Thermal protection of structural steel

Transcription

1 Thermal protection of structural steel J. E. J. Staggs Energy Research Institute School of Process, Environment and Materials Engineering University of Leeds Leeds LS2 9JT United Kingdom

2 Overview Thermal insulation has a twofold role for steel protection: To minimise the temperature difference between the exposed coating surface and the steel substrate. To maximise the time that it takes the steel temperature to reach a critical value. Whether the insulation layer is formed in-situ (as in the case of intumescents) or is static, it must possess certain desirable characteristics and these are discussed first. An alternative strategy to thermal insulation is to use a reactive heatsink coating. Two types are investigated: A coating that endothrmically degrades with no volume change on heating A sacrificial ablative coating that vaporises on heating.

3 Thermal Insulation Consider an inert layer of thermal insulation covering a vulnerable substrate, subject to an external heat flux on its exposed surface: Heat l T It transpires that the temperature difference T between the exposed and unexposed surfaces depends on two important material characteristics: The conduction heat transfer coefficient λ = λ l The thermal diffusion timescale l lρc = = α λ t D 2

4 Thermal Insulation Two observations are immediately apparent: To limit the temperature of a vulnerable substrate, the conduction heat transfer coefficient (CHTC) must be as small as possible. To maximise the time taken for a vulnerable substrate to reach a specific temperature, the diffusion time scale must be as large as possible. So: how do we make the CHTC small? λ = λ l SMALL BIG How do we make t D big? t D = lρc λ BIG SMALL

5 Thermal Insulation Porous solids (with pores sufficiently small to eliminate internal convection) are the most effective insulators The thermal conductivity of a porous solid lies between two bounds: λ / λ s Upper Bound Λ Λ + ϕ ( 1 Λ) λ 1 ϕ λ s ( 1 Λ) The actual thermal conductivity of a real porous solid depends on the shape, distribution and to a lesser extent size of the pores. But in all cases, thermal conductivity is a decreasing function of porosity Lower Bound Porosity So, it seems to make sense to make porosity ϕ as large as possible, correct?

6 Thermal Insulation Unfortunately no! The situation in reality is more complicated and there are two important factors that interfere with this simple approach. Factor 1: Heat Transfer Enhancement by Radiation As temperature increases, radiation heat transfer across the pores themselves provides an additional heat flux that becomes increasingly significant. For very small pores, it transpires that this additional heat transfer may be accounted for by an augmentation to the thermal conductivity: Radiation λ eff 3 T = λ + ϕλr 1 3 Ta Radiation enhancement

7 Thermal Insulation Increasing temperature will always increase thermal conductivity, implying that thermal insulation effectiveness reduces with temperature. Increasing porosity can have the effect of increasing the overall effective thermal conductivity. λ eff 3 T = λ + ϕλr 1 3 Ta 0.6 Best Fit Experimental Results 0.5 Effective TC / Wm -1 K Temperature / K

8 Thermal Insulation 3 T λeff = λ + ϕλr The term λ R in the radiation augmentation 1 3 Ta to total thermal conductivity is an increasing function of pore size. This implies that for the same overall porosity ϕ, a solid with many small pores will have lower total thermal conductivity than a solid with few large pores. More internal radiation transfer in this region than this region

9 Thermal Insulation Factor 2: Effect of Increasing Porosity on Diffusion Time Scale The density and specific heat capacity of a porous solid are c ρ = ( 1 ϕ ) ρ s + ϕρ0 ( 1 ϕ ) ρ s ( 1 ϕρ 0 / ρ ) cs + ϕρ0c0 / cs = ρ respectively, where the subscripts 0 and s again denote a pore property and a solid (skeletal) property respectively Hence from the definition of diffusion time scale, it follows that t ~ 1 ϕ /. Now, a desirable property is that increasing D ( ) λ porosity also increases the diffusion time scale. l lρc = = α λ t D 2 In other words, it is necessary that ( 1 ϕ )/ λ is an increasing ~ λ = λ / 1 ϕ is a decreasing function of ϕ, or equivalently ( ) function of ϕ.

10 Thermal Insulation Therefore a strict requirement of the porous solid should be that ~ dλ < 0. dϕ 1.0 Λ Λ + ϕ ( 1 Λ) λ 1 ϕ λ s ( 1 Λ) The functional dependence of λ ~ on porosity is determined largely by pore shape and distribution and a reasonable question is whether or not ~ 0.6 λ is always a decreasing function of porosity. λ s, for 0.0 ~ example, we find that d λ / dϕ = Λ /( 1 ϕ ) 2, which is always positive. This means that increasing porosity would actually reduce Porosity the diffusion time scale. Hence any material with a thermal conductivity - porosity functional dependence close to the upper bound would not make a good protector. If we look at the thermal conductivity upper bound / λ = 1Lower ϕ( 1Bound Λ) λ / λ s Upper Bound

11 Thermal Insulation Numerical results showing failure time as a function of porosity for TC upper bound

12 Heat Sink Coating An alternative approach to purely conductive protection or intumescent chars is to use a reactive heat sink coating. Consider a reactive coating P that endothermically degrades on heating to give P * * : P P with reaction heat H J/kg. The important feature of the process is that it consumes energy and so the coating acts as a heat sink. Important examples of materials in this category are alumina trihydrate and magnesium hydroxide. A characteristic feature of heat sink coatings is that they act to control the local temperature, until the virgin coating P is exhausted. Whilst the degradation reaction proceeds, the local temperature will be approximately equal to the characteristic kinetic temperature of the degradation reaction. This is determined by an interaction between the degradation kinetics and the local heating rate.

13 Heat Sink Coating Definition of characteristic kinetic temperature at a given heating rate

14 Heat Sink Coating The graph shows numerical results for the thermal histories of the exposed surface, midpoint and the unexposed surface. Degradation at the exposed surface occurs as soon as the CKT is attained. At the midpoint, there is an induction period (labelled I on the figure) caused by thermal diffusion. The temperature remains close to the CKT until all reactant has been consumed (region II). After this, there is an interplay between heat diffusing from above and also being diffused away to lower regions where the degradation reaction is still proceeding (region III). When all reactant throughout has been consumed, the temperature increases purely by diffusion to the adiabatic limit (region IV). At the unexposed face, temperature increases until the characteristic kinetic temperature is reached and the degradation reaction switches on. During degradation, the temperature is controlled by the reaction until conversion is complete. After this point, the temperature then increases to the adiabatic limit.

15 Heat Sink Coating Hence the effectiveness of a heat-sink coating is determined by two main measures: The characteristic kinetic temperature of the coating at the interface with the substrate. The length of time taken for total conversion of the coating. For a simple heat-sink coating undergoing a single-step first order Arrhenius degradation process (with pre-exponential factor A and activation temperature T A ), subject to a fixed heat flux on the exposed surface, it transpires that the important parameters are: The coating Damköhler number: D = ln = ln( ) The coating Stefan number: S H = ct A The dimensionless external heat flux: 2 l A α q η = λ T A At D

16 Heat Sink Coating The overall performance of the heat-sink coating is determined by a combination of the three parameters above, together with the diffusion time scale and CHTC already discussed. lρ H The approximate duration of the heat-sink phase will scale like t HS ~ q Coating Thickness: 0 mm 2.5 mm 5.0 mm 7.5 mm 10.0 mm 750 Temperature / K Coating begins to dehydrate Coating anhydrous Numerical results for substrate temperature of magnesium hydroxide coated sample in a standard furnace test Time / s

17 Ablative Coating An ablative is a sacrificial coating that is thermally eroded during the heating cycle. Coatings of this type are used on space vehicles. The coating is assumed to be inert until the ablation temperature T abl is reached. At this point, the coating starts to vaporise. Vaporisation of the coating is endothermic, much like the heat sink coating considered above. The local temperature during ablation is controlled by the vaporisation process and limited to the ablation temperature. The most important difference between the two approaches is that during the ablation process, the volume of coating reduces as it vaporises and so its conduction heat transfer coefficient increases.

18 Ablative Coating Substrate fails fails Induction Ablation Post-Ablation Idealised behaviour of an ablative coating in a furnace test.

19 Ablative Coating Let H be the latent heat of vaporisation and c the specific heat capacity of the coating. If the coating is exposed to an external heat flux, then the steady ablation rate (mass flux of vaporised coating) will be m = c q ( T T ) + H abl a So, assuming that the temperature is sufficient for the coating to ablate, the timescale for which the coating can provide protection will be ( T T ) lρc abl a t abl ~ 1+ q c H ( T ) abl Ta

20 Ablative Coating There are three possible failure modes for the coated substrate, termed inductive failure, ablative failure and post ablative failure: 1. Inductive failure. The substrate reaches its failure temperature during the induction phase (where the temperature of the exposed surface of the coating increases to its ablation temperature); the coating has not yet started to ablate. 2. Ablative failure. The steel sample reaches its failure temperature during ablation of the coating, but before all of the coating is consumed. 3. Post ablative failure. The steel sample reaches its failure temperature after all of the coating has been consumed.

21 Ablative Coating Failure Time / s Coating Thermal Conductivity = 0.5 Wm -1 K -1 T abl = T fail Post-Ablative Failure Ablative Failure Ablative Failure Ablative Failure Ablative Failure Ablative Failure Inductive Failure Inductive Failure Inductive Failure Initial Coating Thickness 20 mm 15 mm 10 mm 5 mm 1 mm Ablation Temperature /K Numerical results for varying ablative thicknesses The conduction heat transfer coefficient is a critical parameter. Failure time does not always increase with ablation temperature. When λ 50 Wm -2 K -1, failure time increases to a maximum when the ablation temperature corresponds to the failure temperature and then decreases. When λ 50 Wm -2 K -1, failure time continues to increase for a finite range of ablation temperature. This is because the coating is acting both as a sacrificial barrier and a thermally insulating layer. The insulating layer delays diffusion of heat to the substrate thereby increasing the overall thermal resistance despite the fact that failure occurs before all of the coating is consumed.

22 Conclusion For insulators, the most important thermal parameters are the conduction heat transfer coefficient and the thermal diffusion time scale. The effectiveness of porous thermal insulators decreases with temperature and is strongly dependent on pore shape (and distribution). Pore shape (and distribution) should be such that the complimentary thermal conductivity λ / (1 ϕ) is a decreasing function of ϕ. For a given porosity, a char or insulator with many small pores is better than few large pores. Both heat sink and reactive coatings control the local temperature by an endothermic degradation reaction. The characteristic kinetic temperature of the reaction is therefore important for performance. For both heat sink and ablative coatings, the total coating reactivity surface density E = lρ H is a critical parameter. The time for which the substrate temperature is controlled is an increasing function of E.