Supersonic Heat Research Articles

Supersonic heat wave in low density foams generated by soft X-radiation from a Z-pinch plasma

Abstract An intense soft X-ray pulse of radiation ≈1 TW/cm2 generates in low (less than 50 mg/cm3) density foam nonlinear radiative heat waves, which propagate with a velocity several times higher than the sound velocity. A foam density of 5 mg/cm3 was achieved in experiments. The experimental measurements are compared with the one-dimensional computer simulations results.

Analysis of Non-Fourier Conduction Waves from a Reciprocating Heat Source

The temperature proe les that result when a point heat source is swept back and forth along a rod in which heat travels at e nite speed are examined. Green’ s functions are used to solve the hyperbolic heat equation for cases in which the source speed is half, equal to, and double, the natural thermal wave speed of the rod material. Rod temperatures are found to depend on the value of the thermal Mach number that characterizes each heating scenario. For subsonic heating, temperatures decrease smoothly ahead of the source, but drop off sharply in its wake. In supersonic heating, the temperature proe le e ips, moving the sharp drop in rod temperature to the source’ s leading edge. For transonic heating, the temperature proe les have sharp drops on both sides of the source, producing a local spike that grows with time. In all cases, the source generates three distinct wave fronts as it slides along the rod: a primary front moving with the source and two startup fronts traveling at the rod thermal wave speed. These fronts interact to produce local variations in rod temperatures that would not be predicted by Fourier’ s law.

Supersonic radiative heat waves in low-density high-Z material.

The propagation of a radiation heat wave through lead-doped foam with a density of 80 mg/${\mathrm{cm}}^{3}$ was experimentally investigated. The wave is driven by 100--150 eV Hohlraum radiation generated in 1--3 mm diam gold cavities heated by a 2.5 kJ, 0.8 ns laser pulse (wavelength 0.35 \ensuremath{\mu}m). The propagation velocity was obtained from the delayed onset of intense thermal emission from the rear side of the foam sample. The results agree with theoretical predictions for a nonablative heat wave and with numerical simulations, and indicate that the radiation heat wave propagates with a velocity that is larger than the sound velocity in the heated foam.

Heating of underdense plasmas by intense short-pulse lasers.

A one-dimensional model in cylindrical geometry which incorporates tunnel ionization, nonlinear inverse bremsstrahlung, and radial heat conduction is used to predict the spatial and temporal temperature distribution in an undercritical plasma irradiated axially by a short-pulse laser. Results from the calculation are compared to available experimental data using a 12 ps KrF laser and to previous work in a regime relevant to proposed recombination optical-field ionized xuv lasers in the transient regime, e.g., Li-like neon. The calculated temperature is too high for lasing to the ground state because of the large contribution from inverse bremsstrahlung for pulse lengths greater than 100 fs. It is shown that for small filaments, additional cooling by supersonic heat conduction on a few picosecond time scale could be used efficiently to generate inversion between excited states in the quasi-steady-state regime.

Supersonic leeward heating of a triangular wing

Supersonic leeward heating of a triangular wing

Moisture absorption in graphite/epoxy laminates

This work investigates the uptake of moisture by XAS-914C and AS4/3501-6 graphite/epoxy composite laminates under a range of temperature and humidity conditions. From the experiments, the diffusion coefficients of moisture in a number of laminates have been determined, together with the equilibrium moisture levels in the matrix. The effects of thermal spiking (thermal transients simulating supersonic heating of military aircraft) on moisture uptake were determined experimentally using a number of combinations of spiking and moisturising conditions. Thermal spiking was found to be damaging when moisture was present in the laminate, and spiking during moisturising was found to be more severe than thermal spiking of material conditioned to equilibrium moisture levels. The pronounced effects of repeated thermal spiking on moisture uptake suggest a progressive form of spiking damage, and a simple model is proposed of a damage zone progressing through the laminate during successive moisturising then spiking cycles.

The x-ray-driven heating wave

The heating of matter by a source of intense x rays is studied under conditions where the energy transport in the hot material is carried by the flux of incident photons. This leads to the formation of a self-similar heating wave. Particular emphasis is given to the ablative heating wave that exists for a time interval in between supersonic heating initially and diffusive heat transport at later times. An approximate, analytic solution of the similarity equations describing the ablative heating wave is given. A power law dependence of the opacity on temperature and density is assumed, which is strictly valid for a fully ionized plasma and monochromatic incident radiation, but possibly also useful to model more complicated situations in terms of effective parameters.

Layers for ion beam energy conversion into black body radiation

The radiation hydrodynamics of material layers for energy conversion of intense ion beams into black body radiation is investigated, both analytically and numerically. Conversion efficiency and hydrodynamic losses are the main topics. The basic scaling relations are derived and compared with computer simulations. Although the analysis is done for slab geometry, a generalization to converters of arbitrary shape and deposition geometry is outlined. The code MINIRA is briefly described. The influence of varying layer density, optical thickness and beam power on radiation emission as well as the effect of Bragg peak deposition are discussed in detail. High conversion efficiencies of more than 50% can be obtained provided that the converter is operated in the radiative regime. For typical beam intensities, this requires low-density layers. Another essential feature is supersonic heat transport which occurs in the radiative regime.

Single and multiple waves induced by power absorption

Sub- and supersonic wave fronts produced by heat input have been generated in a shock tube driven by a step current pulse of variable magnitude (4–50 kA, duration up to 160 μsec). At high current and low fill gas densities, the supersonic mode appears and no substantial compression is possible. The limiting current Ic to reach this supersonic mode is determined as a function of the fill gas pressure. Front velocities, pressures, and electron densities are measured, and the heating characteristic (maximum enthalpy as function of the net absorbed energy flux) is derived. Scaling laws are obtained for the fluid parameters as a function of fill gas density and current. The measurements are interpreted in terms of one-dimensional wave model calculations. Studies with two stepped power pulse reveal that multiple shocks with a region of substantially increased density can be obtained only if the total current It remains below the critical value Ic. For It≳Ic, a supersonic heat wave is created after the transient phase, and multiple shocks with increased density can no longer be achieved.

Influence of supersonic flow heating on the gain of a carbon dioxide gasdynamic laser

Influence of supersonic flow heating on the gain of a carbon dioxide gasdynamic laser

Axial heating of magnetically confined plasma with CO2 lasers

The coupled electron–ion heating equations, neglecting losses, in a CO2 laser heated solenoid are solved for a laser intensity varying with time as I = I0t2/3. An analytical solution, without restriction on the ratio of electron-to-ion temperatures Te/Ti is found, showing Te,i ~ t2/3.The heating wave which propagates along the solenoid is found to be supersonic having a velocity independent of time and varying as I03/5. Low intensity heating is found to maximize Ti/Te and minimize plasma length and laser energy requirements. The heating wave propagation is found to be consistent with an optical thickness of order unity in the heated plasma column. Considerations of electron–ion energy transfer, supersonic heating wave propagation, and laser beam trapping lead to an optimum laser intensity parameter [Formula: see text].

Blast waves with heat transfer

A model is given for blast waves which are dominated by heat transfer rather than by shock heating and adiabatic expansion. The wave motion is attributed to a net heat flow W (watts/cm2) from the expanding hot core to the surrounding cold gas (density ρ1). The surface of the hot core is initially a supersonic heat wave without a shock. It changes into a subsonic heat wave with a leading shock after quickly passing through the detonation mode. A quantitative analysis of the space time trace near the detonation point yields the enthalpy hf and other parameters of the hot core, the thermal response function hf=f (W) of the background medium, and the blast wave energy E0=const ρ1V2sr3H (where Vs is the shock front velocity and rH is the radius of the hot core). The analysis shows the steady transition of such a blast wave from the early stage of a ’’thermal’’ wave with negligible mass motion to the late stage (which approaches ’’classical’’ blast waves) with negligible heat transfer. Applications to laser spark plasmas are discussed.

Potential efficiencies of open- and closed-cycle CO, supersonic, electric-discharge lasers

Computed open- and closed-cycle system efficiencies (laser power output divided by electrical power input) are presented for a CW carbon monoxide, supersonic, electric-discharge laser. Closed-system results include the compressor power required to overcome stagnation pressure losses due to supersonic heat addition and a supersonic diffuser. The paper shows the effect on the system efficiencies of varying several important parameters. These parameters include: gas mixture, gas temperature, gas total temperature, gas density, total discharge energy loading, discharge efficiency, saturated gain coefficient, optical cavity size and location with respect to the discharge, and supersonic diffuser efficiency. Maximum open-cycle efficiency of 80-90% is predicted; the best closed-cycle result is 60-70%.

Overdriven Supersonic Heat Waves

If a supersonic heat wave is overtaken by a shock, either generated externally or'induced by the sudden cooling of the wave front, an overdriven heat wave is formed which is similar to an overdriven detonation. The Mach number of the overdrlven heat wave is proportional to the product of the Mach numbers of the pursuing shock and the heat wave.

Numerical solution of one-dimensional non-steady flow with supersonic and subsonic flows and heat transfer

The mesh method of solving one-dimensional non-steady subsonic flows is extended to cover supersonic flows and heat transfer. An algorithm is presented for the computation of the Riemann variables with friction, area change, heat transfer and entropy gradients.

Boundary-Layer Separation on Slender Cones at Angle of Attack

6 McClure, J. D., On Perturbed Boundary Layer Flows, Fluid Dynamic Research Lab. Rept. 62-2, July 1962, MIT, Cambridge, Mass. 7 Lighthill, M. J., Reflection at a Laminar Boundary Layer of a Weak Steady Disturbance to a Supersonic Stream, Neglecting Velocity and Heat Conduction, Quarterly Journal of Mechanics and Applied Mathematics, Vol. 3, No. 3, March 1950, pp. 302-325. 8 Lighthill, M. J., On Boundary Layers and Upstream Influence II Supersonic Flows Without Separation, Proceedings of the Royal Society, Vol. 217, 1953, pp. 478-507, 9 Benjamin, T. B., Shearing Flow Over a Wavy Boundary, Journal of Fluid Mechanics, Vol. 6, No. 2, 1959, pp. 161-205. 10 Lees, L. and Reshotko, E., Stability of the Compressible Laminar Boundary Layer, Journal of Fluid Mechanics, Vol. 12, No. 4, 1962, pp. 555-590. 11 Inger, G. R., Discontinuous Supersonic Flow Past an Ablating Wavy Wall, AIAA Journal, Vol. 7, No. 4, April 1969, pp. 762-764. 12 Inger, G. R., Rotational Inviscid Supersonic Flow Past a Wavy Wall, Bulletin of the American Physical Society, Vol. 13, No. 11, Nov. 1968, p. 1579. 13 Martellucci, H., Rie, H., and J. F. Somtowski, J. F., Evaluation of Several Eddy Viscosity Models through Comparison with Measurements in Hypersonic Flows, AIAA Paper 69-688, San Francisco, Calif., 1969. 14 Brown, W. B., Stability of Compressible Boundary Layers, AIAA Journal, Vol. 5, No. 10, Oct. 1967, pp. 1753-1759. 15 Lew, H. G. and Li, H., The Role of the Turbulent Viscous Sublayer in the Formation of Surface Patterns, Rept. R68SD12, June 1968, General Electric Missle and Space Div., Valley Forge, Pa. 16 Klein, E. J., Liquid Crystals in Aerodynamic Testing, Astronautics and Aeronautics, Vol. 6, No. 7, July 1968, pp. 20-25. 17 Williams, E. P. and Inger, G. R., Investigations of Ablation Surface Cross Hatching, SAMSO TR-70-246, June 1970, McDonnell Douglas Astronautics, Huhtington Beach, Calif.

Theoretical analyses of electrothermal thrusters with supersonic heat addition

Theoretical performance analyses for electrothermal thrustor using lithium propellant with combination of radioisotope and electrical energy sources

Supersonic combustion of storable liquid fuels in mach 3.0 to 5.0 air streams

Supersonic combustion of reactive aluminum alkyl fuels has been experimentally demonstrated in two-dimensional ducted combustors and adjacent to a flat plate. Fuel was injected from the combustor walls through multiple orifices and ignited spontaneously. Stable supersonic heat release was maintained as evidenced by schlieren and direct motion pictures of the flow field and deduced from static and pitot pressure measurements in the combustion zone. zone. The results from the ducted combustor tests were correlated with simple theoretical models thus enabling a reasonable determination of combustion efficiency to be made. A theoretical model of constant-pressure heat release on a flat plate in supersonic flow is postulated. Normal force, coefficients and specific impulse values are tabulated for a variety of flight Mach Numbers and altitudes. Additional refinements in this theoretical model were required to adequately describe the experimental results. In a test simulating Mach 5 flight at 66,000-feet altitude, a side force specific impulse of 1350 sec was measured at equivalence ratio of one. Combustion was only partially completed 12 in. downstream of fuel injection. Based on the theoretical model an additional 12 in. of combustor length and 36 in. of expansion length would be required to obtain, the estimated theoretical impulse of 5760 sec. The interaction of a vaporizing liquid droplet with a supersonic stream is considered. Additional refinements were made in the existing theories on droplet trajectory to include the influences of a separated zone and the normal component of velocity of the external stream. Calculations of the trajectory and evaporation of the estimated mean droplet size based on the modified technic were in general agreement with the observed fame zone and deduced combustion efficiency.

APPROXIMATE INVERSION OF A CLASS OF LAPLACE TRANSFORMS APPLICABLE TO SUPERSONIC FLOW PROBLEMS

Solution of numerous applied problems requires the inversion of a Laplace transform which involves functions of hypergeometric type. An approximation procedure for inverting transforms of this kind is presented. The method inverts rational function approximations of these transcendents (see Luke (13)), and yields simple and useful expressions for the desired inverse functions. To illustrate the technique, we consider the solution of the wave equation with particular boundary conditions. The functions which arise have numerous applications in supersonic flow, acoustics and heat conduction. In the field of aerodynamics, these include the velocity field of a circular cylinder impulsively moved in the axial direction with constant axial force, the flow past quasi-cylindrical bodies, shock-body interference, wing body interference and the transient motion of a body of revolution in supersonic flow.