Theoretical analysis of the surface temperature regulation of an infrared false target subjected to periodical ambient conditions

Shi-min LI,Hong YE*,Qi-zhao LIN

Department of Thermal Science and Energy Engineering,University of Science and Technology of China,Hefei 230027,China

Available online 12 May 2016

Theoretical analysis of the surface temperature regulation of an infrared false target subjected to periodical ambient conditions

Shi-min LI,Hong YE*,Qi-zhao LIN

Department of Thermal Science and Energy Engineering,University of Science and Technology of China,Hefei 230027,China

Available online 12 May 2016

Infrared false target is an important mean to induce the infrared-guided weapons,and the key issue is how to keep the surface temperature of the infrared false target to be the same as that of the object to be protected.One-dimensional heat transfer models of a metal plate and imitative material were established to explore the influences of the thermophysical properties of imitative material on the surface temperature difference (STD)between the metal plate and imitative material which were subjected to periodical ambient conditions.It is elucidated that the STD is determined by the imitative material’s dimensionless thickness)and the thermal inertia(Pim) .Whenis above 1.0,the STD is invariable as long asPimis a constant.And if the dimensionless thickness of metal plateis also larger than 1.0,the STD approaches to zero as long asis the same as the thermal inertia of metal plate(Pm).Whenis between 0.08 and 1,the STD varies irregularly withHowever,ifis also in the range of 0.08–1,the STD approaches to zero on condition thatis below 0.08,the STD is unchanged whenis a constant.And ifis also less than 0.08,the STD approaches to zero as long as.Furthermore,an applicationoriented discussion indicates that the imitative material can be both light and thin via the application of the phase change material with a preset STD because of its high specific heat capacity during the phase transition process.

?2016 China Ordnance Society.Production and hosting by Elsevier B.V.This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

Infrared false target;Surface temperature;Periodical ambient conditions;Thermal inertia;Dimensionless thickness

1.Introduction

The infrared detection technology has been widely explored in the military domain,such as infrared precise guidance, search and tracking.With its continuous development,the spatial resolution of the infrared detectors is getting higher [1,2],and the infrared image generation models are getting more accurate[3,4].Especially,along with the use of the human visual characteristics for detection,the infrared detection technology has achieved a remarkable development because the human vision has a selective attention property which is helpful to search the target from a complex background quickly and precisely[5,6].The infrared target detection based on visual attention can be sorted into two types.One is that the saliency map is composed of individual feature maps,some of which are extracted from input image[7],and the other is that the saliency map is obtained via the statistical information of natural scene[8].In other words,the infrared detection tends to be combined with the human vision image in the future,which induces the urgent requirement of the infrared defence of the object to be protected.As one of the effective defence technologies,the infrared false target has been extensively studied for decades, and the regulation of its surface temperature,the most important factor in the infrared defence,is increasingly stringent. From the aforementioned relevant introduction about infrared detection,it can be expected that the only way to adapt to the future infrared defence challenges is to develop a false target having the same surface temperature and the same surface radiative properties(solar absorptance and infrared emissivity) as the object to be protected.

It is of vital importance to understand how the thermophysical properties of false target influence the surface temperature difference(STD)between it and the object to be protected. Therefore,the relationship between the STD and the thermophysical property difference between the object to be protected and the false target was discussed subjected to the same periodical ambient conditions,and the rules on how to make the false target have the same surface temperature as theobject to be protected were proposed.Besides,from the perspective of the practical application,the advantages and disadvantages of the phase change material and the non-phase change material were discussed,and the specified properties of the imitative material to make the STD approach to zero were evaluated.

http://dx.doi.org/10.1016/j.dt.2016.04.003

2214-9147/?2016 China Ordnance Society.Production and hosting by Elsevier B.V.This is an open access article under the CC BY-NC-ND license(http:// creativecommons.org/licenses/by-nc-nd/4.0/).

2.Model

The object to be protected discussed here is reasonably assumed as a rectangular cabin,and the focus of exploration is the top cover of cabin which is the most important surface for the infrared defence.Because the top of the object to be protected is usually a metal plate,the goal of the work is to imitate a horizontal metal plate subjected to periodical ambient conditions.The one-dimensional heat transfer models of metal plate and imitative material,i.e.,the featured surfaces of the object to be protected and the false target,were established to explore the influence of the difference of their thermophysical properties on the STD under the same periodical ambient conditions.Their top surfaces are exposed to the ambient environment,and the adiabatic boundary conditions are applied to their bottom surfaces from a practical consideration,as shown in Fig.1.The possible application of metal plate and imitative material would be the surface cover of special equipment usually operating at high or low temperature(relative to the ambient temperature), which would form a strong thermal boundary condition for the bottoms of them.However,there is usually a thick thermal insulation layer around the equipment to make its operation stable.Considering the high-performance of thermal insulation layer,an adiabatic boundary condition over the bottoms of metal plate and imitative material can be a good approximation.

A one-dimensional heat transfer assumption is reasonable for both the metal plate and the imitative material,and their governing equations take the same form

Fig.1.Schematic diagram of metal plate and imitative material.

whereρ,cpandkare density,specific heat capacity and thermal conductivity,respectively.As shown in Fig.1,the boundary conditions of metal plate and imitative material are identical.Their top boundary conditions can be similarly expressed as and the bottom boundary conditions are both adiabatic.In Eq. (2),is the net heat flux into the top boundary,is the solar irradiation absorbed by the top surface,is the radiation heat flux between top surface and sky,andis the convection heat flux between top surface and air.is equal towhere αsrepresents the solar absorptance andGsolrepresents the solar irradiation.Qradis equal toεσwhereε,σ,Tsand Tskyrepresent infrared emissivity,Stefan–Boltzmann constant,top surface temperature and effective sky temperature.Qconvis equal to h( Ts-T∞),wherehrepresents the convection coefficient estimated byh=5. 7+6. 0V[9](V is the wind speed),and T∞r(nóng)epresents the temperature of air flow.The correlation used here for computing convection coefficient is selected according to the recommendation of a survey of wind convection coefficient correlations in Ref.9 which is commonly used to calculate the convection coefficient over a flat plate by taking both the natural and force convections into account.And its reliability has been commonly accepted.

To develop the false target which has the same infrared characteristics as the metal plate,the radiative properties of metal plate and imitative material,i.e.,αsandε,are set to be the same,which can be realized by the same coating.The contact resistance between the coating and the metal plate or the imitative material can both be neglected,and the coating can be very thin so that its influence on the surface temperature can also be neglected.The material properties are assumed to be constant.This assumption was adopted because the metal plate and the imitative material are both not specified,and there are no general variation laws of their properties with temperature so that the variation of properties with temperature is difficult to be considered.Hence,we did not consider the temperature dependencies of the related thermal properties of metal plate and imitative material.However,the results below can be taken as a reasonable approximation.

3.Results and discussion

3.1.Theoretical analysis

Here we define a dimensionless independent variable

wherekim,ρim, andcp,imrepresent thermal conductivity, density,and specific heat capacity,respectively,andrepresents the dimensionless thickness of imitative material and can be given aswhere dimis the thickness ofimitativematerial.IntroducingthethermalinertiaEq.(4)can be expressed as

where Pimrepresents the thermal inertia of imitative material. From Eq.(5),the imitative material’s temperature distribution T(η,t)is related to its thermal inertia(Pim)and dimensionless variable(η)under given periodical ambient conditions.

When the dimensionless thicknessis larger than 1.0, the imitative material can be treated as a semi-infinite solid so that its temperature gradient approaches to zero forη≥1,and its governing equation and boundary conditions form as

in the range of 0≤η≤1.When the lumped capacitance method can be used as a reasonable approximation for the imitative material,its governing equation and boundary conditions can be expressed as

Substituting the dimensionless thicknessfordimandintroducingtheconceptofthethermalinertia,we obtain that

To use Eq.(8)in the calculation of the temperature of imitative material,the criterion about whether the lumped capacitance method can be used as a reasonable approximation for the imitative material must be given.If the top boundary condition is exclusively the convection boundary,the criterion can be expressed as[10]

However,Eq.(9)is not suitable for the imitative material under the complex boundary(convection,solar irradiation radiation,and heat flux between the top surface and the sky).

Considering that the governing equation and boundary conditions of metal plate are the same as those of imitative material,it can be found from Eq.(6)that,when the dimensionless thickness of imitative material is larger than 1.0,the STD is invariable as long as the thermal inertia of imitative material is a constant.Moreover,if the dimensionless thickness of metal plate is also larger than 1.0,the STD approaches to zero as long as the thermal inertia of imitative material is the same as that of metal plate.When the dimensionless thickness of imitative material is less than 1.0,the STD approaches to zero if the thermal inertias and dimensionless thicknesses of metal plate and imitative material are identical.Specially,it can found from Eq.(8)that,when the lumped capacitance method can be used as a reasonable approximation for imitative material,the STD is invariable as long as the product of thermal inertia and dimensionless thickness of imitative material is a constant,i.e.,its volumetric heat capacity is a constant.Besides,if the lumped capacitance method can be also applied to the metal plate,the STD approaches to zero as long as the product of thermal inertia and dimensionless thickness of imitative material is the same as that of the metal plate,i.e.,the product of volumetric heat capacity and thickness of imitative material is the same as those of metal plate.It is worthy to note that the findings from the theoretical analysis hold for arbitrary periodical ambient condition and have no geographical restrictions.

3.2.Numerical verification

To further verify the above findings,anAISI 304#steel plate is taken as an example to calculate the influences of the imitative material’s thermal inertia and dimensionless thickness on the STD when subjected to the same periodical ambient conditions.The thickness of the steel plate is set as 0.05 m.

The material properties used in the calculation are assumed to be constant and given in Table 1.Noticing that the good predictions of steel plate temperature have been obtained based on constant properties[12,13]due to the relative small range of temperature variation,this assumption can be reasonable.Recognizing that the research is in the field of the effective infrared camouflage,the radiative properties,αsandε,of steel plate and imitative material are set as 0.768 and 0.9,respectively, which are the same as those of the green plants[11]and can be obtained by the green coating.The climate data used are the typical meteorological year data offered by the Chinese Architecture-specific Meteorological Data Sets for Thermal Environment Analysis.

Fig.2 shows the daily maximum surface temperature difference(DMSTD)between the metal plate and the imitative material varying with the thermal inertia and dimensionless thickness of imitative material under a typical daily periodical ambient condition of Nanjing.The typical meteorological day isJuly 20 in Nanjing where daily average temperature is the highest within the typical meteorological year.Fig.2(a–c) exhibits the numerical results where the thicknesses of imitative material are 0.01,0.05 and 0.10 m,respectively.Interestingly, the points of the same DMSTD with different combination of thermal inertia and dimensionless thickness of imitative material form the regular lines,the trends of which are similar and independent of the thickness of imitative material.It can be found from Fig.2 that,when the dimensionless thickness of imitative material is larger than 1.0,the STD is invariable as long as the thermal inertia of imitative material is a constant, which has also been explained in Section 3.1.When the lumped capacitance method can be used as a reasonable approximation for the imitative material,as shown in Fig.2,the STD is invariable as long as the thermal inertia and dimensionless thickness of imitative material follow that

Table 1 The material properties[10,11].

Fig.2.The DMSTD varying with the imitative material’s thermal inertia and thickness in Nanjing.The thicknesses of imitative material:(a)0.01 m,(b) 0.05 m and(c)0.10 m.

or

which is consistent with the rules presented in Section 3.1. Especially,because the lumped capacitance method can be also applied to the steel plate,the STD approaches to zero as long as the product of the thermal inertia and the dimensionless thickness of imitative material is the same as that of the steel plate.Thus,the above findings are suitable for the daily periodical ambient condition.

In Section 3.1,it is proposed that Eq.(9)cannot be treated as the criterion about whether the lumped capacitance method can be used as a reasonable approximation for the imitative material under complex boundary.Here,we suggest a new criterion for the object with complex boundary according to the results in Fig.2.When the dimensionless thickness of imitative material is less than 0.08,the lumped capacitance method can be approximately applied to the imitative material.

The annual numerical results are also given to further verify that the above findings are adaptive for arbitrary periodical ambient condition.The annual maximum surface temperature differences(AMSTDs)between steel plate and imitative material varying with the thermal inertia and dimensionless thickness of imitative material are shown in Fig.3,which were subjected to the typical annual periodical ambient conditions of Mohe(Heilongjiang Province,boreal),Nanjing(Jiangsu Province,subtropical)and Guangzhou(Guangdong Province,tropical),respectively.The thicknesses of steel plate and imitative material are both 0.05 m.It can be observed that the trends of the temperature curves with the same AMSTD in Fig.3 are similar to those in Fig.2,proving that the findings from the theoretical analysis are adaptive for arbitrary periodical ambient condition and have no geographical restrictions.

For the sake of clarity,the general laws about the relationship between the STD and the thermophysical property difference between the imitative material and the object to be protected are summarized and listed in Table 2.

3.3.Consideration of practical applications

According to the analysis above,when the thermal inertia of imitative material is a constant,the STD is invariable as long as the dimensionless thickness of imitative material is also a constant.Thus,to imitate an object having specified thermophysical properties,the material with higher volumetricheat capacity possesses the potential to make the imitative material or the false target thinner for a preset STD.Meanwhile, the false target can be lighter with the increase in the material’s specific heat capacity.

Fig.3.The AMSTD varying with the imitative material’s thermal inertia and thickness under the typical annual periodical ambient condition:(a)Mohe, (b)Nanjing and(c)Guangzhou.The thickness of the imitative material is 0.05 m.

Table 2 The laws for imitation of metal plate.

Here we exhibit the practical applications of four materials: paraffin(a typical PCM),high density concrete which has a high volumetric heat capacity and a high density[14],natural rubber,and acrylonitrile–butadiene–styrene(ABS)with high specific heat capacity[14].The thickness of steel is 0.05 m,and the radiative properties,αsandε,of steel plate and imitative material are set as 0.768 and 0.9.Because the necessary condition to make the STD approach to zero is that the thermal inertias of false target and object to be protected are the same, we expected that the thermal inertias of the four materials can be improved to be the same as that of the steel plate,as shown in Table 3.The expected thermal inertia can be obtained by embedding a certain mass ratio of copper sheets into the four materials[8].The thermal conductivity of a composite can be expressed as[15]

where?is the volume fraction of copper sheet;ke,kbmand kcpare the thermal conductivities of composite,base material and copper,respectively.Meanwhile,the volumetric heat capacity of the composite can be calculated[10]

Table 3 The material properties for consideration of practical application[10,14].

Fig.4.The DMSTD varying with the imitative material’s component and thickness.

From Eq.(14),the specified volume fractions of copper sheets to make the thermal inertias of the composites be the same as that of the steel plate can be calculated and shown in Table 3.

To explore the advantages and disadvantages of the four materials in the practical application,the influence of imitative material’s thickness on the STD subjected to the typical daily periodical ambient condition of Nanjing is calculated,as shown in Fig.4.The specified thicknesses of the four materials to make the STD approach to zero and the corresponding areal densities are listed in Table 4.The results in Fig.4 and Table 4 indicate that the specified thickness of paraffin is the thinnest and the corresponding areal density is also the smallest.Except for the paraffin,the application of the high density concrete can make the specified thickness much thinner than that of the natural rubber and theABS,but the corresponding areal density of the high density concrete is much higher than those of the natural rubber and the ABS because the higher volumetric heat capacity of the high density concrete results from its high density.Thus,considering the practical application,the phase change materials(PCMs)have great potential for the false target because of their higher specific and volumetric heat capacities.The results in Table 4 are adaptive for arbitrary periodical ambient condition and have no geographical restrictions.

Table 4 The specified thicknesses of four materials to make the STD approach to zero and the corresponding areal densities

However,it must be noticed that the discussions above are based on that the temperature fluctuation of paraffin is in the range of its phase transition.In other words,the paraffin is always in its phase changing region in the practical application. That may be a reasonable assumption for several days,in which the surface temperature fluctuation of imitative material is smaller than the phase transition range of PCMs.When the imitative material is used subjected to the annual ambient, the results in Table 4 are not suitable and the advantage of the PCM for imitation may disappear.Nevertheless,if the composite PCM,which has a wide phase transition range compared to the annual temperature fluctuation of steel plate, can be made of a series of PCMs with different phase transition temperatures in the future,the lighter and thinner imitative material will be obtained.Thus,the application of phase change materials can lead to the lighter and thinner false target possessing the same surface temperature as the object to be protected.

4.Conclusions

The influences of the imitative material’s thermophysical properties on the STD were analyzed when subjected to periodical ambient conditions,and the key factors were found to be its dimensionless thicknessand thermal inertia(Pim). Whenis more than 1.0,the STD is invariable as long asPimis a constant.And if the dimensionless thickness of metal plateis also larger than 1.0,the STD approaches to zero as long asPimis the same as the thermal inertia of metal plate.Whenis between 0.08 and 1,the STD varies irregularly with Pimand.However,ifis also in the range of 0.08–1,the STD approaches to zero forWhenis below 0.08,the STD is unchanged whenis a constant. And ifis also smaller than 0.08,the STD approaches to zero as long asBesides,the application of PCMs leads to a lighter and thinner false target for a preset STD.

Acknowledgment

The work was funded by the National Natural Science Foundation of China(No.51576188).

References

[1]Kim S.Target attribute-based false alarm rejection in small infrared target detection.Proc SPIE 2012;8537.

[2]Kim S.Analysis of small infrared target features and learning-based false detection removal for infrared search and track.Pattern Anal Appl 2014;17:883–900.

[3]Duong N,Wegener M.Validation of the sensorvision thermal emission model.DTIC Document.2001.

[4]Li CC,Si JN,Abousleman GP.Low false alarm target detection and tracking within strong clutters in outdoor infrared videos.Opt Eng 2010;49.

[5]Wang X,Lv GF,Xu LZ.Infrared dim target detection based on visual attention.Infrared Phys Technol 2012;55:513–21.

[6]Kim W,Kim C.Spatiotemporal saliency detection using textural contrast and its applications.IEEE Trans Circuits Syst Video Technol 2014;24:646–59.

[7]Itti L,Koch C,Niebur E.A model of saliency-based visual attention for rapid scene analysis.IEEE Trans Pattern Anal Mach Intell 1998; 20:1254–9.

[8]Hou M,Zi B,Xie C.Occurrence and removal form of tin in Furong polymetallic ore field of Qitianling,Hunan Province.Geol Miner Resour South China 2007;1:001.

[9]Palyvos JA.A survey of wind convection coefficient correlations for building envelope energy systems’modeling.Appl Therm Eng 2008; 28:801–8.

[10]Incropera FP.Fundamentals of heat and mass transfer.USA:John Wiley &Sons;2011.

[11]Ye H,Yuan Z,Zhang SQ.The heat and mass transfer analysis of a leaf. J Bionic Eng 2013;10:170–6.

[12]Hong Y,Jiang L.Theoretical investigation and experimental verification of passive simulation of metal plate infrared thermal characteristics with that of PCM.J China Ordnance 2007;3.

[13]Marcos D,Pino FJ,Bordons C,Guerra JJ.The development and validation of a thermal model for the cabin of a vehicle.Appl Therm Eng 2014;66:646–56.

[14]Fernandez AI,Martinez M,Segarra M,Martorell I,Cabeza LF.Selection of materials with potential in sensible thermal energy storage.Sol Energy Mater Sol Cells 2010;94:1723–9.

[15]Carson JK,Lovatt SJ,Tanner DJ,Cleland AC.Thermal conductivity bounds for isotropic,porous materials.Int J Heat Mass Transf 2005; 48:2150–8.

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12 March 2016;revised 22 April 2016;accepted 25 April 2016