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An earlier analysis of a viscous mixing region with heat addition interacting with a supersonic external flow has been extended to include cases with a sloped wall beneath the viscous region. Also, cases with a supersonic to subsonic transition at the viscous throat have been studied for the first time. Limitations on the allowable heating value of the fuel that correspond to smooth subsonic to supersonic, or supersonic to subsonic transitions, are delineated and explained. The effects of wall slope at the throat and external Mach number on these limitations are shown. The results of calculations for representative cases show that it is possible to cancel base drag and even produce net thrust for cases with downward sloped walls if the initial Mach number in the viscous zone is supersonic prior to addition of heat. This corresponds to a supersonic to subsonic transition. For an initially subsonic flow, the results indicate pressures below the freestream static pressure throughout the flowfield. This means that only very limited drag from flameholders, such that the flow remains supersonic before heat addition, are advisable. Finally, some directions for future work are outlined.

In inany applications of slot injection in supersonic or hypersonic flow, the static pressures of the external and injectant streams are not matched. We have developed a simplified analysis of cases with initial pressure mismatch for tangential slat injection into a hypersonic ( o r supersonic) external flow having a thick, turbulent initial boundary layer including tho effects of turbulentmiuing, viscid/inviscid'interaction, skin friction and heat transfer and heat release for reactive injectants. The treatment uses hypersonic (or supersoni.c) small disturbance theory, R power law shape for the initial boundary layer velocity profile and a Crscco integral to get the temperature profile, a turbulent entrainment model including the effect oE a Convective Mach Number, a quasi-1D assumption in the miring and burning region, an instantaneous, one-step heat release modo1 and simple models of skin friction and heat transfer. 'The initial adjustments at the slot lip and further interactions with the viscous regions by waves reflected off the lower wall are treated with weak, locally inviscid waves. Laminar cases can also he handled. Good agreement of predictions with experiment for several experimental cases for gross flayfield variables such as p(x), A ( r ) , M(x) , T,(x), ete. was achieved. Both overand underexpanded cases were treated. The calculations need only about 1-2 seconds of CPU time on an Amdahl 5890 c lass csmputer. Lastly, calculations for combustor flowfields for a generic Scramjet vehicle at a flight Mach number of 10 with 0 . 8 5 pj/p, 2 1.25 are @"en and discussed . I

A range of boundary value problems is solved that describe the steady state temperature distribution in a solid circular cylinder of infinite length, moving in the direction of its axis. The cylinder is heated by a hot gas flowing perpendicularly to the cylinder. The problems differ in complexity depending on whether or not the cylinder is radially isothermal and the gas temperature uniform. Dimensionless charts are presented. This work pertains to the “moving wire techniques” for studying polymer flammability and measuring heat transfer from gases.

This paper deals with the problem of fire resistance where walls of a structure must be penetrated with electric cables or air channels. It attempts to provide helpful information to those involved in the design, architecture and inspection of such buildings.

Recent far ultraviolet spectra of four nightside auroras observed with the extreme ultraviolet (e.u.v.) spectrometer abroad the STP 78−1 satellite (Bowyer et al. , 1981) are discussed in terms of two secondary electron flux distribution models. One of these is based on calculations published by Rees and Maeda (1973) and the other on electron flux observations. Using the 1084 A NII line as the norm, the relative intensities of several lines in the range 900–1400 A could be fitted equally well by either model, indicating that some of these emission ratios are somewhat independent of the energy dependence of the secondary electron flux. The ratio of the NI 1243 A to 1084 A emission is seen to yield an effective correlation for the other observed emissions and a reasonably consistent estimate of the penetration depth of the aurora.

In this paper we investigate the influence of the range of the potential on the phase diagram for higher-neighbor Ising systems on the face-centered-cubic lattice. The density weight factors and lattice constants needed to evaluate the diagrams that contribute to the first six terms in the high-temperature expansion at arbitrary density are obtained. The resulting expression for the free energy is in the form of a series in the density and the four coupling constants ${J}_{1}$, ${J}_{2}$, ${J}_{3}$, and ${J}_{4}$ describing the potential energy as a function of interatomic distance. Differentiation of this expression with respect to density yields a series for the chemical potential. The phase diagram is obtained by straightforward analysis of this series. The results show that the coexistence curve depends on the effective number of nearest neighbors but is insensitive to the shape of the potential.

A simplified analysis that, however, treats all the primary physical and chemical processes of the flow has been developed. Numerical examples based on realistic values of the airstream and fuel conditions and parameters are used to illustrate the behavior of the resulting flow. It is shown that base burning at low fuel flow rates is attractive for base drag reduction. It is further shown that external burning adjacent to the base region is unattractive for base drag reduction or propulsion, either by itself or combined with base burning.

A hole in a wall weakens the wall's ability to withstand fire. Key parameters that control the safety of the system are identified through a calculation of the temperatures. To obtain the most severe case, a steady state is assumed. The mass flow rate ṁ g through the hole and the thickness l of the wall are the most important parameters. These may be grouped with the gas viscosity μ g to form the dimensionless quantity ṁ g /lμ g . When the value of this quantity is near 1, the back face of the wall and the emerging gases are cool. They are dangerously hot when ṁ g /lμ g is near 100.

The accurate prediction of nozzle flows for ramjets and scramjets is important for design and system performance analysis. The problem is made complex by the presence of strongly nonuniform entrance profiles, especially for scramjets (which have no throat at the end of the combustor). Thus, turbulent mixing and, often, chemical reactions can be expected to be under way during the expansion process. The rapid expansion common in nozzles implies substantial radial pressure gradients. Taken together, these requirements lead to the necessity of utilizing the full Navier-Stokes equations for a compressible, multicomponent, turbulent flow with finite-rate chemistry. For this work, the unsplit, explicit, MacCprmack unsteady/finite-difference method was used to solve the equations of motion. Turbulence transport is represented with a turbulent kinetic energy model. Chemistry is treated at this time by either frozen equilibrium or a simple, global finite-rate model. Calculations are presented for a typical scramjet case where the effects of nonuniform inflow profiles on the nozzle flowfield and performance are shown for different nozzle designs.

A calculation procedure for predicting turbulent mixing and burning.and skin friction and wall heat transfer in a scramjet combustor with a central fuel jet from a gas generator has been developed. All the important physical and chemical processes have been modeled, including the upstream influence of heat release on the initial conditions and the pressure distribution in the duct. Calculations for a representative engine with Shelldyne H fuel at Mach 4 and 7 indicate that a combustor 1 to 2 m long is sufficient to insure complete heat release but that substantial nonuniformity of the combustor exit flow would still exist. The skin friction and wall heat transfer are both shown to be very sensitive to the local pressure gradient and to the impingement of combustion products and turbulence from the central jet mixing and burning zone. However, the responses of these two quantities are not of the same importance, and they are not in phase.

This paper attempts to predict from first principles the behavior of fire propagating in slug flow in a thermally thin fuel-lined duct. The duct can lose heat to the surroundings. Extinction and acceleration limits are explored and the propagation speed calculated. The results indicate that a number of the trends observed by Roberts and Clough in thermally thick ducts are also possible in thin ducts.

A numerical procedure based on the full Navier-Stokes equations as applied to the flow near a body/propeller system is developed. The flow is assumed axisymmetric, and the unsteady equations of motion are cast in terms of a stream function, one vorticity component, and the peripheral velocity. The voricity equation and the peripheral momentum equation are solved by an Alternating Difference Implicit technique, and the Poisson equation for the stream function is solved by direct matrix reduction. The propeller is modeled as a an actuator disk, and the direct simulation of a given actual propeller is considered in detail. Turbulent transport is modeled by an integrated Turbulent Kinetic Energy equation with a simple extension to represent the effects of swirl. Detailed comparisons with wind tunnel measurements at x/D = 2 show a good prediction of the axial velocity but an underprediction of the swirl level.

The approach taken has been to utilize experimental heat loss data in a computer synthesization of operating boundaries. Further selective running was then undertaken to confirm the results obtained.

A new method of measuring molecular diffusion coefficients of gases which makes use of precise sampling and gas analysis downstream of an essentially point source of trace gas in a uniform carrier gas has been recently described in several publications. The technique is especially adapted for determinations at elevated temperatures. The present paper is a discussion of binary diffusion data over the temperature range 300°–1150° K for all of the gas pairs studied at APL to date. These include HeN 2 , CO 2 N 2 , HeA, CO 2 O 2 , CH 4 O 2 , H 2 O 2 , COO 2 and H 2 OO 2 . The data cover a wide enough range in temperature and are of sufficient precision (∼±2 per cent) so that it is possible to examine them in terms of the kinetic theory of dilute gases and the intermolecular potential energy functions characterizing binary collision processes. The three functions used for which the necessary collision integrals had already been evaluated are the inverse power point center of repulsion potential, the Lennard-Jones (12ndash;6) potential, and the modified Buckingham (Exp-6) potential. In addition, the collision integrals for the exponential point center of repulsion potential were evaluated by numerical means. The details of this calculation, which was performed on the Univac 1103 Digital Computer, will be published elsewhere. It is shown that while all four potentials can be fitted to the data about equally well, the actual potentials obtained in this way may be quite different. Conversely, however, the high temperature diffusion coefficients predicted from the four potentials fitted at lower temperatures agree rather well.

The subject to be discussed is that in which many elementary chemical reactions occur simultaneously in a gas undergoing laminar, steady, adiabatic flow through a supersonic expanzion nozzle. Some general comments on the techniques involved in the numerical analysis of this type of non-equilibrium flow with a high-speed digital computer will be given, but the emphasis throughout is on the chemical kinetic aspects of the problem. All internal degrees of freedom of the molecules are assumed to be in equilibrium with the local translational temperature everywhere. The flow is taken to be one dimensional in the usual fluid dynamic sense. The interaction between chemical and fluid dynamic variables is illustrated by actual results on two types of mixtures. The first is characteristic of many ordinary solid or liquid rocket propellant exhaust gases and contains the species H2, H2O, CO, CO2, H, and OH. The reasons for assuming that these take part in four elementary (reversible) reactions of importance are given. The second example considers a mixture containing the active species H2, H2O, O2, H, OH, and O such as would be involved in a hydrogen-fueled ramjet, where eight elementary reactions are used. The relative significance of two-body and three-body reactions in influencing the gas composition and other flow variables is discussed. Some indication of the sensitivity of the results to the magnitudes assumed for the rate constants will be given. The degree of utility and validity of various popular approximations in this field is assessed, and some practical implications pointed out.

Initial air boundary layer effect on ignition of slot-injected gaseous hydrogen in supersonic airstream, discussing isotherm and streamline patterns

The general equations governing the behaviour of a low velocity steady state, premixed, laminar flame are given for the case of spherical symmetry, and the differences from the plane flame pointed out. Numerical solutions obtained on the IBM-650 computer for the simple A → B flame with Lewis number unity are discussed. Two innovations introduced in this type of calculation are : (a) the integrations were performed by starting at the cold instead of the hot boundary, which was simpler in this case, and (b) the flameholder temperature was regarded is the eigenvalue instead of the mass fow rate. The definition of burning velocity is discussed, and is dependence on radius of curvature in clearly shown by the results. The relation between flameholder heat loss and stability is examined in the light of a recent discovery by Hirschfelder and co-workers. The advantages of the spherical flame for flame structure studies are described.

Fig. 2 Curvature of the diffracted shock. Numbers on the curves express the angle of yaw in degrees. with m and k taking the limiting values [5/(7)] (1 +^tan £) and[l/(7)](l+itan£). These results simplify to Lighthill's Eqs. (53) and (54) when the angle of yaw tends to zero, i.e., when the shock line is parallel to the leading edge of the wedge. Numerical computations were carried out for the complete ranges of the shock strength and the angle of yaw consistent with conical flowfields, i.e., within the limits depicted in Fig. 1. A few sample curves (Fig. 2) showing the dependence of curvature on the angle of yaw have been presented to bring out the following observations. 1) The effect of the yaw reduces the curvature of the diffracted shock near the intersection of the diffracted shock and the cone of disturbance and increases it towards the intersection of the diffracted shock and the wedge, thereby resulting in a shift of the point of maximum curvature towards the wedge surface. This is apparent from computations for £ 0.5,0.33333, and 0.20723. 2) For high shock strengths the shock is concave to the still air near the wedge surface changing to convex through a point of inflexion. This point of inflexion is forced towards the wedge surface with an increase in the angle of yaw as depicted for shock with infinite strength ({ = 0). 3) The effect of the angle of yaw is more dominant when we approach the upper limit of the angle of yaw, i.e., the curvature is very sensitive to small changes in the angle of yaw when the upper limit is approached. This is similar to the sensitivity of the pressure perturbations to small changes in the angles of yaw as exhibited in Chester's Fig. 5.

A simplified analysis of tangential slot injection into a hypersonic (or supersonic) external flow having a thick. turbulent initial boundary layer including the effects of turbulent mixing, viscid/inviscid interaction, modest initial pressure mismatch. skin friction and heat transfer and heat release for reactive injectants is derived. The treatment uses hypersonic (or supersonic) small disturbance theory, a power law shape for the initial boundary layer velocity profile and a Crocco integral to get the temperature profile, a turbulent entrainment model including the effect of a Convective Mach Number, a quasi-1D assumption in the mixing and burning region, an instantaneous, onestep heat release model and simple models of skin friction and heat transfer. Good agreement o f predictions with experiment for several cases without and with burning for gross flowfield variables such as P(x), A(x), M(x), T o ( x ) , etc. was achieved The calculations need only about 1-2 seconds of CPU time on an Amdahl 5890 class computer. Lastly, calculations for combustor flowfields for a generic Scramjet vehicle at a flight Mach number of 10 with a realistic range of values for the boundary layer thickness at the injection station and slot height and injection Mach number and total temperature are given and discussed. v

Analytical approximations of the stratified, laminar flow past a flat plate are considered. Perturbation solutions are obtained for the flow on the plate and in the far wake with a boundary-layer type of approximation and for the whole flowfield with a low Reynolds' number approximation. The boundary-layer approximate solutions show that the wall shear on the plate is increased and that the rate of decay of the velocity defect in the wake is markedly increased. In the low Reynolds' number regime, the effects of the stratification are much larger ahead of and behind the plate than on the plate itself.

ASIMPLE analysis of the base pressure on a projectile with mass addition was sought, so that base drag reduction due to injection could be estimated. A numerical treatment was rejected, since only limited success has been achieved with this approach for simpler problems of the same type.1 The Crocco-Lees2'3'4 approach was not used, since it does not permit easy extension for injection3 or axisymmetric geometry.5'6 The approach of Refs. 7 and 8 that was successful for planar problems with injection was chosen as the starting point. That approach involves separate models for separate regions—the main mixing region, the corner/base region, and a recirculation region for low injection rates joined together. The main problem in any axisymmetric analysis is the selection of a pressure-angle relationship. For the planar arrangement, we used9

The magnetic field data acquired by the TRIAD satellite sometimes show variations with periods longer than 10 min and with amplitudes of a few thousand nanoTeslas due to attitude oscillations. From a study of 150 passes, the principal oscillations of TRIAD have been identified as the well-known librations of a gravity-stabilized satellite. The libration periods are approximately T0/2 and T0/(3)1/2, where T0 is the orbit period of about 100 min. The amplitude and phase of these librations appear to change over periods of a few days, and sometimes they vanish altogether. By use of data acquired over several consecutive TRIAD orbits, these attitude variations can be numerically evaluated and removed, leaving the disturbances associated with Birkeland currents. The establishment of a ‘base line’ for the TRIAD observations by using this technique has permitted, for the first time, a preliminary evaluation of the ‘current-free’ magnetic field disturbance due to large-scale Birkeland currents. Data acquired from three consecutive TRIAD passes (spanning more than 3 hours) show nearly the same magnetic disturbance profile, which extends as far as 10 degrees in latitude from a single (net) region 1 Birkeland current sheet. These observations confirm the permanent and global nature of large-scale Birkeland currents.