Harold Mirels

Test Time in Low‐Pressure Shock Tubes

The reduction of test time in low pressure shock tubes, due to a laminar wall boundary layer, has been analytically investigated. In previous studies by Roshko and Hooker the flow was considered in a contact surface fixed coordinate system. In the present study it was assumed that the shock moves with uniform velocity, and the flow was investigated in a shock fixed coordinate system. Unlike the previous studies, the variation of free stream conditions between the shock and contact surface was taken into account. It was found that β, a parameter defined by Roshko, is considerably larger than the estimates made by Roshko and Hooker except for very strong shocks. Since test time is proportional to β−2, previous estimates of test time are too large, particularly for weak shocks. The present estimates for β appear to agree with existing experimental data to within about 10 percent for shock Mach numbers greater than 5. In other respects, the basic theory is in general agreement with the previous results of Roshko.

Flow Nonuniformity in Shock Tubes Operating at Maximum Test Times

Shock tube flow nonuniformity is investigated in the limit where the shock and contact surface have reached their maximum separation. Ideal gases are considered. It is found that all fluid properties increase in value between the shock and contact surface. The nonuniformity is greatest when γ (ratio of specific heats) is large and Ms (shock Mach number) is low. For γ = 53 and Ms ≥ 3, the static temperature, density, and pressure increase by about 8, 12, and 20%, respectively; the stagnation temperature increases by about 35%, and the stagnation pressure, dynamic pressure, and stagnation point heat transfer increase by about a factor of 2. These results apply to turbulent as well as laminar boundary layers. The variation of flow properties with distance behind the shock, as well as particle time of flight, is given for both wholly laminar and wholly turbulent wall boundary layers. These results are particularly important for chemical rate and heat transfer studies.

CORRELATION FORMULAS FOR LAMINAR SHOCK TUBE BOUNDARY LAYER.

The laminar boundary layer behind a moving shock is studied. The major objective is to obtain improved correlation formulas (valid for large W, where W is the density ratio across the shock) and to simplify the procedure for obtaining boundary‐layer parameters. Numerical solutions for shear, heat transfer, and boundary‐layer thicknesses are presented for 1 ≤ W ≤ ∞, σ = 0.67, 0.72, and 1.0 (σ is the Prandtl number) assuming constant ρμ (ρ is the density and μ, the viscosity) and an ideal gas. Correlation formulas are obtained which agree with these numerical results to within fractions of a percent. Approximate corrections for variable ρμ and real‐gas effects are then introduced. Charts and tables are presented which describe boundary layers in air (Ms ≤ 22) and argon (Ms ≤ 10).

PRELIMINARY PERFORMANCE OF A cw CHEMICAL LASER

Preliminary performance of a cw chemical laser is presented. Hydrogen is diffused into a supersonic stream containing F atoms. Population inversion is due to the reaction H2+F→ HF(v)+H, ΔH=−31.7 kcal/mole, v=1, 2. An atomic F flow rate of 0.030 moles/sec has produced 475 W of laser power in the 3‐μ region. This represents 12% of the chemical energy involved in the above reaction. Zero power gain is 8%/cm. Spectroscopic observations of laser transitions are included.

Performance of cw HF Chemical Laser with N2 or He Diluent

Recent experimental results on the performance of a continuous HF (or DF) chemical laser are reported. In this device, an arc‐heated diluent is mixed in a plenum with SF6 to provide F atoms. The mixture is expanded to form a supersonic jet into which H2 (or D2) is diffused. Population inversion and lasing are due to the reaction H2+F=HF(v)+H; v≤3 and Δ H=−31.7 kcal. Power levels above 1 kW have been obtained in a N2 diluent gas flow, and levels above 1.7 kW have been obtained in a He diluent gas flow. Specific power yields are 43 and 108 kW sec/lb for the N2 and He systems, respectively. The variation of laser power and efficiency with cavity optical axis location and SF6 mass flow are reported for both N2 and He systems. A spectrum of the HF laser operating in a He flow is also presented that gives evidence of v=3 partial inversion.

Simplified Model of CW Diffusion-Type Chemical Laser

Abstract : A simplified analytical model of a diffusion-type HF chemical laser is presented. In this device, H2 is diffused into a supersonic stream to react with F atoms and form vibrationally excited HF that is made to lase. The reaction between H2 and F is assumed to commence at a flame sheet. A two-vibrational level model for the HF molecule is adopted. The dependence of laser amplifier and oscillator performance on diffusion rate, forward reaction rate, collisional deactivation rate, and radiative deactivation rate is determined. (Author)

COMPARISON OF HF AND DF CONTINUOUS CHEMICAL LASERS: I. POWER

Abstract : A continuous DF chemical laser radiating at approximately 4 microns is reported. Population inversion is obtained by diffusing D2 into a supersonic free jet containing F atoms. The performance of the DF laser is compared with a similar HF laser previously reported. The ratio of DF to HF laser output power is 0.7 for fixed supersonic jet conditions and the same molar flow of H2 and D2. The efficiency of conversion of chemical energy to laser energy is approximately 12% and 8% for the HF and DF lasers, respectively. (Author)

Numerical study of a diffusion-type chemical laser.

The theoretical performance of an HF diffusion-type chemical laser is investigated by means of exact numerical solutions for the laminar diffusion of a finite stream of H/sub 2/ into a semi-infinite stream containing F and a diluent in the presence of an incident coherent radiation field. This flow model corresponds to flow in a single semichannel of a diffusion-type chemical laser. The initial flow velocity, temperature, and hydrogen stream thickness is held constant, and the effect of pressure level, initial fluorine partial pressure, and incident radiation intensity on peak integrated gain, axial extent of the lasing region, laser output power, and chemical efficiency is investigated

Power and efficiency of a continuous HF chemical laser

Experimental measurements of laser power output and chemical efficiency are reported for a continuous HF chemical laser. In this device, arc-heated N 2 is mixed in a plenum with SF 6 to provide F atoms. The mixture is expanded to form a supersonic jet into which H 2 is diffused. Population inversion and lasing are due to H 2 + F → HF(υ) + H, \upsilon \leq 3, \Delta H = -31.7 kcal. Power levels up to 1 kW have been obtained. The efficiency of conversion of chemical energy to laser power is 16 percent at low SF 6 flow rates and approximately 10 percent at peak power. For a fixed arc power, addition of O 2 into the plenum raises peak power by about 25 percent under present operating conditions and reduces sulphur deposition on mirror surfaces. The presence of HF and DF in the plenums of DF and HF lasers, respectively, did not appear to degrade laser performance. (HF and DF levels up to 10 percent of the local F concentration were studied.) However, the presence of HF and DF in the plenums of HF and DF lasers, respectively, did degrade laser output. For given flow conditions, peak net laser power was obtained when the optical cavity axis was about 2 cm downstream of the H 2 injection station. The net output power was reduced to zero when the cavity axis location was increased to 5 cm.

Hypersonic Flow over Slender Bodies Associated with Power-Law Shocks

Publisher Summary The method of “inner and outer expansions” is used to obtain uniformly valid solutions far downstream from the blunt nose of slender bodies. The inner expansion describes the flow in the entropy layer, the outer expansion describes the flow external to the entropy layer, and the two expansions are combined to give a uniformly valid description of the entire far-downstream flow. Explicit expressions were obtained for the asymptotic shape of the body as x -+ m, corresponding to a given one- or two-dimensional blast wave. Equation can be used to find the asymptotic body shape associated with any given power law shock. The pressure distribution on the body is found from the zero order similarity solution. This equation can also be used to find the asymptotic shock shape and surface pressure distribution associated with a given power-law body.