Stagnation Point Heat Transfer Rates Research Articles

Scaling of Convective Heat Transfer Enhancement Due to Flow Pulsation in an Axisymmetric Impinging Jet

Impinging jets are widely used to achieve a high local convective heat flux, with applications in high power density electronics and various other industrial fields. The heat transfer to steady impinging jets has been extensively researched, yet the understanding of pulsating impinging jets remains incomplete. Although some studies have shown a significant enhancement compared to steady jets, others have shown reductions in heat transfer rate, without consensus on the heat transfer mechanisms that determine this behavior. This study investigates the local convective heat transfer to a pulsating air jet from a long straight circular pipe nozzle impinging onto a smooth planar surface (nozzle-to-surface spacing 1 ≤ H/D ≤ 6, Reynolds numbers 6000 ≤ Re ≤ 14,000, pulsation frequency 9 Hz ≤ f ≤ 55Hz, Strouhal number 0.007 ≤ Sr = fD/Um ≤ 0.1). A different behavior is observed for the heat transfer enhancement in (i) the stagnation zone, (ii) the wall jet region and overall area average. Two different modified Strouhal numbers have been identified to scale the heat transfer enhancement in both regions: (i) Sr(H/D) and (ii) SrRe0.5. The average heat transfer rate increases by up to 75–85% for SrRe0.5 ≅ 8 (Sr = 0.1, Re = 6000), independent of nozzle-to-surface spacing. The stagnation heat transfer rate increases with nozzle-to-surface distance H/D. For H/D = 1 and low pulsation frequency (Sr < 0.025), a reduction in stagnation point heat transfer rate by 13% is observed, increasing to positive enhancements for Sr(H/D) > 0.1 up to a maximum enhancement of 48% at Sr(H/D) = 0.6.

A simplified trajectory analysis model for small satellite payload recovery from low Earth orbit

The reentry trajectories of a small mass at low Earth orbit were analyzed with a modified three degree-of-freedom trajectory simulation. An estimate of the stagnation point heating was also made. The mass deployed an inflatable, three-element drag disk decelerator that was modeled as a single circular disk, trailing the payload, normal to the direction of flight. The downrange distance decreased and the time of flight increased with increased decelerator area. The stagnation-point heat transfer rates with a decelerator of sufficiently low ballistic coefficient of 24 Pa was 5–10 percent that of a typical ballistic reentry vehicle with a ballistic coefficient of 4.8 kPa. The study did not find that staged deployment of the decelerator disks provided any aerodynamic advantages, particularly in view of the anticipated complexities involved in deploying such a system. Finally, skip trajectories yielded slightly lower stagnation-point heat transfer than the non-lifting case. However, they may not be advantageous since the increased flight time would expose the decelerator to a longer period of heating, thereby possibly requiring more extensive thermal protection and a potential to damage on-board sensors and instruments.

Hypersonic flow diagnostic studies in a large arc-heated wind tunnel

This study consisted of the experimental investigation of test flow in an arc-heated hypersonic wind tunnel. These tests utilized a high-voltage d.c. arc heater which operated at input powers in excess of 50 Mw and provided reservoir pressures ranging from 100 to 1500 psi and bulk enthalpies from 1500 to 4000 Btu/lb. Local freestream measurements of Pitot pressure, mass flux, stagnation point heat-transfer rate, and wall static pressures were obtained at the exit of a nominal 2-ft-diam conical nozzle. Stagnation enthalpy profiles at the nozzle exit became peaked at high stagnation pressures. From these data, center line enthalpies as high as 6500 Btu/lb were indicated in the flow. Selective comparisons between theory and experiment are presented. At a reservoir enthalpy of approximately 2500 Btu/lb and for stagnation pressures in excess of 500 psi, the expanded flow data were in good agreement with equilibrium expansion theory. However, below 500 psi, the data compared more closely with nonequilibrium theory with the flow frozen downstream of the nozzle throat.

Experimental study of high-enthalpy shock- tunnel flow. II - Nozzle-flow characteristics.

The duration of uniform flow and wall boundary-layer growth have been measured in the conical nozzle of a reflected-shock tunnel operating at high-enthalpy conditions. Experiments were performed in air for shock-tube Mach numbers of 16.5 and 11.5, with corresponding initial driven-tube pressures of 0.5 and 10.0 torr, respectively. Several different diagnostic techniques were used to measure the uniform-flow period and the results are compared. Radiation-intensity and electron-density measurements were found to be the most sensitive flow indicators. The boundary-layer displacement-thickness growth on the nozzle wall was determined for both of the aforementioned experimental conditions using velocity and density profiles deduced from Pitot-pressure and stagnation-point heat-transfer measurements. Good agreement was found between experimental and theoretical Pi tot pressures at comparable inviscid area ratios. The measured boundary-layer and displacement thicknesses are compared with the results of two typical prediction techniques. ART I of this paper describes the studies of the shock-tube flow and nozzle starting time. The purpose of Part II is to describe the subsequent nozzle-flow experiments in which the test time and the boundary-layer growth were experimentally determined for high-enthalpy reflected-shock conditions. The results are presented here because boundary-layer measurements obtained for such flow conditions are relatively scarce in the literature. The nozzle boundary layer was investigated with the aid of radial surveys of Pitot pressure and stagnation-point heattransfer rate at several axial locations. These measurements were used to deduce the local velocity and density relative to the corresponding values on the nozzle centerline, and the experimentally determined profiles were used to calculate the appropriate boundary-layer displacement thickness. Many authors111 have proposed techniques that may be used to predict the boundary-layer growth on the wall of a conical nozzle, and the present results can be used to test these techniques. However, the major emphasis of Pt. II has been placed on the experimental measurements, with only a limited comparison with prediction. Two particular prediction techniques2-5 have been selected as typical and the experimentally determined boundary-layer and displacement thicknesses are compared with these. The experimental apparatus used in this work was described in detail in Pt. I. The first part of Sec. 2 of Pt. II presents the experimentally determined test time at different locations in the nozzle and compares the results of the various diagnostic techniques. Section 2 concludes with a discussion of the boundary-layer data obtained at each of the experimental conditions and compares the results with existing prediction techniques.

Stagnation point heat transfer measurements in partially ionized air

Abstract : Experimental measurements of convective stagnation point heat transfer in partially ionized air at stimulated flight velocities up to 55,000 fps are presented. Stagnation point heat transfer rates were measured in an arc-driven shock tube with calorimetric heat transfer gages, either coated with silicon-monoxide films or uncoated. The data are compared to theoretical predictions made with a simple binary diffusion model of partially ionized diatomic gas, nitrogen, whose transport properties were estimated from measured and calculated cross-section data. Stagnation point heat transfer rates calculated from this model for both a frozen and an equilibrium boundary layer, as well as equilibrium boundary layer results from other available calculations using more elaborate models of air, are compared to the data. It is concluded that the transport properties of air up to 15,000 K are known to reasonable accuracy and that heat conduction by electrons does not present a serious engineering problem for flight velocities up to 50,000 fps.

Heat Transfer in Planetary Atmospheres at Super-Satellite Speeds

The equilibrium boundary layer flow at the stagnation point of a blunt body at very high enthalpies in air and in the simulated atmosphere of Venus (C02) has been calculated. The effects of dissociation and ionization are taken into account by means of the total thermodynamic and transport property concept. Correlation of the numerical results shows that a single simple equation will predict the stagnation point heat transfer rate at flight velocities between 6000 and 50,000 fps. Wall temperatures between 540° and 5400°R and stagnation pressures between 0.001 and 100 atm were considered. The same correlation equation is valid in Earth's atmosphere, as well as in the simulated atmosphere of Venus. The theoretical results are compared with experimental heat transfer data obtained in partially ionized air and in CO2. The agreement between theory and experiment is satisfactory. It is also shown that reasonable results for the heat transfer from an ionized boundary layer can be obtained from the results of Fay and Riddell by consistently neglecting the effects of ionization.

Mass Transfer and Shock Generated Vorticity

The effects of shock generated vorticity and mass transfer on stagnation point heat transfer rates are investigated. The complete incompressible Navier-Stokes equations are considered in the flow region between the bow shock and the surface of spheres and cylinders. Boundary conditions are applied immediately behind the shock and at the wall. The numerical solutions to the flow equations with air injected into the shock layer, show tha t the interaction between the vorticity generated by the wall and by the curved shock reduces the effectiveness of mass transfer cooling. The reduction in heat transfer rates due to mass injection is substantially less than predicted by boundary layer theory at Reynolds numbers below 10 for spheres and 10 for cylinders. The heat transfer rates with mass injection were found to be 200 to 300 per cent greater than corresponding boundary layer values for the extreme cases investigated (strong shock, Re = 10 and large air injection rates). These heat transfer rates are, however, less than the zero mass injection values. It is also shown for a sphere and for Pr =1 .0 tha t the increase in heat transfer is primarily dependent on the inverse of the difference between the vorticity at the wall and the vorticity immediately behind the shock.

The Effect of Shock-Generated Vorticity, Surface Slip, and Temperature Jump on Stagnation-Point Heat-Transfer Rates

The Effect of Shock-Generated Vorticity, Surface Slip, and Temperature Jump on Stagnation-Point Heat-Transfer Rates