentally in Gr/Cu. Finally, simulation of the actual fiber distribution of particular specimens had little effect on the predicted thermal expansion.

Bednarcyk, Brett A.↗
NASA NTRS1994

Effects of Thermal Cycling on Thermal Expansion and Mechanical Properties of Sic Fiber-reinforced Reaction-bonded Si3n4 Composites

Thermal expansion curves for SiC fiber-reinforced reaction-bonded Si3N4 matrix composites (SiC/RBSN) and unreinforced RBSN were measured from 25 to 1400 C in nitrogen and in oxygen. The effects of fiber/matrix bonding and cycling on the thermal expansion curves and room-temperature tensile properties of unidirectional composites were determined. The measured thermal expansion curves were compared with those predicted from composite theory. Predicted thermal expansion curves parallel to the fiber direction for both bonding cases were similar to that of the weakly bonded composites, but those normal to the fiber direction for both bonding cases resulted in no net dimensional changes at room temperature, and no loss in tensile properties from the as-fabricated condition. In contrast, thermal cycling in oxygen for both composites caused volume expansion primarily due to internal oxidation of RBSN. Cyclic oxidation affected the mechanical properties of the weakly bonded SiC/RBSN composites the most, resulting in loss of strain capability beyond matrix fracture and catastrophic, brittle fracture. Increased bonding between the SiC fiber and RBSN matrix due to oxidation of the carbon-rich fiber surface coating and an altered residual stress pattern in the composite due to internal oxidation of the matrix are the main reasons for the poor mechanical performance of these composites.

Bhatt, R. T.↗
NASA NTRS1996

An Experimental and Computational Investigation of a Translating Throat Single Expansion-Ramp Nozzle

A translating throat single expansion-ramp nozzle (SERN) concept was designed to improve the off-design performance of a SERN with a large, fixed expansion ratio. The concept of translating the nozzle throat provides the SERN with a variable expansion ratio. An experimental and computational study was conducted to predict and verify the internal performance of this concept. Three nozzles with expansion ratios designed for low, intermediate, and high Mach number operating conditions were tested in the Jet-Exit Test Facility at the NASA Langley Research Center. Each nozzle was tested with a concave and a convex geometric expansion ramp surface design. Internal nozzle performance, paint-oil flow and focusing Schlieren flow visualization were obtained for nozzle pressure ratios (NPR's) up to 13. The Navier-Stokes code, PAB3D, with a k-epsilon turbulence model was utilized to verify experimental results at selected NPR's and to predict the performance at conditions unattainable in the test facility. Two-dimensional simulations were computed with near static free-stream conditions and at nozzle pressure ratios of 5, 9, and 13 for the concave ramp, low Mach number configuration and at the design NPR of 102 for the concave ramp, high Mach number configuration. Remarkable similarities between predicted and experimental flow characteristics, as well as performance quantities, were obtained.

Deere, Karen A.↗
NASA NTRS1996

An experimental and computational investigation of a translating throat single expansion-ramp nozzle

A translating throat single expansion-ramp nozzle (SERN) concept was designed to improve the off-design performance of a SERN with a large, fixed expansion ratio. The concept of translating the nozzle throat provides the SERN with a variable expansion ratio. An experimental and computational study was conducted to predict and verify the internal performance of this concept. Three nozzles with expansion ratios designed for low, intermediate, and high Mach number operating conditions were tested in the Jet-Exit Test Facility at the NASA Langley Research Center. Each nozzle was tested with a concave and a convex geometric expansion ramp surface design. Internal nozzle performance, paint-oil flow and focusing Schlieren flow visualization were obtained for nozzle pressure ratios (NPR's) up to 13. The Navier-Stokes code, PAB3D, with a k-epsilon turbulence model was utilized to verify experimental results at selected NPRs and to predict the performance at conditions unattainable in the test facility. Two-dimensional simulations were computed with near static free-stream conditions and at nozzle pressure ratios of 5, 9, and 13 for the concave ramp, low Mach number configuration and at the design NPR of 102 for the concave ramp, high Mach number configuration. Remarkable similarities between predicted and experimental flow characteristics, as well as performance quantities, were obtained.

Deere, Karen A.↗
NASA NTRS1986

Expansion and photosynthetic rate of leaves of soybean plants during onset of and recovery from nitrogen stress

This study reports on the effects of nitrogen stress and restoration of nitrogen availability after a period of stress on expansion and photosynthetic rate of soybean leaves of differing maturity. We hypothesized that nitrogen resupply would lead to additional accumulation of reduced nitrogen in the leaves and, ultimately, resumption of leaf initiation and expansion and photosynthetic activity. In continuously nitrogen-stressed plants, expansion of middle trifoliolates of main-stem trifoliates and leaf area at full expansion were severely restricted. Leaves showing the greatest effects were initiated after removal of nitrogen. When the reduced nitrogen concentration in mature leaves of continuously stressed plants fell below 9 mg dm-2, the photosynthetic rate per unit leaf decreased rapidly, reaching a minimum of ca. 6-8 mg dm-2 h-1. The older mature leaves tended to abscise at this point, while the youngest leaves remained on the plant and continued to photosynthesize slowly. When nitrogen was resupplied, leaf expansion and final leaf area increased. Leaf initiation was also stimulated as reduced nitrogen levels rose in the leaves. Photosynthetic rates of the oldest and youngest pair of mature leaves returned to values comparable to those of similar-aged leaves of nonstressed soybean plants.

NASA Discipline Number 61-10↗
NASA NTRS2010

Thermal Expansion of Vacuum Plasma Sprayed Coatings

Metallic Cu-8%Cr, Cu-26%Cr, Cu-8%Cr-1%Al, NiAl and NiCrAlY monolithic coatings were fabricated by vacuum plasma spray deposition processes for thermal expansion property measurements between 293 and 1223 K. The corrected thermal expansion, (DL/L(sub 0) varies with the absolute temperature, T, as (DL/L(sub 0) = A(T - 293)(sup 3) + BIT - 293)(sup 2) + C(T - 293) + D, where, A, B, C and D are thermal, regression constants. Excellent reproducibility was observed for all of the coatings except for data obtained on the Cu-8%Cr and Cu-26%Cr coatings in the first heat-up cycle, which deviated from those determined in the subsequent cycles. This deviation is attributed to the presence of residual stresses developed during the spraying of the coatings, which are relieved after the first heat-up cycle. In the cases of Cu-8%Cr and NiAl, the thermal expansion data were observed to be reproducible for three specimens. The linear expansion data for Cu-8% Cr and Cu-26%Cr agree extremely well with rule of mixture (ROM) predictions. Comparison of the data for the Cu-8%Cr coating with literature data for Cr and Cu revealed that the thermal expansion behavior of this alloy is determined by the Cu-rich matrix. The data for NiAl and NiCrAlY are in excellent agreement with published results irrespective of composition and the methods used for processing the materials. The implications of these results on coating GRCop-84 copper alloy combustor liners for reusable launch vehicles are discussed.

Raj, S V.↗
NASA NTRS2011

Relationship Between the Expansion Speed and Radial Speed of CMEs Confirmed Using Quadrature Observations from SOHO and STEREO

It is difficult to measure the true speed of Earth-directed CMEs from a coronagraph along the Sun-Earth line because of the occulting disk. However, the expansion speed (the speed with which the CME appears to spread in the sky plane) can be measured by such coronagraph. In order to convert the expansion speed to radial speed (which is important for space weather applications) one can use empirical relationship between the two that assumes an average width for all CMEs. If we have the width information from quadrature observations, we can confirm the relationship between expansion and radial speeds derived by Gopalswamy et al. (2009, CEAB, 33, 115,2009). The STEREO spacecraft were in quadrature with SOHO (STEREO-A ahead of Earth by 87 and STEREO-B 94 behind Earth) on 2011 February 15, when a fast Earth-directed CME occurred. The CME was observed as a halo by the Large-Angle and Spectrometric Coronagraph (LASCO) on board SOHO. The sky-plane speed was measured by SOHO/LASCO as the expansion speed, while the radial speed was measured by STEREO-A and STEREO-B. In addition, STEREO-A and STEREO-B images measured the width of the CME, which is unknown from Earth view. From the SOHO and STEREO measurements, we confirm the relationship between the expansion speed (Vexp ) and radial speed (Vrad ) derived previously from geometrical considerations (Gopalswamy et al. 2009): Vrad = 1/2 (1 + cot w) Vexp, where w is the half width of the CME. STEREO-B images of the CME, we found that CME had a full width of 75 degrees, so w = 37.5 degrees. This gives the relation as Vrad = 1.15 Vexp. From LASCO observations, we measured Vexp = 897 km/s, so we get the radial speed as 1033 km/s. Direct measurement of radial speed from STEREO gives 945 km/s (STEREO-A) and 1057 km/s (STEREO-B). These numbers are different only by 2.3% and 8.5% (for STEREO-A and STEREO-B, respectively) from the computed value.

Gopalswamy, Nat↗
DOE OSTI2014

Lattice-structures and constructs with designed thermal expansion coefficients

A thermal expansion-managed lattice structure having a plurality of unit cells each having flexure bearing-mounted tabs supported on a base and actuated by thermal expansion of an actuator having a thermal expansion coefficient greater than the base and arranged so that the tab is inwardly displaced into a base cavity. The flexure bearing-mounted tabs are connected to other flexure-bearing-mounted tabs of adjacent unit cells so that the adjacent unit cells are spaced from each other to accommodate thermal expansion of individual unit cells while maintaining a desired bulk thermal expansion coefficient of the lattice structure as a whole.

42 ENGINEERING↗
DOE OSTI2021

Method for tuning thermal expansion properties in an additive manufacturing feedstock material

A feedstock material for use in an additive manufacturing apparatus is prepared from a first material and a metal organic framework (MOF). The MOF comprises a plurality of nodes and a plurality of linkers, the plurality of linkers coupled to the plurality of nodes, thereby forming a framework. The MOF has a lower coefficient of thermal expansion than a coefficient of thermal expansion for the first material. As a result, the feedstock material has a reduced coefficient of thermal expansion as compared to the first material alone and thus exhibits low thermal expansion as its temperature is increased. The coefficient of thermal expansion for the MOF may be modified by using a different plurality of nodes and/or a different plurality of linkers, as well as by incorporating guest molecules or atoms into the framework of the MOF.

Burtch, Nicholas C.↗
DOE OSTI2013

Analysis of Lattice Baryon Masses in 1/Nc expansion

The 1/Nc expansion of QCD is a perturbative and successful framework for the phenomenology of ground state and excited state baryons. As proposed in [1], it is a systematic expansion in powers of 1/Nc and a good approximation, qualitatively and quantitatively, when Nc=3. The 1/Nc expansion has been applied to the ground state baryons including studies of SU(6) spin-flavor symmetry in [2]. A framework was suggested in [3] for excited baryons based on the 1/Nc expansion was implemented and analyzed with the physical masses from the Particle Data Group. And a successful calculation of the spin identified spectrum of Nucleons and Deltas has been carried out in lattice QCD [4]. Using mass operators organized according to the 1/Nc expansion, the analysis of lattice baryon masses has been completed for the negative parity baryons in the multiplet [70,1]? of the SU(6)×O(3) representation, and results for that multiplet and the rest of the multiplets will be presented in this talk.\\[4pt] [1] G. 'tHooft Nucl.Phys.B72, 461(1974).\\[0pt] [2] R.F. Dashen, E.E. Jenkins, and A.V. Manohar Phys.Rev.D51 (1995).\\[0pt] [3] C.E. Carlson, C.D. Carone, J.L. Goity, R.F. Lebed Phys.Rev.D59 (1999).\\[0pt] [4] R.G. Edwards, J.J. Dudek, D.G. Richards, S.J. Wallace Phys.Rev.D84 (2011).

Fernando, Ishara↗
DOE OSTI2010

The $\hbar$ Expansion in Quantum Field Theory

We show how expansions in powers of Planck's constant {h_bar} = h = 2{pi} can give new insights into perturbative and nonperturbative properties of quantum field theories. Since {h_bar} is a fundamental parameter, exact Lorentz invariance and gauge invariance are maintained at each order of the expansion. The physics of the {h_bar} expansion depends on the scheme; i.e., different expansions are obtained depending on which quantities (momenta, couplings and masses) are assumed to be independent of {h_bar}. We show that if the coupling and mass parameters appearing in the Lagrangian density are taken to be independent of {h_bar}, then each loop in perturbation theory brings a factor of {h_bar}. In the case of quantum electrodynamics, this scheme implies that the classical charge e, as well as the fine structure constant are linear in {h_bar}. The connection between the number of loops and factors of {h_bar} is more subtle for bound states since the binding energies and bound-state momenta themselves scale with {h_bar}. The {h_bar} expansion allows one to identify equal-time relativistic bound states in QED and QCD which are of lowest order in {h_bar} and transform dynamically under Lorentz boosts. The possibility to use retarded propagators at the Born level gives valence-like wave-functions which implicitly describe the sea constituents of the bound states normally present in its Fock state representation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Surviving nanoscale interfacial stability in extreme thermal expansion contrast Zn(CN) 2 -epoxy resin matrix composites

Here, we report the remarkable stability at the nanoscale matrix-filler interface in a series of overall low coefficient of thermal expansion (CTE) zinc cyanide (ZC)/epoxy resin composites. These interfaces demonstrate the stability of highly contrasting materials. These composites are designed to optimize the properties of both materials: epoxy resins are valued for their high strength, superb chemical resistance, low dielectric properties, and adhesive abilities. ZC, a model flexible framework, exhibits negative thermal expansion (NTE) behavior and compensates for the epoxy resin’s detrimentally large thermal expansion values. Filled resins minimize the native 65 ppm/°C CTE values to 19 ppm/° C over a wide temperature range while maintaining linearity, yielding composites compatible with typical metal and ceramic substrates’—commonly bonded to the resin— 0–20 ppm/° C CTE values. Additionally, with significant intrinsic differences in the materials, we use wide-angle X-ray diffraction and atomic force microscopy to elucidate thermal movement. The ZC/epoxy interface is surprisingly resilient over 1,000 cycles between -55° C and 75° C, extremes typical to aerospace applications. Further, we show that the resin viscosity remains less than 21 Pa*s at up to 30 vol% ZC, an important consideration for workability. We also discuss settling distribution, glass transition temperature, flexural strength, and longevity. All results point favorably towards practical implementation in low thermal expansion application needs: filling the gap in component design.

42 ENGINEERING↗
DOE OSTI2010

Defect structure, electronic conductivity and expansion of properties of (La{sub 1-x}Sr{sub x}){sub s}Co{sub 1-y}Ni{sub y}O{sub 3-{delta}}

This study reports on oxygen nonstoichiometry, electronic conductivity and lattice expansion of three compositions as function of T and P{sub O{sub 2}} in the (La{sub 1-x}Sr{sub x}){sub s}Co{sub 1-y}Ni{sub y}O{sub 3-{delta}}(x=0.1, y=0.4; x=0.1, y=0.3; x=0.2, y=0.2) materials system. The nonstoichiometry data were successfully fitted using the itinerant electron model which indicates the existence of delocalized electronic states. This was also reflected in the high electronic conductivities, above 1000 S cm{sup -1}, measured for all three compositions. The electronic conductivity was shown to decrease linearly with the oxygen nonstoichiometry parameter, {delta}, supporting that the conductivity is dependent on p-type charge carriers. Comparing calculated p-type mobilities with data reported in literature on La{sub 1-x}Sr{sub x}CoO{sub 3} indicated that Ni-substitution into (La{sub 1-x}Sr{sub x}){sub s}CoO{sub 3-{delta}}increases the p-type mobility. The electronic conductivity was also found to be dependent on intrinsic charge related to spin excitations and Ni substitution rather than the p-type charge. A conductivity mechanism is hypothesized including a metallic like conductivity of the p-type charge and a small polaron conductivity of the intrinsic charge. Lattice expansion as function of T and {delta} was successfully described using first and second order thermal and chemical expansion coefficients. Substituting 10% Co with Ni in (La{sub 0.6}Sr{sub 0.4}){sub 0.99}CoO{sub 3-{delta}}was found to decrease the apparent thermal expansion with about 25%. - Graphical Abstract: Electronic conductivity as function of temperature for (La{sub 0.8}Sr{sub 0.2}){sub 0.99}Co{sub 0.8}Ni{sub 0.2}O{sub 3-{delta}}. A model with metallic like conductivity for the extrinsic p-type charge carrier (due to Sr substitution) and small polaron conductivity for intrinsic charge carriers (due to Co spin transitions) was found to best describe the total conductivity.

36 MATERIALS SCIENCE↗
DOE OSTI2016

Problems and solutions for the analysis of somatic CAG repeat expansion and their relationship to Huntington's disease toxicity

Huntington’s Disease is caused by inheritance of a single disease-length allele harboring an expanded CAG repeat, which continues to expand in somatic tissues with age. Whether somatic expansion contributed to toxicity was unknown. From extensive work from multiple laboratories, it has been made clear that toxicity depended on length of the inherited allele, but whether preventing or delaying somatic repeat expansion in vivo would be beneficial was unknown, since the inherited disease allele was still expressed. In Budworth et al., we provided definitive evidence that suppressing the somatic expansion in mice substantially delays disease onset in littermates that inherit the same disease-length allele. This key discovery opens the door for therapeutic approaches targeted at stopping or shortening the CAG tract during life. The analysis was difficult and, at times, non-standard. Here, we take the opportunity to discuss the challenges, the analytical solutions, and to address some controversial issues with respect to expansion biology.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2016

Initial Comparison of Direct and Legacy Modeling Approaches for Radial Core Expansion Analysis

Radial core expansion in sodium-cooled fast reactors provides an important reactivity feedback effect. As the reactor power increases due to normal start up conditions or accident scenarios, the core and surrounding materials heat up, causing both grid plate expansion and bowing of the assembly ducts. When the core restraint system is designed correctly, the resulting structural deformations introduce negative reactivity which decreases the reactor power. Historically, an indirect procedure has been used to estimate the reactivity feedback due to structural deformation which relies upon perturbation theory and coupling legacy physics codes with limited geometry capabilities. With advancements in modeling and simulation, radial core expansion phenomena can now be modeled directly, providing an assessment of the accuracy of the reactivity feedback coefficients generated by indirect legacy methods. Recently a new capability was added to the PROTEUS-SN unstructured geometry neutron transport solver to analyze deformed meshes quickly and directly. By supplying the deformed mesh in addition to the base configuration input files, PROTEUS-SN automatically processes material adjustments including calculation of region densities to conserve mass, calculation of isotopic densities according to material models (for example, sodium density as a function of temperature), and subsequent re-homogenization of materials. To verify the new capability of directly simulating deformed meshes, PROTEUS-SN was used to compute reactivity feedback for a series of contrived yet representative deformed configurations for the Advanced Burner Test Reactor design. The indirect legacy procedure was also performed to generate reactivity feedback coefficients for the same deformed configurations. Interestingly, the legacy procedure consistently overestimated reactivity feedbacks by 35% compared to direct simulations by PROTEUS-SN. This overestimation indicates that the legacy procedures are in fact not conservative and could be overestimating reactivity feedback effects that are closely tied to reactor safety. We conclude that there is indeed value in performing direct simulation of deformed meshes despite the increased computational expense. PROTEUS-SN is already part of the SHARP multi-physics toolkit where both thermal hydraulics and structural mechanical feedback modeling can be applied but this is the first comparison of direct simulation to legacy techniques for radial core expansion.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2019

Synchrotron Based Measurement of the Temperature Dependent Thermal Expansion Coefficient of Ammonium Perchlorate

Ammonium perchlorate is commonly used as an oxidizer in solid rocket propellant. Having a knowledge of its thermal expansion properties is essential for its application in different environments. Knowledge of thermal expansion properties is also useful for the prediction of propellant mechanical properties and response of propellant slow cook off applications. X-ray diffraction analysis was performed on ammonium perchlorate at temperatures ranging from 260 K to 500 K. From there, Bragg peaks were indexed by fitting theoretical values of 2θ to the 2θ values of peaks obtained from the experiment. Additionally, the Miller indices along with the 2θ values were then used to solve for the lattice parameters at each temperature. The lattice parameters, in nanometers, range from 0.9201 to 0.9373, 0.5805 to 0.5865, and 0.7439 to 0.7535 for a , b , and c , respectively. The measurement of the lattice parameter expansion leads to the determination of the temperature dependent thermal expansion coefficients within the temperature range. The lattice parameter values also lead to the determination of strain and stress on the ammonium perchlorate crystal. Direct measurement of the strain within the crystal lattice provides a more accurate measurement method over traditional optical-based techniques.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2018

Large N expansion of the moments and free energy of Sachdev-Ye-Kitaev model, and the enumeration of intersection graphs

In this paper we explain the relation between the free energy of the SYK model for N Majorana fermions with a random q-body interaction and the moments of its spectral density. The high temperature expansion of the free energy gives the cumulants of the spectral density. Using that the cumulants are extensive we find the p dependence of the 1/N 2 correction of the 2p-th moments obtained in [1]. Conversely, the 1/N 2 corrections to the moments give the correction (even q) to the β 6 coefficient of the high temperature expansion of the free energy for arbitrary q. Our result agrees with the 1/q 3 correction obtained by Tarnopolsky using a mean field expansion. These considerations also lead to a more powerful method for solving the moment problem and intersection-graph enumeration problems. We take advantage of this and push the moment calculation to 1/N 3 order and find surprisingly simple enumeration identities for intersection graphs. The 1/N 3 corrections to the moments, give corrections to the β 8 coefficient (for even q) of the high temperature expansion of the free energy which have not been calculated before. Results for odd q, where the SYK “Hamiltonian” is the supercharge of a supersymmetric theory are discussed as well.

1/N Expansion↗
DOE OSTI2010

Baroclinic vortex sheet production by shocks and expansion waves

Vortex sheet production by shocks and expansion waves refracting at a density discontinuity was examined and compared using an analytical solution and numerical simulations. The analytical solution showed that with a small exception, vortex sheet strength is generally stronger in fast/slow shock refractions. In contrast, expansion waves generated a stronger vortex sheet in slow/fast refractions. This difference results in larger vorticity deposited by shocks in fast/slow refractions and by expansion waves in slow/fast refractions. Shock refractions become irregular and the analytical solution fails when either incident, transmitted or reflected shock, exceeded the angle limit for an attached shock. To investigate vortex sheet production outside the range of analytical solutions and to verify the applicability of the planar-interface analytical solution to a curved interface, shock refraction through a sinusoidal interface was numerically simulated in the shock frame of reference. It is found that variation in the local incidence angle along the curved interface creates pressure waves that affect the level of deposited vorticity. This contributes to the difference between predictions from local analysis and numerical computation. Furthermore, an interesting behavior of the shock and expansion wave-deposited vorticity in supersonic ramp flow was discovered. When the high- and low-density streams were swapped, while keeping the incident flow Mach numbers constant, a vortex sheet of equal magnitude but of opposite sign was generated.

97 MATHEMATICS AND COMPUTING↗