Problems on High Speed flow heat transfer:












Aerodynamic heating:

Aerodynamic heating is the heating of a solid body produced by the passage of fluid (such as air) over a body such as a meteor, missile, or airplane. It is a form of forced convection in that the flow field is created by forces beyond those associated with the thermal processes. The heat transfer essentially occurs at the vehicle surface where aerodynamic viscous forces ensures that the flow is at zero speed relative to the body for a very thin layer of molecules at the surface.

When fluid flow slows down its kinetic energy is converted to heat; in high speed flows, tremendous energy is represented by the mean motion of the flow. As the flow is slowed to near zero speed, its temperature increases, the gradient in the speed in a direction normal to the surface allows small scale mass transport effects to dissipate the temperature in the outward direction and thus the temperature at the surface is less than the stagnation temperature; the actual temperature is referred to as the recovery temperature. These viscous dissipative effects to neighbouring sub-layers make the boundary layer slow down via a non-isentropic process. Heat then conducts into the surface material from the higher temperature air. The result is an increase in the temperature of the material and a loss of energy from the flow. The forced convection ensures that other material replenishes the gases that have cooled to continue the process.

The stagnation and the recovery temperature of a flow increases with the speed of the flow and are greater at high speeds. The total thermal loading of the structure is a function of both the recovery temperature and the mass flow rate of the flow. Aerodynamic heating is greatest at high speed and in the lower atmosphere where the density is greater. In addition to the convective process described above, there is also radiative heat transfer from the flow to the body and vice versa with the net direction set by the relative temperature of each.

Aerodynamic heating increases with the speed of the vehicle and is continuous from zero speed. It produces much less heating at subsonic speeds but becomes more important at supersonic speeds. At these speeds it can induce temperatures that begin to weaken the materials that compose the object. The heating effects are greatest at leading edges. Aerodynamic heating is dealt with by the use of high temperature alloys for metals, the addition of insulation of the exterior of the vehicle, or the use of ablative material.

Aerodynamic heating is a concern for supersonic and hypersonic aircraft. The Concorde dealt with the increased heat loads at its leading edges by the use of high temperature materials and the design of heat sinks into the aircraft structure at the leading edges. Higher speed aircraft such as the SR-71 deal with the issue by the use of insulating material and material selection on the exterior of the vehicles. Some designs for hypersonic missiles would employ liquid cooling of the leading edges (usually the fuel en route to the engine).

Re-entry vehicles

Aerodynamic heating is also a topic of concern in re-entry vehicles. The heating induced by the very high speeds of re-entry of greater than Mach 20 is sufficient to destroy the structure of the vehicle. The early space capsules such as those on Mercury, Gemini, and Apollo were given blunt shapes to produce a stand-off bow shock. As a result most of the heat is dissipated to surrounding air without transferring through the vehicle structure. Additionally, these vehicles had ablative material that sublimates into a gas at high temperature. The act of sublimation absorbs the thermal energy from the aerodynamic heating and erodes the material away as opposed to heating the capsule. The surface of the heat shield for the Mercury spacecraft had a coating of aluminium with glassfiber in many layers. As the temperature rose to 2,000 °F (1,100 °C) the layers would evaporate and take the heat with it. The spacecraft would become hot but not harmfully so.[1] The Space Shuttle used insulating tiles on its lower surface to absorb and radiate heat while preventing conduction to the aluminium airframe. The compromise of the heat shield during lift-off of Space Shuttle Columbia contributed to its destruction upon re-entry.


Ablation is a means of thermal protection based on physicochemical transformations of solid substances by convective or radiation heat flow. The heat-shield effect is the sum of the heat of phase and chemical transformations of the substance and the reduction of the heat flow when the ablation products are forced into the surrounding medium (see Heat Protection). Ablation can be referred to as a sacrificial method of heat protection, since in order to maintain acceptable heat conditions in a body, its surface layer is partially destroyed. Ablation can, as a rule, be allowed in objects of single application; for instance, the re-entry space vehicles, combustion chambers and the nozzle units of solid-propellant rocket engines. The use of ablative facing has a number of advantages over other methods of heat protection. The main advantage is the self-regulation process, i.e., the change in the ablation rate depending on the level of pressure and temperature of the gas flowing across the surface. Thanks to high values of heat of physicochemical transformations and to the injection heat effect, the use of ablative facing materials exceeds substantially in efficiency that of systems functioning on the heat storage principle or on the principle of convective cooling (see Heat Protection). Together with penetrating cooling, ablative facings form the class of active heat protection, the basis for which is the direct effect on the process of heat transfer from the surrounding medium to the body.

The most commonly used ablative materials are the composites, i.e., materials consisting of a high-melting point matrix and an organic binder. The matrix can be glass, asbestos, carbon or polymer fibers braided in different ways. In some cases, a honeycomb construction can be used, filled with a mixture of organic and nonorganic substances and possessing high heat-insulating characteristics (as used, for instance, on the space vehicle ”Apollo”).

Shown in Figure 1 is a schematic model of the destruction of a composite material from a high-melting point matrix and an organic binder. The characteristic property of such heat-shielding coverings is the presence of two fronts or zones, to be more exact, in which physicochemical transformations take place. In convective heating, a viscous melt film can be formed on the surface of such composite materials. Despite its thinness, the film strongly affects the destruction process. In particular, the coalescence of particles of the surface layer prevents their erosion blow-off by the flow. The melt film also reduces the rate of oxidation of chemically-active components of the material by the incoming flow of gas.


Figure 1. Schematic model for the destruction of an ablating composite material.

Further into the surface lies a comparatively thick layer of charred organic binder reinforced by high-melting fibers. Still deeper is the thermal decomposition zone, where a mixture of volatile and solid (coke) components is formed. The volatile components filtered through the porous matrix are injected into the boundary layer of the incoming gas flow. An intensive sublimation of glass or other oxides which form high-melting fibers occurs on the surface of the melt film. The fraction of gaseous ablation products in the total ablation mass can, therefore, be high. The particles of coke are practically pure carbon; thus, at the melting temperature of glass they remain solid. The spreading film of glass “breaks out” the porous structure of the charred layer and carries away the particles of coke. The later, in turn, affects the flow of the melt, increasing its effective viscosity (see Melting).

At high temperatures, the coke particles in the melt film are not inert components – they interact actively both with glass and with any oxidant present in the gas flow. Tens of various strongly interacting components can exist in the boundary layer over the surface of the composite heat-shielding covering. The choice of a theoretical model for the destruction process of such materials, presents considerable difficulties. However, on the basis of extensive experimental and theoretical studies of thermophysical, thermodynamic and strength phenomena which attend the process of the incident flow effect, we have succeeded in creating a schematic model or a mechanism for the destruction of a heat-facing layer. Such a mechanism has been designed only for some classical representatives of the range of composites (see Sublimation,Melting). At the same time, advances in chemistry and materials technology extend the possibilities of selecting improved ablation materials. In this context, a demand arose for some unique parameter to compare various types of ablative materials convenient for both theoretical and experimental studies. One such parameter is the effective enthalpy of destruction, symbolized as heff.

The effective enthalpy defines the total thermal energy expenditure necessary to break down a unit mass of ablative material. The problem of comparing numerous ablative materials is most easily demonstrated for a quasi-stationary destruction (see Heat Conduction) when the velocity of all isotherms or destruction fronts inside the material coincides with the velocity of the outer surface displacement. In this case, the temperature profile inside the heat-shielding covering is described by a set of exponents, and the heat flux clip_image046 spent on heating inner layers does not depend on the material thermal conductivity λ.

Let us first consider a destruction process under conditions of exposure to convective heating. The thermal balance on a destructing surface (Figure 2) can be written as follows:




Figure 2. Destruction process with convective heating.

Here, (α/cp)0 is the heat transfer coefficient, and he and hw are the enthalpies of the gases in the incoming flow and the wall, respectively. In contrast to a non-destructing ablative facing, the convective heat flux clip_image050 supplied from without is expended not only for heating the material ( clip_image046[1] ) and by radiant re-emission of the four heated surfaces ( εσT4W ) but also for the surface (with mass loss rate clip_image051 and bulk (with mass loss rate clip_image052 physicochemical transformations, whose thermal effects are evaluated as ΔQw and ΔQ. If a melt film is formed on the surface of a heat-shielding covering, then clip_image053 , where clip_image054 is the mass loss rate of a substance in a molten form. The total thermal effect of the bulk failure ΔQ contains not only the heat of matrix melting, but also the thermal effect of the thermal decomposition of an organic binder, the heat of heterogeneous interaction between the glass and coke inside the charred layer, etc. In a similar manner, the thermal effect of surface destruction ΔQw must account for the thermal effect of evaporation of a melted film and the burning of the coke particles in the incoming flow of gas.

Gaseous ablation products which penetrate into the boundary layer cause a reduction of a convective heat flow due to the so-called “injection effect.” We can evaluate the blocking action of the injection effect by a linear approximation (see Heat Protection):


Here, γ is the dimensionless coefficient of injection (γ < 1), which in the general case depends on flow conditions in the boundary layer (laminar or turbulent) and the ratio of molecular masses of the gas injected and the incoming flow. Unlike other effects influencing the absorption of the heat energy supplied, the injection effect rises steeply with the increasing velocity or temperature of the incoming flow and finally becomes predominant.

If we denote the share of gaseous ablation products in the total mass loss of the substance by Г (Г = clip_image054[1] / clip_image052[1] ), then we can obtain a generalized characteristic of destruction power, namely, the effective enthalpy of destruction, heff:


The effective enthalpy determines the amount of heat which can be “blocked” when breaking down a unit mass of covering material (whose surface temperature is Tw) through physicochemical processes. The higher the effective enthalpy, the better the heat-shielding material. We place emphasis on the independence of the effective enthalpy from the geometrical dimensions or the shape of the body. Actually, as distinct from a heat flux whose value, with the given parameters of the incoming flow (pe, he), is inversely proportional to clip_image057 (where RN is the typical dimension of the body; for instance, the radius of curvature in the vicinity of the critical point), the effective enthalpy is unaffected either by the shape or the dimension of the body. This qualifies it as a parameter for relating laboratory and real heat-loading situations.

We can see from the definition of effective enthalpy that in all cases when Г ≠ 0, it must increase substantially with the rise in the enthalpy of the stagnated flow he. The parameters of the incoming gas flow (pressure Pe and enthalpy he) can effect heff through changes in the temperature of the destructing surface Tw, the fraction of the ablation which is in gaseous form Г and the thermal effect of surface processes ΔQw. The effect of surface temperature Tw on heff can be considered to be rather limited. A typical dependence of Tw, Г and heff on enthalpy he and pressure Pe in breaking down glass reinforced plastics in an air flow is shown in Figures 3, 4 and 5. The flow condition (laminar or turbulent) in the boundary layer determines the injection coefficient γ (see Heat Protection), which affects radically the dependence of heffon he (Figure 6 ). If the ablative material does not contain oxides, then, as a rule, the share of gasification Г is close to unity. For graphite-like heat-shield covering, in particular, Г = 1. In this case, however, the thermal effect of surface processes ΔQw varies from a negative value on carbon burning C + O2 = CO2 to a positive value upon its sublimation. An extra liberation of heat upon burning brings about surface overheating relative to the equilibrium value of the temperature for a heat-insulated wall. In this case, the effective enthalpy becomes negative and the notion of heff loses practical sense. The dimensional rate of destruction is often used as an alternative parameter for generalizing the experimental and the design data:


Its advantage is that the function clip_image059 (he ) is always positive and besides, the temperature of the destructing surface Tw and the emissivity ε are not warranted. Typical dependences of clip_image059[1] on the stagnation enthalpy he for Teflon, glass-reinforced plastic and graphite breaking down in air flow are shown in Figure 7.


Figure 3. The share of gasification as a function of stagnation enthalpy of incoming gas he.


Figure 4.


Figure 5.


Figure 6.


Figure 7. Dimensionless destruction rate ( clip_image059[2] ) as a function of stagnation enthalpy (he) for various materials breaking down in an air flow.

Combined radiation-convection heating of the surface of an ablative material can considerably change the mechanism of its destruction. The injection of gaseous disintegration products in cases where they do not possess high absorption coefficients, slightly reduces the intensity of the radiation component clip_image065 of the heat flow. As the clip_image066 ratio grows, the mechanism of destruction of the majority of ablative materials more closely resembles sublimation and thermal decomposition. This is due to a rapid decrease in the contribution of convective and diffusion transfer in the boundary layer while injecting gaseous products, to the ceasing of melt film flow and to the absence of burning on the destructing surface.

The heat balance on the surface of an ablative material in case of high levels of radiation of heat flows clip_image065[1] is simplified as follows:


Here, Kα, w is the absorption coefficient, which depends on the spectrum of incident radiation heat flow clip_image068 (λ) and on the spectral distribution of the destructing surface emissivity ελ (λ):


When no mechanical cracking or melting of a heat-shielding material occurs, the total rate of ablation clip_image052[2] coincides with clip_image051[1] and the notion of effective enthalpy of the material under intensive radiation heat influence can be introduced as:


Table 1 shows the results of the evaluation of parameters h, Kα, w (in the 0.2 < λ < 1 μm spectral range) and hR for various substances.

Table 1.


h, kJ/kg 

Kα, w 

hR, kJ/kg









Magnesium oxide








An analysis of the data presented in Table 1 allows us to reach a paradoxical conclusion: under the influence of intensive radiation, the effective enthalpies of destruction of graphite and Teflon become about equal. We should note that the ablation rate of graphite, as compared to magnesium oxide, does not differ so strongly as the other values of the effective enthalpies given in the table. This is associated with the fact that the temperature of graphite destruction is almost half as great, and, therefore, the levels of the reemitted energy clip_image071 differ by an order of magnitude. Nonetheless, the main conclusion that can be drawn in analysing Table 1 is that by decreasing the absorption coefficient of the destructing surface (Kα, w), we can obtain a greater efficiency of ablation than by increasing the heat of sublimation.


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