Stagnation Point Heat Research Articles

電磁力による空力加熱低減法の超軌道速度飛行体への適用

An applicability of the electrodynamic heat shield system to super-orbital reentry vehicles was investigated. In the case of the super-orbital reentry flight, due to the strong ionization reactions inside the shock layer, the heat shield system which utilizes the electromagnetic force is expected to work well. In the present study, in order to evaluate the reentry heating reduction by this heat shield system, we performed a CFD analysis including thermochemical non-equilibrium effects and an electromagnetic force. The flight condition used for the present study is that the velocity is 11.6km/s at the altitude of 64km at which the stagnation point heat flux of the MUSES-C reentry capsule is considered to be the maximum value. From our CFD results, we found that the heat flux to the vehicle could be reduced by up to 50%. Additionally, it was also found that the drag coefficient increased with the magnetic field strength, and the maximum value of the drag coefficient was 2.0 with the magnetic field strength of 0.6[T].

Distortion of upstream disturbances in a Hiemenz boundary layer

A theoretical analysis of the distortion of unsteady three-dimensional disturbances in a Hiemenz boundary layer and its effect on the heat transfer enhancement is presented. It is shown that the disturbance length scale is a critical parameter in determining the amplification ratio of the incoming vorticity. For large disturbance length scales, the amplification ratio increases when the length scale decreases, and a maximum value occurs at a length scale close to five times the boundary-layer thickness. The unsteadiness of the disturbances is found to reduce the vorticity amplification, but the effect is second order when the frequency is low compared to the mean flow strain rate. The impinging disturbances induce large-amplitude vorticity of opposite sign at the wall whose magnitude controls the heat transfer enhancement. As an application of the present analysis, a new scaling correlation is derived for stagnation-point heat transfer in the presence of free-stream turbulence. The theoretical correlation, expressed in terms of turbulence intensity, integral length scale and mean flow Reynolds number, agrees reasonably well with recent experimental data.

Elemental Demixing in Air and Carbon Dioxide Stagnation Line Flows

The influence of elemental fraction variations on the computation of thermochemical equilibrium flows is analyzed for both air and carbon dioxide mixtures. First the thermochemical equilibrium stagnation line equations for a mixture of perfect gases are presented for both the cases of constant and variable elemental fractions. Then, the equilibrium computations are compared with several chemical regimes to better analyze the influence of chemistry on wall heat flux and to observe the elemental fractions behavior along a stagnation line. The results of several computations are presented to highlight the effects of elemental demixing on the stagnation point heat flux and chemical equilibrium composition for air and carbon dioxide mixtures. Moreover, in the chemical nonequilibrium computations, the characteristic time of chemistry is artificially decreased and in the limit the chemical equilibrium regime, with variable elemental fractions, is achieved. Finally the effects of outer edge elemental fractions on the heat flux map is analyzed, showing the need to add them to the list of parameters of the methodology currently used to determine catalycity properties of thermal protection materials.

Temperature distribution and heat transfer characteristics of an inverse diffusion flame with circumferentially arranged fuel ports

Experiments were conducted on IDFs burning butane. The flame holder has a central air jet surrounded by 12 circumferentially arranged fuel jets. The flame consisted of a short entrainment zone and a long mixing and combustion zone with intense combustion. The temperature profiles of the flame showed a cool core at low flame heights, which disappeared at high flame heights. The stagnation point heat flux and radial heat flux distribution of the same flame, upon impinging on a flat plate, also indicated a cool core at low nozzle-to-plate distance but disappeared at high nozzle-to-plate distance.

Computation of combined turbulent convective and impingement heat transfer

Impingement and forced convection are preferable methods for cooling gas turbine components. However, influences of various design parameters like crossflow and surface enlargements (like ribs) are not well understood. Thus there is a request for reliable and cost‐effective computational prediction methods, due to the experimental difficulties. Such methods could be based on the numerical solution of the Reynolds‐averaged Navier‐Stokes equations, the energy equation and models for the turbulence field. This paper describes some recent advances and efforts to develop and validate computational methods for simulation of impingement and forced convection cooling in generic geometries of relevance in gas turbine cooling. Single unconfined round air jets, confined jets with crossflow, and three‐dimensional ribbed ducts are considered. The numerical approach is based on the finite volume method and uses a co‐located computational grid. The considered turbulence models are all the so‐called low Reynolds number models. Our recent investigations show that linear and non‐linear two‐equation turbulence models can be used for impinging jet heat transfer predictions with reasonable success. However, the computational results also suggest that an application of a realizability constraint is necessary to avoid over‐prediction of the stagnation point heat transfer coefficients. For situations with combined forced convection and impingement cooling it was revealed that as the crossflow is squeezed under the jet, the heat transfer coefficient is reduced. In addition, inline V‐shaped 45° ribs pointing upstream performed superior compared to those pointing downstream and transverse ribs.

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.

Heat transfer predictions with a cubic k– ε model for axisymmetric turbulent jets impinging onto a flat plate

Local heat transfer in turbulent axisymmetric jets, impinging onto a flat plate, is predicted with a cubic k– ε model. Both the constitutive law for the Reynolds stresses and the transport equation for the dissipation rate ε contribute to improved heat transfer predictions. The stagnation point value and the shape of the profiles of the Nusselt number are well predicted for different distances between the nozzle and the flat plate. Accurate flow field predictions, obtained with the presented turbulence model, are the basis for the quality of the heat transfer results. The influence of the nozzle–plate distance on the stagnation point Nusselt number, is also correctly captured. For a fixed nozzle–plate distance, the influence of the Reynolds number on the stagnation point heat transfer is correctly reproduced. Comparisons are made to experimental data and to results from a low-Reynolds standard k– ε model [1] and the v 2– f model [2].

Simulation of convective heat flux and heat penetration for a spacecraft at re-entry

A closed-form simulation model is presented for the convective heat transfer to a space vehicle at re-entry. The analysis is based on given trajectory data, i.e. on vehicle velocity vs. flight altitude. Hence, the uniqueness of the subject engineering method is that it does not solve the equations of motion, but assumes an analytical expression for the flight trajectory together with an isothermal atmosphere. The obtained results for both global and local (e.g. the stagnation point) heat transfers to the vehicle are further used for the prediction of the one-dimensional heat penetration into the vehicle structure. This also includes the accumulated (or integrated) heat load as function of the time of descent. Comparisons of results from the present method with published data for the Space Shuttle and for the European Atmospheric Reentry Demonstrator are presented, both for peak heat loads at stagnation point and integrated reference heat load.

Heat transfer due to a round jet impinging normal to a circular cylinder

An experimental investigations of heat transfer for a stationary isothermal circular cylinder exposed normal to an impinging round air-jet has been reported. The circumferential heat transfer distributions as well as axial Nusselt number is measured. The measurements are taken as a function of the Reynolds number ranging from 3.8 × 103 to 4 × 104, the cylinder separation distance to the nozzle diameter (z/d) varying from 7 to 30, and the nozzle to cylinder diameter ratio (d/D) changing from 0.06 to 0.14. The output results indicated that the axial and radial distributions of the local heat transfer peaked at the impingement point. The heat transfer rate increases as the values of z decreases, for the same d and Re. The drop-off of the Nusselt number with increasing axial distance or radial angle from the impingement point was more pronounced for smaller z and d. The peripheral and surface average Nusselt numbers were determined by integration. The experimental data was used to produce correlations for both average and stagnation point heat transfer.

Influence of molecular vibration and transport model on computation of the wall heat flux

Zuppardi and Verde (Improved Fay–Riddell prcoedure to compute the stagnation point heat flux, Journal of Spacecraft and Rockets 35(3) (1998) 403–405) introduced some operating improvements in the Fay–Riddell computing procedure for the solution of the laminar boundary layer and for the computation of the heat flux at the stagnation point of spherical bodies in high speed, non-equilibrium dissociating air. Zuppardi and Verde pointed out that the most important improvements were related to the computation both of vibrational temperatures and of Prandtl and Lewis numbers. Vibrational temperatures were computed only as functions of the free stream thermodynamic parameters. Prandtl and Lewis numbers were computed as functions of both the free stream and the local thermodynamic parameters in the boundary layer. The Chapman–Enskog theory with the Lennard–Jones collision integrals were used to compute the transport coefficients. In the present paper the effects of the variability of the vibrational temperatures also in the boundary layer, and of using the more updated collision integrals by Yun and Mason (Collision integrals for the transport properties of dissociating air at high temperature, The Physics of Fluid 5(4) (1962) 380–386) have been evaluated. The results showed that the influence of these factors on the profile of the thermo-fluid–dynamic parameters in the boundary layer was negligible, but it was important on the wall heat flux. The inclusion of the variability of molecular vibration improved the matching both with Navier–Stokes results and experimental data.

Stagnation-Point Heat Transfer Rates for Pioneer-Venus Probes

Summary The convective and radiative heat transfer rates are calculated for the stagnation region of the Pioneer- Venus Probe vehicles during their entry flights into the planet Venus. The nonequilibrium thermochemical state of the flow is calculated using a viscous shock layer method accounting for oxidation of heatshield surface by atomic oxygen and for pyrolysis-gas injection. Radiative transport along the stagnation streamline is calculated using a lineby-line technique and tangent-slab approximation. For both radiative and convective heating rates, the present results are substantially smaller than the earlier values obtained assuming equilibrium.

Improved Fay-Riddell Procedure to Compute the Stagnation Point Heat Flux

Improved Fay-Riddell Procedure to Compute the Stagnation Point Heat Flux

Heat flux on partially catalytic surfaces in hypersonic flows

The combined effects of the chemical nonequilibrium and the surface catalysis on the stagnation-point heat flux of a blunt body are investigated by Navier-Stokes calculations on a spherical model under Scirocco Plasma Wind Tunnel conditions. The freestream properties in the test section are found by means of a preliminary nonequilibrium, full Navier-Stokes computation of the nozzle flow expansion. All available numerical heat flux results are correlated as a function of a dimensionless parameter, including the simultaneous effects of the finite-gas and the surface-phase reactions. The proposed parameter, which takes into account simultaneously the nonequilibrium effects in the bulk and surface phases, correlates well with the numerical results over a blunt-body stagnation region. The final correlation formula for the stagnation heat flux can be used to correlate experimental results on different materials with known catalytic coefficients or, conversely, to determine the surface catalytic efficiency of different thermal protection materials. Nomenclature a = speed of sound, m/s cp =

Heat Transfer and Film Cooling Effectiveness in a Linear Airfoil Cascade

A warm (315°C) wind tunnel test facility equipped with a linear cascade of film cooled vane airfoils was used in the simultaneous determination of the local gas side heat transfer coefficients and the adiabatic film cooling effectiveness. The test rig can be operated in either a steady-state or a transient mode. The steady-state operation provides adiabatic film cooling effectiveness values while the transient mode generates data for the determination of the local heat transfer coefficients from the temperature–time variations and of the film effectiveness from the steady wall temperatures within the same aerothermal environment. The linear cascade consists of five airfoils. The 14 percent cascade inlet free-stream turbulence intensity is generated by a perforated plate, positioned upstream of the airfoil leading edge. For the first transient tests, five cylinders having roughly the same blockage as the initial 20 percent axial chord of the airfoils were used. The cylinder stagnation point heat transfer coefficients compare well with values calculated from correlations. Static pressure distributions measured over an instrumented airfoil agree with inviscid predictions. Heat transfer coefficients and adiabatic film cooling effectiveness results were obtained with a smooth airfoil having three separate film injection locations, two along the suction side, and the third one covering the leading edge showerhead region. Near the film injection locations, the heat transfer coefficients increase with the blowing film. At the termination of the film cooled airfoil tests, the film holes were plugged and heat transfer tests were conducted with non-film cooled airfoils. These results agree with boundary layer code predictions.

Impingement heat transfer and recovery effect with submerged jets of large Prandtl number liquid—II. Initially laminar confined slot jets

Local measurements were made to determine recovery factors and heat transfer coefficients resulting from the impingement of transformer oil jets issuing from tiny slot nozzles of 0.091, 0.146, and 0.234 mm in width. This study focused on initially laminar jets in the range of jet Reynolds number between 55 and 415, and fluid Prandtl number between 200 and 270. Lateral distribution of local recovery factor was measured at various Reynolds numbers and nozzle-to-plate distances. Stagnation point heat transfer coefficient was collected and correlated as a function of jet Reynolds number, nozzle-to-plate spacing and nozzle width. Twenty seven lateral profiles of local heat transfer were obtained and correlated. Nonmonotonic variation and unusual behavior of local heat transfer were observed and attributed to possible transition from laminar to turbulent regime. Based on the measured local data, integral average heat transfer rate was determined and correlated.

Heat Transfer from Single and Arrays of Impinging Water Jets(I)-Single Water Jet-

The heat transfer characteristics of free surface water jet impinging normally against a flat uniform heat flux surface were investigated. This deals with the effect of three nozzle configurations (Cone type, Reverse cone type, Vertical circular type) on the local and the average heat transfer. Heat transfer measurements were made for water jet issuing from a nozzle of which exit diameter 8 mm. The experimental conditions investigated are Reynolds number range of 27000 ~ 70000( =3 ~ 8 m/s), nozzle-to-target plate distances H/D=2 ~ 10, and radial distance from the stagnation point r/D ~ = 0 ~ 7.42. For all jet velocities of H/D=2, the local Nusselt number decreased monotonically with increasing radial distance. However, for H/D from 4 to 10, and for the jet velocity .geq.7 m/s for Cone type nozzle and .geq.6 m/s for the other type nozzles, the Nusselt number distributions exhibited secondary peaks at r/D=3 ~ 3.5. For Reverse cone type nozzle and Vertical circular nozzle, the maximum stagnation point heat transfer and the maximum average heat transfer occurs at H/D=8. But for the Cone type nozzle, the maximum stagnation and average heat transfer occurs at H/D=10, 4, respectively. From the optimum nozzle-to-target plate distance, the stagnation and the average heat transfer reveal the following ranking: Reverse cone type nozzle, Vertical circular type nozzle, Cone type nozzle.ozzle.

High enthalpy nozzle flow sensitivity study and effects on heat transfer

The sensitivity of the flow along the nozzle and in the test section of high enthalpy wind tunnels to the thermochemical response of the nozzle expansion process, as well as effects on the pressure and heat transfer distributions over the Electre blunt cone standard test model, are examined in the framework of properly characterizing the test section flow field in such facilities. Particularly sensitive to the thermochemical behaviour of the nozzle flow, in the facilities under consideration, are the static pressure, static temperature and Mach number, whereas stagnation point (pitot) pressure and heat transfer data or freestream velocity are inadequate for the characterization of the thermochemical state of the flow. The Electre and nozzle wall pressure data in the F4 arc jet wind tunnel suggest, in contrast to nonequilibrium computations, that the flow in the F4 nozzle is close to equilibrium. In the HEG and, to some extent, the T5 piston-driven shock tunnels, there are indications that significant heat losses occur in the reservoir. Lastly, simple semi-empirical formulations for stagnation point heating are shown to perform reasonably well in high enthalpy flow conditions.

NUMERICAL PREDICTION OF SEMI-CONFINED JET IMPINGEMENT AND COMPARISON WITH EXPERIMENTAL DATA

The standard k–ε eddy viscosity model of turbulence in conjunction with the logarithmic law of the wall has been applied to the prediction of a fully developed turbulent axisymmetric jet impinging within a semi-confined space. A single geometry with a Reynolds number of 20,000 and a nozzle-to-plate spacing of two diameters has been considered with inlet boundary conditions based on measured profiles of velocity and turbulence. Velocity, turbulence and heat transfer data have been obtained using laser–Doppler anemometry and liquid crystal thermography respectively. In the developing wall jet, numerical results of heat transfer compare to within 20% of experiment where isotropy prevails and the trends in turbulent kinetic energy are predicted. However, stagnation point heat transfer is overpredicted by about 300%, which is attributed directly to the turbulence model and inapplicability of the wall function.

Effects of freestream nonequilibrium on convective heat transfer to a blunt body

The axisymmetric Navier- Stokes equations are solved numerically for nonequilibrium airflows over a hemisphere. A formulation with a three-temperature thermochemical model has been employed to simulate vibrationally excited and partially dissociated airflow. A flow condition that has a total enthalpy of 25 MJ/kg and a surface pressure of 0.076 atm is studied. Computed stagnation point heat transfer using finite catalytic boundary conditions at the surface is compared with classical results. Departures from the classical heat transfer predictions caused by nonequilibrium effects are assessed for arcjet testing applications. A Damkohler number analysis is used to characterize the extent of flowfield nonequilibrium. It is shown that characterization of the thermodynamic state of the gas at the boundary-layer edge and within the boundary layer is needed to interpret the heat transfer measurements and to determine the surface catalytic efficiency.

Effect of nozzle geometry and semi-confinement on the potential core of a turbulent axisymmetric free jet

The effects of nozzle geometry and confinement on the potential core and subsequent axial development of a turbulent axisymmetric air jet at a Reynolds number of 22 500 have been studied. Four jet exit conditions, namely, flat and fully developed velocity profiles for unconfined and semi-confined cases were investigated. Mean velocity and turbulence profiles were measured using laser-Doppler anemometry. Liquid crystal thermography used in steady state enabled optimal nozzle to plate spacing to be established for maximum heat transfer. Preliminary results presented here indicate that the length of the potential core is greater for the fully developed jet exit profile and is further extended by semi-confinement. The semi-confinement reduces the stagnation point heat transfer by up to ten per cent.