Stagnation Point Heat Research Articles

Influence of the velocity gradient on the stagnation point heating in hypersonic flow

In a number of experimental and numerical publications a deviation has been found between the measured or computed stagnation point heat flux and that given by the theory of Fay and Riddell. Since the formula of Fay and Riddell is used in many applications to yield a reference heat flux for experiments performed in wind tunnels, for flight testing and numerical simulations, it is important that this reference heat flux is as accurate as possible. There are some shortcomings in experiments and numerical simulations which are responsible in some part for the deviations observed. But, as will be shown in the present paper, there is also a shortcoming on the theoretical side which plays a major role in the deviation between the theoretical and experimental/numerical stagnation point heat fluxes. This is caused by the method used so far to determine the tangential velocity gradient at the stagnation point. This value is important for the stagnation point heat flux, which so far has been determined by a simple Newtonian flow model. In the present paper a new expression for the tangential velocity gradient is derived, which is based on a more realistic flow model. An integral method is used to solve the conservation equations and, for the stagnation point, yields an explicit solution of the tangential velocity gradient. The solution achieved is also valid for high temperature flows with real gas effects. A comparison of numerical and experimental results shows good agreement with the stagnation point heat flux according to the theory of Fay and Riddell, if the tangential velocity gradient is determined by the new theory presented in this paper.

Dissociative cooling - Effect on stagnation heat transfer of gas mixture injection

By embedding a dissociating material into the porous outer structure of a projectile, stagnation-point heat transfer may be reduced by transpiration cooling resulting from the outflow of the dissociated gas products. The principal material considered is ammonium chloride, NHLjCl, which dissociates at temperatures over 613 K, hence providing additional heat-transfer reduction. Stagnation-point heat-transfer solutions for the injection of the dissociation products of NH^Cl into both equilibrium and frozen boundary layers are presented and compared with those for the injection of other gases such as helium. Results show that dissociative cooling has the potential to provide a significant reduction in stagnation-point heat transfer as temperatures rise, because the gas injection rate increases with the temperature of the NH4C1 interface.

Use of a laser-induced fluorescence thermal imaging system for local jet impingement heat transfer measurement

In this paper the efficacy of a novel thermal imaging system designed for use in the study of local convective heat transfer is examined. The transient temperature measurements employed to calculate local heat transfer coefficients in this study rely on the temperature-sensitive fluorescence properties of a europium-doped lanthanum oxysulfide (La 2O 2S:Eu 3+) thermographic phosphor. A series of temperature-time data sets acquired during the heat-up of a test surface, oriented normal to an impinging heated jet, are used to calculate the local heat transfer coefficient about the stagnation point. These results are qualitatively compared to theoretical predictions and previous experimental observations to evaluate the ability to detect expected flow-field phenomena, such as the initial thinning of the boundary layer near the stagnation point and the eventual laminar to turbulent transition of boundary-layer flow away from the stagnation point. In addition, the measured stagnation point Nusselt number data are compared with theoretical and pertinent empirical data. The agreement of the stagnation point heat transfer in this comparison is excellent, with the variation between measured values based on the laser-induced fluorescence transient surface temperature measurements and existing data well within the bounds of the experimental measurement uncertainty of the present technique.

Wall Roughness Effects on Stagnation-Point Heat Transfer Beneath an Impinging Liquid Jet

Jet impingement cooling applications often involve rough surfaces, yet few studies have examined the role of wall roughness. Surface protrusions can pierce the thermal sublayer in the stagnation region and increase the heat transfer. In this paper, the effect of surface roughness on the stagnation-point heat transfer of an impinging unsubmerged liquid jet is investigated. Experiments were performed in which a fully developed turbulent water jet struck a uniformly heated rough surface. Heat transfer measurements were made for jets of diameters 4.4–9.0 mm over a Reynolds number range of 20,000–84,000. The Prandtl number was held nearly constant at 8.2–9.1. Results are presented for nine well-characterized rough surfaces with root-mean-square average roughness heights ranging from 4.7 to 28.2 μm. Measured values of the local Nusselt number for the rough plates are compared with those for a smooth wall, and increases of as much as 50 percent are observed. Heat transfer in the stagnation zone is scaled with Reynolds number and a roughness parameter. For a given roughness height and jet diameter, the minimum Reynolds number required to increase heat transfer above that of a smooth plate is established. A correlation for smooth wall heat transfer is also given.

The Effect of a Turbulent Wake on the Stagnation Point: Part II—Heat Transfer Results

A phenomenological model is proposed that relates the effect of free-stream turbulence to the increase in stagnation point heat transfer. The model requires both turbulence intensity and energy spectra as inputs to the unsteady velocity at the edge of the boundary layer. The form of the edge velocity contains both a pulsation of the incoming flow and an oscillation of the streamlines. The incompressible unsteady and time-averaged boundary layer response is determined by solving the momentum and energy equations. The model allows for arbitrary two-dimensional geometry; however, results are given only for a circular cylinder. The time-averaged Nusselt number is determined theoretically and compared to existing experimental data.

Computation of nonequilibrium hypersonic flowfields around hemisphere cylinders

Hypersonic flows past hemisphere cylinders at zero incidence in chemical and thermal nonequilibrium are investigated for a range of Mach numbers from 10 to 18. The numerical code shows excellent comparison for surface pressure and heat transfer prediction with recent experiments conducted in a shock tunnel. The numerical code also compares well for stagnation point heat flux predictions at altitudes of 22 and 37 km with a set of earlier experiments. Numerical solutions with the vibrational equilibrium model are compared with those of multitemperature nonequilibrium. The stagnation point heat transfer is 10-23% higher for the nonequilibrium solutions in the Mach number range of 12-18. The importance of a multitemperature model for accurate prediction of stagnation properties, particularly the heat transfer, is noted. The variation in computed shockstandoff distance substantiates that the Mach number independence principle applicable to ideal gases does not hold for dissociating flows. Over the range of Mach numbers, the noticeable influence of vibrational relaxation on the temperature distributions and mass concentrations in the vicinity of shocks is shown in the present study.

An improved method to determine free stream conditions in hypersonic facilities

For determing pressure coefficients and Stanton numbers from the measured surface pressures and heat fluxes at a model surface, the dynamic pressure, mass flux and the total enthalpy of the free stream have to be known. Usually these values are determined by computing the wind tunnel nozzle flow. But a lot of uncertainties enter the computation which may lead to unreliable results. Therefore, a simple method was developed which yields the desired free stream conditions with high accuracy. This could be achieved by using mainly values which are measured within the test section. The method requires the measurement of the Pilot pressure, the stagnation point heat flux on a sphere and the static pressure of the free stream. For the static pressure an estimated value can also be used, because it has no large influence on the result. Some simple considerations show that the derived method is also valid for nonequilibrium free stream conditions. With the procedure presented the accuracy of the pressure coefficients and Stanton numbers could be increased significantly. Further, it improved the repeatability of these test results. This is very important for fundamental research, for the design of hypersonic vehicles as well as for CFD-validation with experimental data. The application of the method presented is not limited to short duration facilities, it can also be used for continuously working wind tunnels.

Local Characteristics of Convective Heat Transfer From Simulated Microelectronic Chips to Impinging Submerged Round Water Jets

An experimental study was performed to investigate the local characteristics of heat transfer from vertical simulated micro-chips to impinging submerged circular water jets. The effects of jet velocity, and nozzle-to-plate spacing were studied in the range of Re = 5.0 × 103 ˜ 3.6 × 104. Heat transfer rates at the stagnation point and local heat transfer distributions were correlated. Transition from laminar to turbulent flow was observed.

Heat transfer to impinging isothermal gas and flame jets

Heat transfer characteristics of single and multiple isothermal turbulent air and flame jets impinging on surfaces are reviewed. Both circular and slot two-dimensional jets are considered, and the effect of crossflow on impingement heat transfer is included. The emphasis is on physical phenomena and not on comparison of published empirical correlations or comparisons of theory and experiments. The review focuses on applications in the materials or comparisons of theory and experiments. The review focuses on applications in the materials processing field. In spite of the fact that there are many differences in the jet characteristics (ie, axial velocity and turbulence intensity) of isothermal and flame jets, the stagnation point heat transfer of these different jets can be described in a similar way. Areas needing research attention are also identified.

Stagnation-Point Heat Transfer During Impingement of Laminar Liquid Jets: Analysis Including Surface Tension

The stagnation-zone characteristics of an impinging liquid jet are of great interest because the maximum heat transfer coefficient occurs in that region. This paper is an analytical study of the fluid flow and heat transfer in the stagnation zone of an unsubmerged liquid jet. The role of surface tension is emphasized. Stagnation-zone transport is strongly dependent on the potential flow above the boundary layer. Only a few studies have examined the potential flow of an unsubmerged jet, each using approximate potential flow theory and neglecting surface tension. In this paper, numerical solutions for a laminar unsubmerged jet are obtained, using a simulation method for steady, inviscid, incompressible flow with surface tension. A series solution that satisfies the boundary conditions in an approximate manner is constructed in terms of Legendre functions. Numerical solution of the momentum equation shows that surface tension has an effect on the stagnation-point flow field when the Weber number is small. Solutions of the associated boundary layer problem are used to obtain predictions of the influence of Weber number on the stagnation-zone heat transfer. The results are validated by comparison to measurements at high Weber number.

Conditions of simulation of stagnation point heat transfer from a high-enthalpy flow

The problem of local simulation of stagnation point heat transfer to a blunt body is solved within the framework of boundary layer theory on the assumption that the simulation subsonic high-enthalpy flow is in equilibrium outside the boundary layer on the model, while the parameters of the natural flow are in equilibrium at the outer edge of the boundary layer on the body. The parameters of the simulating subsonic flow are expressed in terms of the total enthalpyH 0, the stagnation point pressurep w and the velocityV 1 for the natural free-stream flow in the form of universal functions of the dimensionless modeling coefficientsξ=R m * /R b * (ξ ≤ξ.<1),ζ=V 1/√2H 0 ξ (ζ ≤ ζ.<1) whereR m * and R b * are the effective radii of the model and the body at their stagnation points. Approximate conditions for modeling the heat transfer from a high-enthalpy (including hypersonic) flow to the stagnation point on a blunt body by means of hyposonic (M≪1) flows, corresponding to the case ζ2≪1, are obtained. The possibilities of complete local simulation of hypersonic nonequilibrium heat transfer to the stagnation point on a blunt body in the hyposonic dissociated air jets of a VGU-2 100-kilowatt induction plasma generator [4, 5] are analyzed.

Two-phase mass injection from the stagnation zone of a blunt body in a hypersonic flow

A mathematical model of the hypersonic steady gas flow over the stagnation zone of an axisymmetric blunt body ~Mth given twophase injection from the surface is proposed. The two-continuum model of a dusty gas [3] is used for describing the flow in the region of the walt. The problem is solved in the boundary layer and thin viscous shock layer approximations. On the basis of the numerical calculations the distribution of the parameters of the carrier and dispersed phases near the axis of symmetry is obtained. The similarity parameters determining the convective heat transfer are found. The stagnation point heat fluxes w~th and without particles are compared. The range of parameters on which particles can significantly reduce the heat transfer is determined. Research into the thermal erosion behavior of various materials in high-enthalpy gas flows and, moreover, the development of new active thermal protection techniques [1--3] make it necessary to investigate the effect on the thermal load of dispersed particles introduced into the flow from the body surface. In the above-mentioned applications a mixture of gas and disperse particles, which then move in a narrow region near the wall, is injected from the surface. Two-phase injection into a supersonic flow without allowance for the viscosity and thermal conductivity of the carder phase was previously considered in [4]. The influence of particles on the flow in the boundary layer without injection effects was investigated in [5, 6].

Aerothermodynamics of a 1.6-meter-diameter sphere in hypersonic rarefied flow

Results of a numerical study using the direct simulation Monte Carlo (DSMC) method are presented for hypersonic rarefied flow about a 1.6-m-diameter sphere. The flow conditions considered are those experienced by a typical satellite in orbit or by a space vehicle during entry. The altitude range considered is that from 90 to 200 km, which encompasses the near continuum, transitional and free-molecular flow regimes. A freestream velocity of 7.5 km/s is assumed in the simulations. The results show that transitional effects are significant at all altitudes below 200 km, but at 200 km the flow about the sphere attains the free-molecular limit. Very little chemical activity is present above 120 km. Both the stagnation point heat transfer and the sphere drag approach their respective free molecule values at 200 km. Results highlight the thermal and chemical nonequilibrium nature of the flowfield. Nonequilibrium effects on the surface heating and body drag are also investigated.

Stagnation point heat flux in hypersonic high enthalpy flow

The paper describes stagnation point heat flux measurements at a range of enthalpies relevant to re-entry speeds of aero-assisted space transfer vehicles (ASTVs) and proposed space planes, using the Australian National University Free Piston Shock Tunnel T3. The unique feature of these experiments is that they were conducted in the ‘straight through’ (reflectionless) mode which enabled higher enthalpies and densities hitherto unattained.

Prediction of stagnation point heat transfer for a slot jet impinging on a flat surface

The fluid flow and heat transfer for a slot jet impinging on a flat plate has been analysed for different nozzle-to-plate spacing. The available potential flow solution has been used to solve the boundary layer and energy equations by using the Blasius-Frossling series solution method. The friction factor and Nusselt number have been evaluated as a function of the dimensionless distance from the stagnation point. Correlation for the Stanton number at the Stagnation point, is obtained in terms of velocity gradient at the stagnation point and Reynolds number.

Spacecraft thermal energy accommodation from atomic recombination

Measurements of atomic recombination probabilities important in determining energy release to reusable spacecraft thermal protection surfaces during reentry are presented. An experimental apparatus constructed to examine recombination of atomic oxygen from thermal protection and reference materials at reentry temperatures is described. The materials are examined under ultrahigh vacuum conditions to develop and maintain well characterized surface conditions that are free of contamination. When compared with stagnation point heat transfer measurements performed in arc jet facilities, these measurements indicate that a significant fraction of the excess energy available from atom recombination is removed from the surface as metastable O2.

Influence of High Mainstream Turbulence on Leading Edge Heat Transfer

The influence of high mainstream turbulence on leading edge heat transfer was studied. High mainstream turbulence was produced by a bar grid (Tu = 3.3–5.1 percent), passive grid (Tu = 7.6–9.7 percent), and jet grid (Tu = 12.9–15.2 percent). Experiments were performed using a blunt body with a semicylinder leading edge and flat sidewalls. The mainstream Reynolds numbers based on leading edge diameter were 25,000, 40,000, and 100,000. Spanwise and streamwise distributions of local heat transfer coefficients on the leading edge and flat sidewall were obtained. The results indicate that the leading edge heat transfer increases significantly with increasing mainstream turbulence intensity, but the effect diminishes at the end of the flat sidewall because of turbulence decay. Stagnation point heat transfer results for high turbulence intensity flows agree with the Lowery and Vachon correlation, but the overall heat transfer results for the leading edge quarter-cylinder region are higher than their overall correlation for the entire circular cylinder region. High mainstream turbulence tends not to shift the location of the separation-reattachment region. The reattachment heat transfer results are about the same regardless of mainstream turbulence levels and are much higher than the turbulent flat plate correlation.

Prediction of stagnation point heat transfer for a single round jet impinging on a concave hemispherical surface

This paper deals with a systematic procedure for assessment of fluid flow and heat transfer parameters for a single round jet impinging on a concave hemispherical surface. Based on Scholkemeier's modifications of the Karman-Pohlhausen integral method, expressions are derived for evaluation of the momentum thickness, boundary layer thickness and the displacement thickness at the stagnation point. This is followed by the estimation of thermal boundary layer thickness and local heat transfer coefficients. A correlation is presented for the Nusselt number at the stagnation point as a function of the Reynolds number for different non-dimensional distances from the exit plane of the jet to the impingement surface.

Stagnation point heat transfer from turbulent low reynolds number jets and flame jets

The flow structure and heat transfer of impinging flame jets as well as impinging isothermal jets from two rapid-heating burners were measured. The separation distance between burner and plate varied from 1 to 12 burner diameters. The Reynolds numbers of the examined isothermal jets were 3300–10000. From the flame jets Re = 1700−4250. Stagnation point Nusselt numbers were determined in two ways: from heat flux density measurements and from measurements of the radial velocity gradient in the vicinity of the stagnation point. With this last parameter a first estimate could be made of the heat transfer coefficient. It is shown that heat transfer from isothermal and flame jets can be described in the same way with this velocity gradient and a turbulence enhancement factor. The results from flame jets agreed quantitatively with the results from isothermal jets if the fluid properties in the heat transfer correlation were taken at a temperature belonging to the averaged enthalpy of the boundary layer along the plate.

Stagnation Point and Surface Heat Transfer for a Turbine Stage: Prediction and Comparison With Data

Predictions using turbulence models are reported for the time-averaged heat-flux distributions on the vane and blade surfaces of the Garrett TFE 731-2 HP and Teledyne CAE 702 HP turbines. To provide the proper initial conditions for the boundary layer solution, the stagnation point process starting from the far free stream is considered. The mean velocity and temperature and the turbulence variation along the stagnation streamline are predicted with a Reynolds stress model so as to resolve accurately the turbulent normal stresses that govern the production of turbulence in the stagnating flow. Using the results from the stagnation solution as initial conditions, the k–ε model equations in boundary layer form are solved at midspan for the pressure and suction sides of the vane and the blade, using a pressure distribution obtained from inviscid codes. The predicted surface heat transfer distributions are compared with measurements from short-duration full-stage rotating turbine measurements.