Frozen Boundary Layer Research Articles

Analysis of catalytic heat transfer for a multi-species gas mixture

Stagnation point catalytic heat transfer model for a multi-species gas mixture has been developed in this work. The analysis extends the existing tertiary gas mixture catalytic model that assumes thermochemical equilibrium at the edge of a chemically frozen boundary layer. The catalytic heat transfer is computed numerically by solving the governing equations with matrix diagonalization and shooting methods. The present model is applied to compute the heat transfer for both tertiary gas mixture O-O2-Ar and quinary gas mixture O-O2-N-N2-Ar. For the case of the tertiary gas mixture, the present model predicts in the finite-catalytic region, the stagnation-point heat transfer due to recombination is similar with that of the existing models of Goulard and Park. In the highly-catalytic region, however, noticeable differences are observed owing to how the species mass fraction at the wall is computed. Unlike the Goulard approach treating the oxygen and nitrogen as a single recombination efficiency, in the case of the quinary gas mixture, the oxygen recombination efficiency needs to be decoupled with that of nitrogen. The present global model for the tertiary gas mixture is also compared with the Computational Fluid Dynamics (CFD) approach. The results suggest that the present model predicts a similar diffusive stagnation heat transfer to that of the CFD approach, within some acceptable range, when a zero backward reaction rate constant is assumed in the chemical reaction modeling.

Reentry trajectory and survivability estimation of small space debris with catalytic recombination

A code has been developed to analyze reentry trajectories and survivability of space debris. In particular, an attention was given to small sizes. Based on simple shapes such as a sphere, a cylinder, and a box with sizes of 12.5–50cm, reentry trajectories were calculated. Materials considered were graphite epoxy, aluminum, and titanium. In total, 120 different cases were examined. The results were compared and validated with various existing codes. Good agreement was found. In the heat transfer calculation, all of the existing codes used the well known Lees’ and Fay and Riddell’s formulae which assume an equilibrium boundary layer flow with a super-catalytic wall where the surface recombination efficiency is regarded infinity. In the case of small space debris having sizes of 2.5–10cm, however, the flow residence time behind a shock wave is far too short, so that the super-catalytic assumption leads to over-estimation of surface heat transfer rates. Assuming a frozen boundary layer, a finite catalytic recombination can be considered and the results were compared with that of the super-catalytic cases. Both hollow and solid spheres were considered with different sizes and materials. In total, 24 different cases were examined. The results showed that, 16 out of 24 cases survived, while only 8 cases for the super-catalytic and 19 cases for the non-catalytic walls survived, implying the importance of catalytic wall effects for the study of small space debris.

Analysis of a number of elements in the mechanism of mass entrainment of carbon material within the framework of the complete thermochemical model of its destruction

The results of a numerical solution of the equations constructed for a frozen boundary layer on the surface of a carbon material, with allowance for the complete thermochemical model of the entrainment of its mass, are presented. The results obtained are compared with the data that correspond to the use of the analogy between the processes of heat and mass transfer in a boundary layer and of the simplified model of the mass entrainment of the materials of the class considered. The results of comparison between experimental and calculated-theoretical data on the rate of destruction of the ATJ-grade graphite are also presented.

Recasting the Fay-Riddell formulae for computing the stagnation point heat flux

The Fay-Riddell formulae, used to compute the heat flux at the stagnation point of spherical bodies in very high speed, laminar flow and dissociating air, have been revived and recast. As these formulae were obtained by fitting a number of results of the original Fay-Riddell computing procedure, which suffered from inaccuracies concerning operative parameters, it is to be expected that these inaccuracies also influence the correctness of the formulae. A sensitivity analysis has been made in order to identify the most critical parameter. Recast formulae have been calibrated using the results of the improved version of the Fay-Riddell computing procedure and then validated both by numerical results of a Navier-Stokes code and by experimental data. For this purpose two sets of heat flux measurements have been made in HEBDAF (high enthalpy blown-down arc facility) at the University of Naples, matching the operating conditions of the formula for a frozen boundary layer and non-catalytic wall. Recast formulae are valid in the range of free-stream total enthalpy between 3 and 37 MJ/kg.

Modelling high temperature salt condensation; Fick and Soret diffusion effects

The need for developing models to understand the fouling mechanisms in heat exchangers arises from the enormous cost that this entails to the European Community (approximately 10,000 MECU per year). This paper is addressed to developing a general mathematical model based on local thermochemical equilibrium (LTCE), incorporating mass conservation constraints which allow for deposition. This calculation has been performed in an entirely novel way using a stochastic optimisation technique and can deal with complex multi-species, multi-phase systems involving non-ideal equations of states. The flux estimation is based on Fick and Soret diffusion effects in the chemically frozen boundary layer (CFBL). The physical properties of the system at various temperatures are computed with the help of the Chapman-Enskog theory for the Lennard-Jones (6–12) potential. We describe a novel probe which has been designed for the measurement of high temperature condensation.

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.

Heat transfer during mixed convection on a vertical surface in a porous medium with deviation from Darcy's law

I. G.R. Inger, "An analogy between boundaryilayer pressure gradient and chemical reaction-rate effects," J. Aerospace Sci., 27, No. 12 (1960). 2. O.V. Dobrocheev, "Investigation of the boundary layer of a slightly ionized gas with nonequilibrium particle recombination," Author's Abstract of Candidates Dissertation, ENIN, Moscow (1979). 3. V.M. Ievlev, Turbulent Flows of High Temperature Continuous Media [in Russian], Nauka, Moscow (1975). 4. A.M. Leonttev, A. N. Oblivin, and P. N. Romanenko, "Investigation of the drag and heat transfer in a turbulent air flow in axisymmetric channels with longitudinal pressure gradient," Zh. Prikl. Mekh. Tekh. Fiz., No. 5 (1961). 5. O.V. Dobrocheev, V. P. Motulevich, and E. D. Sergievskii, '~Comparative analysis of nonequilibrium boundary-layer analysis methods," Tr. Mosk. Energ. Inst., No. 395 (1979). 6. V.P. Motulevich, O. V. Dobrocheev, and N. V. Khandurov," Chemically nonequilibrium turbulent boundary layer of a slightly ionized gas," Tr. MLTI, No. 112 (1978). 7. ~ P. S. Roganov, Experimental~Investigation of Heat Transfer Processes in a Frozen Boundary Layer [in Russian], Author's Abstract of Candidates Dissertation, Moscow Higher Techn. Inst. Moscow (1979). 8. A.B. Garyaev, O. V. Dobrocheev, and V. P. Motulevich, "Model to compute longitudinal velocity fluctuations on a plate," Inzh.-Fiz. Zh., 49, No. 5 (1985).

Theoretical and Experimental Studies of the Deposition of Na2 SO 4 from Seeded Combustion Gases

The deposition of sodium sulfate from flames containing sodium and sulfur is regarded as one of the fundamental steps in the phenomenon of “hot corrosion” of turbine components. Recently, a local thermochemical equilibrium (LTCE) method of predicting condensation temperatures of sodium sulfate in flame environments was described. This paper presents results of an experimental study to test the validity of the theoretical dew point predictions and to provide the basis for developing a deposition rate theory. Experiments were run in a Mach 0.3 atmospheric pressure laboratory burner rig. Flames were doped with sea salt, , and , respectively. Deposits were collected on cylindical platinum targets placed in the combustion products stream, and the deposition rate was studied as a function of collector temperature. Experimental deposition onset temperatures checked within experimental error with LTCE‐predicted temperatures. A multicomponent mass transfer equation was developed to predict the rate of deposition of via vapor transport at temperatures below the deposition onset temperature. The phenomena of species transport by simultaneous Fick diffusion, Soret (thermal) diffusion, convection, and turbulence are included, subject to the basic assumption that no reaction or phase change occur within the diffusion boundary layers. The present formulation is sufficiently general to include the transport of particles, provided they are small enough to be formally treated as heavy molecules. Agreement between maximum deposition rates predicted by this chemically frozen boundary layer (CFBL) theory and those obtained in the seeded laboratory burner experiments is good, but the predicted dependence on surface temperature exhibits plateau‐like behavior not evident in the present experimental results.

Some peculiarities of radiative heat transfer in a boundary layer in chemical equilibrium

A theoretical study is performed of certain physical aspects of radiative-convective heat exchange in a viscous, thermally conductive, hypersonic shock layer in the presence of equilibrium chemical reactions between components of the incident gas and decomposition products of a heat-shield material. The results obtained reveal a number of peculiarities which qualitatively distinguish the character of interaction of radiant fluxes from the high-temperature nonviscous portion with the chemically equilibrium and frozen boundary layer. At the present time a number of studies [1–4] has been published on this problem. In [1] the flow of selectively radiating air was studied in the region between the departing shock wave and a surface through which equilibrium air is blown into the boundary layer. In [2] special attention was turned to analysis of results and a description of numerical solution methods for the equations. In [3, 4] the problem was solved in the nonviscous formulation, where the mixing zone degenerates into a contact discontinuity. A previous study by the present authors [5] presented an example of flow and heat-exchange calculation in a shock layer at each point of which thermodynamic equilibrium was assumed to exist.

High Enthalpy Hypersonic Boundary-Layer Flow

A theoretical and experimental study of an ionizing laminar boundary layer formed by a very high enthalpy flow (in excess of 12 eV per atom or 7000 cal/gm) with allowance for the presence of helium driver gas is described. The theoretical investigation has shown that the use of variable transport properties and their respective derivatives is very important in the solution of equilibrium boundary layer equations of high enthalpy flow. The effect of low level helium contamination on the surface heat transfer rate is minimal. The variation of ionization is much smaller in a chemically frozen boundary layer solution than in an equilibrium boundary layer calculation and consequently, the variation of the transport properties in the case of the former was not essential in the integration. The experiments have been conducted in a free piston shock tunnel, and a detailed study of its nozzle operation, including the effects of low levels of helium driver gas contamination has been made. Neither the extreme solutions of an equilibrium nor of a frozen boundary layer will adequately predict surface heat transfer rate in very high enthalpy flows.

A study of radiation properties of oxide-metal composites.

Simulation of Convective and Radiative Entry Heating, Advances in Hypervelocity Techniques, edited by A. M. Krill, Plenum, New York, 1962. 5 Marvin, J. G. and Pope, R. B., Laminar Convective Heating and Ablation in the Mars Atmosphere, AIAA Journal, Vol. 5, No. 2, Feb. 1967, pp. 240-248. 6 Wilson, G. R. (compiler), Thermophysical Properties of Six Charring Ablators from 140° to 700 °K and Two Chars from 800° to 3000°K, TN D-2991, Oct. 1965, NASA. 7 Parker, J. A., Needs for Characterization and Process Control of Low-Density Composites for Aerospace Application, presented at International Society of Plastics Institute, New York, June 1966. 8 Vojvodich, N. S. and Pope, R. B., /The Influence of Ablation on Stagnation Region Convective Heating for Dissociated and Partially Ionized Boundary Layer Flows, Proceedings of the 1965 Heat Transfer and Fluid Mechanics Institute, edited by A. F. Charwat et al., Stanford University Press, Stanford, Calif., 1965. 9 Pope, R. B., Stagnation-Point Convective Heat Transfer in Frozen Boundary Layers, Paper 68-15, Jan. 1968, AIAA. 10 Scala, S. M. and Gilbert, L. M., Sublimation of Graphite at Hypersonic Speeds, AIAA Journal, Vol. 3, No. 9, Sept. 1965, pp. 1635-1644. 11 Wakefield, R. M., Lundell, J. H., and Dickey, R. R., The Effect of Oxygen Depletion in Gas-Phase Chemical Reactions on the Surface Recession of Charring Ablators, Paper 68-302, April 1968, AIAA. 12 Emmons, H. W. and Leigh, D., Tabulation of the Blasius Function with Blowing and Suction, Combustion Aerodynamics Lab. Interim TR9 Nov. 1953, Div. of Applied Science, Harvard Univ.

Stagnation-point convective heat transfer in frozen boundary layers.

Stagnation point convective heat transfer in frozen boundary layers to surfaces having widely differing catalytic activity in ionized flows

Graphite combustion in a chemical-equilibrium boundary layer

The mechanism of graphite decomposition in a dissociated air stream in the presence of heterogeneous reactions on the surface and nonequilibrium evaporation for the case of a frozen boundary layer is studied in [1, 2]. Examples of the calculation of graphite decomposition in an oxygen stream with equilibrium [3] and nonequilibrium [4] chemical reactions in the boundary layer are presented in [3, 4]. The effect of the chemical reactions in the boundary layer on the rate of mass transfer and on the surface temperature with variation of the external flow parameters (p, Te) remains unexplained. The present paper is devoted to a study of the mechanism of graphite ablation over a wide range of temperatures and pressures with air flow about the body in the case of an equilibrium boundary layer. The effect of the individual components on the heat and mass transfer processes is investigated.

NONEQUILIBRIUM DISSOCIATING FLOW OVER A CUSPED BODY

19 Inger, G. R., Specific heat inequality effect in the chemically frozen stagnation point boundary layer, ARS J. 30, 1028-1029 (1960). 20 Teare, J. D., Hamerling, P., and Kivel, B., Theory of the shock front. II. High temperature reaction rates, Res. Note 133, Avco Research Lab., Boston, Mass. (June 1959). 21 Benson, S. W. and Fueno, T., The mechanism of atom recombination by consecutive vibrational deactivations, J. Chem. Phys. 36,1597-1604 (1962). 22 Rosner, D. E., Recent advances in convective heat transfer with dissociation and atom recombination, Jet Propulsion 28, 445-451(1958). 23 Rosner, D. E., Chemically frozen boundary layers with catalytic surface reaction, J. Aerospace Sci. 26, 281-286 (1959). 24 Rosner, D. E., Boundary conditions for the flow of a multicomponent gas, Jet Propulsion 28, 555-556 (1958). 25 Inger, G. R., An analogy between boundary layer pressure gradient and chemical reaction rate effects, J. Aerospace Sci. 27,1028-1029(1960). 26 Chung, P. M., A simplified study of the nonequilibrium Couette and boundary layer flows with air injection, NASA TN D-306 (February 1960).

Chemically Frozen Boundary Layer with Surface Reactions behind a Strong Moving Shock

Surface recombination of dissociated atoms is studied behind a strong shock moving into a stationary diatomic gas. The chemically frozen laminar boundary layer is analyzed behind the moving shock. A solution is obtained for surface distribution of atoms and heat transfer when the atom concentration varies arbitrarily in the inviscid dissociating gas stream and, at the same time, the surface has an arbitrary but uniform catalycity. The applicability of the theory to the chemical diagnostics of shock tubes is studied.

Chemically Frozen Boundary Layers with Catalytic Surface Reaction

When a fluid boundary layer containing a single reactant develops along a solid surface which acts chemically as a distribution for this species, its steady-state concentration along the surface, and, hence, the reaction rate distribution depends both upon the true surface chemical kinetics and a combination of convective and diffusive transport through the fluid. Considered here is a simple approximate method for studying this streamwise distribution of reaction rate in terms of the shear and temperature distributions along the surface. The method is based upon a treatment of the concentration integral equation which initially parallels Liepmann's recent treatment of the energy integral equation but which ultimately leads to a differential equation for the concentration distribution of reactant along the surface. This approach to mass transfer problems, which is intended to bring out clearly the role of the governing catalytic parameter as well as several interesting properties of solutions, is then compared with alternate techniques, in particular with that of Chambre and Acrivos.~ The reactant concentration is considered to be so small that constant diffusion coefficient, D, viscosity coefficient, n, Prandtl Number for diffusion (Schmidt Number), PTD = n/(pD), can be assumed, and the fluid is taken to be incompressible, with catalyzed reaction taking place only at the wall. Thus, the hydrodynamic field is unaltered by the surface reaction, and only the effect of small surface temperature differences on the kinetics of the wall reaction—i.e., the effective sink strength—are taken into account. Extension to the case of several reactants is discussed, and an interpretation of the governing catalytic parameter as a ratio of characteristics times is given.