Numerical study on similarity of plume infrared radiation between reduced-scale solid rocket motors

Zhang Xiaoying,Chen Huandong

aSino-French Institute of Nuclear Engineering and Technology,Sun Yat-sen University,Zhuhai 519082,China

bSchool of Electricity,South China University of Technology,Guangzhou 510640,China

Numerical study on similarity of plume infrared radiation between reduced-scale solid rocket motors

Zhang Xiaoyinga,*,Chen Huandongb

aSino-French Institute of Nuclear Engineering and Technology,Sun Yat-sen University,Zhuhai 519082,China

bSchool of Electricity,South China University of Technology,Guangzhou 510640,China

This study seeks to determine the similarities in plume radiation between reduced and full-scale solid rocket models in ground test conditions through investigation of flow and radiation for a series of scale ratios ranging from 0.1 to 1.The radiative transfer equation(RTE)considering gas and particle radiation in a non-uniform plume has been adopted and solved by the finite volume method(FVM)to compute the three dimensional,spectral and directional radiation of a plume in the infrared waveband 2–6 μm.Conditions at wavelengths 2.7 μm and 4.3 μm are discussed in detail,and ratios of plume radiation for reduced-scale through full-scale models are examined.This work shows that,with increasing scale ratio of a computed rocket motor,area of the hightemperature core increases as a 2 power function of the scale ratio,and the radiation intensity of the plume increases with 2–2.5 power of the scale ratio.The infrared radiation of plume gases shows a strong spectral dependency,while that of Al2O3particles shows spectral continuity of gray media.Spectral radiation intensity of a computed solid rocket plume’s high temperature core increases significantly in peak radiation spectra of plume gases CO and CO2.Al2O3particles are the major radiation component in a rocket plume.There is good similarity between contours of plume spectral radiance from different scale models of computed rockets,and there are two peak spectra of radiation intensity at wavebands 2.7–3.0 μm and 4.2–4.6 μm.Directed radiation intensity of the entire plume volume will rise with increasing elevation angle.

1.Introduction

The plume radiation of solid rockets is an important tracking target in strategic attack and is an essential problem in thermal protection design of rocket motors.Most published experimental research of rocket plume radiation is conducted with reduced-scale models.The similarity in test results between reduced-scale and full-sized model is a key consideration for applying them to thermal analysis of actual rocket motors.

Given the complexity of the plumes from solid rocket motors,plume radiation varies significantly in spectrum and direction,thus causing difficulty in fully investigating characteristics of the similarity problem through experimental study.Ground testing usually needs to be per formed in a huge enclosed area to avoid environment influences.1Also,to establish similarity rules between the plume radiation of a reducedscale rocket model and a full-sized rocket motor,experiments with multiple motor sizes of similar geometry must be conducted.From the perspectives of technique and economy,experimental methods are very difficult to per form,so related research in this area has not yet been reported.

Several works on the theoretical aspects of this study havefocused on the similarity problem of gas and particle radiation.Forward peak-light scattering and the integral similarity method(aka the Delta-M method),which analyzes the truncation error in the Legendre progression of high-polarity scattering phasefunctions and forward-scattering peak cones,have been studied.2Change in the self-similarity of transmittance depth and radiation energy in a cool medium,with time,boundary temperature,and medium density have been investigated.3Duracz and Mccormick focused on two similarity parameters:the ratio of radiation intensity and irradiance,and their relation to single-scattering albedo,and dissymmetry coefficient in optically thick media.4Similarity of the forward scattering portion and number of incident energy scattering directions in the radiation transmission equation of anisotropic scattering media have been studied by Mitrescu and Stephens.5Considering temperature and radiation of jet nozzles,Bril et al.studied similarities of the near-nozzle temperature and concentration fields,as well as the non-dimensional radiant intensity determined by the outlet parameters,radiation wavelength, and the temperature gradient of absorptivity.6

The plume radiation of a solid rocket motor is a multidimensional problem of high-order calculus that involves the radiation of a strong spectral sensitive gas and scattering of multiple groups of Al2O3particles.The radiative gases in the plume consist of H2O,CO2,CO,HCl and OH,with each gas having thousands of spectral lines in the infrared waveband.7The spectral properties of gases are always solved with the waveband model8,9or the weighted-sum-of -gray-gases model.10Considering radiation of Al2O3particles,particle concentration and size have important effects on spectral properties of particles11,which are commonly solved with the Mie theory.12,13In calculating the 3D spectral radiance of an abs orptive/emissive/scattering medium,the Monte Carlo methods,14streaming model,15discrete-ordinate method,16and finite volume methods(FVM)17have been widely adopted.As a better compromise of computational accuracy and execution time,the FVM is of ten suggested to solve the 3D spectral radiance of an inhomogeneous absorption–emission–scattering medium with a divergent form.

As similarity of plume infrared radiation between reducedscale and full-sized rocket motors is still not fully studied,this work aims to contribute to the numerical research on similarity of plume radiation with a group of scaled rocket motors of similar geometry and flow data.This study adopts the geometric and operational parameters of Trident D5 rocket motor ground testing.A CFD code is used to compute the axissymmetric flow parameter inside the nozzle and the plume in a series of scaled model rockets with the same total temperature and pressure at the rocket nozzle inlet.The weightedsum-of -gray-gases model is adopted to compute the spectral absorptivity of gas molecules H2O,CO2,CO,HCl and OH,and the Mie scattering theory is used to compute the spectral absorption/scattering coefficient and phasefunction of Al2O3particles of eight diameters.Finally,the FVM is used to solve the RTE equation,and corresponding code is developed to compute the 3D spectral radiance of a plume in infrared waveband 2–6 μm.Also,the directed radiation intensity from the plume’s hot core with gas temperature exceeding 500 K is calculated by integrating radiance on plume peripheral surface in one direction,and the ratio of radiation intensity for the reduced-scale plume to that of full-sized rocket motors is to be derived.

2.Calculation of plumeflow field

To obtain flow parameters of the rocket motor plume and that of reduced-scale models,the Chemical Equilibrium and Application(CEA)program is adopted to compute the compound chemical equilibrium components of propellants and the inlet flow parameters.A CFD code is then used to per form simulation of flow parameters in the nozzle and of the plume.The time-marchingmethod andadvection upstream splitting method(AUSM)spatial discretization schemes are chosen for a numerical solution.Blending of the plume and atmosphere,and the resulting secondary combustion of H2,CO and HCl will be computed with a finite rate chemistry model of 12 components and 17 reactions,18where the k–ε turbulence model is adopted.To simulate temperature and size distribution of Al2O3particles,the Lagrangian trajectory model of particles is used to compute the exchange of energy and momentum between particles and gases,while the self combustion,evaporation,collision and polymerization of particles is neglected.Distribution of particle diameters is determined based on the Braithwaite size distribution function.19

The Trident D5 solid rocket uses a composite propellant that contains Al as 10%of its weight.In calculating plumeflow data of thefull-scale motor and reduced-scale models,the same input data are used:pressure is 9 MPa,and temperature is 3750 K.Thefull-scale rocket motor has a nozzle of 1.55 m length,0.35 m throat diameter and 9.7 ratio of area expansion in ground testing.The reduced-scale model has the same geometry,but with a reduced diameter and length.

Flow field of plumes for thefull-sized Trident D5rocket motor and models with scale ratios between 0.1 and 0.9 have been computed.Fig.1 shows contours of flow data for thefull sized motor,including gas temperature(tg),pressure(pg)and volumefractions of H2O,CO2and CO.Concentration(Amp)and temperature(tp)of one group of Al2O3particles with diameters(dp)of 8 μm are also represented.Contours of flow data for the 9 reduced-scale models are highly similar with that of thefull-sized motor in Fig.1,only varying in plume size.The ratio between the length or radius of each plume’s hot core at different scales is almost equal to the ratio of geometric size.The high temperature area is separately distributed in the plume,and a secondary high temperature area can be easily found downstream of the first at the nozzle outlet,where volumefractions of H2O and CO2are very high because of secondary combustion.The volumefraction of CO is consistently high in central areas of the plume.According to volumefraction,major radiative gases of the plume are CO,H2O and CO2;Volumefractions of HCl and OH are very small.In viewing temperature and concentration of Al2O3particles with 8 μm diameter,it is found that particle temperature remains consistently high in the center of a plume,while the concentration is higher in outer areas.As less gas friction and resistance acts on particles in outer areas with small volumefractions,Al2O3particles spread to those areas more easily.

Fig.1 Flow data of plumefrom thefull-sized rocket motor.

3.Computation scheme of plume radiation

3.1.Calculation model of plume 3D directed spectral radiance

According to published research on rocket plume radiation,20a directed spectral radiance i′λ（S）travelling along the path dS in non-uniform absorption/emission/scattering media will have thefollowing increment:where λ is the wavelength;κnand σ are the absorption coefficient and scattering coefficient,respectively; Φ（S，S′）is the scattering phasefunction;ω′is the solid angle;is the radiance of blackbody;S′is scattering direction vector.

The first term at right hand of Eq.(1)is radiance attenuation by absorption and scattering of gases and particles;the second term is radiance increased by emission of gases and particles;the third term is radiance increased by particle scattering from radiance of other directions.To integrate Eq.(1)with FVM,a cylindrical control volume is usually chosen for symmetric cases.But,it is found that numerical convergence for a coefficient matrix of the integrated equations is very poor.Area differences exist between the two radial oppositefaces of the cylindrical control volume,diminishing the superiority of a diagonal term in the coefficient matrix.On the other hand,a cuboid control volume is a better choice,avoiding that problem while being used to derive an integral RTE with improved convergence.There fore,the calculation domain is expanded into a large cuboid that contains the entire plume volume.Size of the calculation domain is determined by the length and the outer radius of plume hot volume at the end of the CFD domain.The calculation domain of plume radiance is then subdivided into orthogonal small cuboid control volumes as shown in Fig.2.W，E，N，S，R，F，P are the symbols of control volume whereas w，e，n，s，r，f are the surface symbols of control volume.The number of control volumes in the calculation domain is Nx×Ny×Nz=80×40×40.Each control volume in the plume is bound by six neighboring control volumes.

Radiance of each control volume P is toward all directions in the radiation sphere that contains P.To discretize radiance directions,the whole sphere is equally divided into series of solid angles.Each solid angle is defined by two angles,elevation angle θ and azimuth angle φ.The elevation angle θ is included between the radiation direction and the plume central axis.The azimuth angle φ is included between the projection of radiance direction on plume cross section and the polar axis z.The numbers for discretized solid angles are Nθ×Nφ=19×37.

In integrating Eq.(1)on volume P and applying Gaussian integration methods,integration on volume P can be transferred into integration on its six bounding faces.The integral radiation equation can be derived as Eq.(2),which connects the directed spectral radiance of Pat direction S with radiance of its neighboring control volumes in that direction.Note that all computation in this work is based on wavelength λ; for brevity,the subscript ‘λ” will be deleted in following text.

Fig.2 Cuboid control volumes in calculation domain.

Fig.3 Radiance rotation rule of symmetric control volumes.

Eq.(2)is a nonlinear equation as the source radiancein particle scattering is determined by radiance of P in all other directions.The symbolsrepresent corresponding radiances of neighboring control volumes;Δω and Δω′are solid angle of computed radiance and solid angle of incident,respectively; ΔAw，ΔAe，ΔAn，ΔAs，ΔAr，ΔAfare surface areas of w，e，n，s，r，f,respectively;Similarly,Dkare the cosine of solid angle in surface normalof w，e，n，s，r，f;and nkis the unit normal vector;ΔVPis the volume of control volume P.So,Eq.(2)must be coupled and solved on all control volumes and all discrete directions.Considering the symmetric characteristics of plumeflow and radiance,only equations of control volumes across the symmetry plane x–z are coupled and solved.The matrix dimensions are still enormous even in that case,making the equations unable to be solved with any iteration algorithm in one loop.A cyclic iteration algorithm with iterative modification bPhas been proposed in this study.In each cycle,bPis first calculated with radiance computed from the last cycle.Then a Gaussian iteration algorithm will be used to solve the radiance equations and compute a new radiance group for each control volume.The cyclic iteration will continue on until a convergence is met.

According to symmetry of plumeflow data and radiance,the control volumes apart from the x–z plane have the same magnitude and distribution those on the x–z plane,but orientation for radiance spheres of the other control volumes are different.Radiance of two control volumes in same axial and radial position,but with different circumferential position,would satisfy a rotation rule of radiance vectors.As shown in Fig.3,if the circumferential angle between the two control volumes,M and N in same axial and radial position is θ,radianceof M at direction S1has equal value to radianceof N at direction S2,where S2is formed by rotating S1by θ clockwise in the cross section y–z plane;r1and r2are the radius of different center of circle.

3.2.Calculation of radiative properties of plume

The spectral absorption coefficient κνof each gas composition is calculated with data of spectral lines in the 2004 edition of the HITRAN molecular spectroscopic database.21HITRAN 2004 consists of detailed data that serves as input for radiative transfer calculation codes,to include:individual line parameters for microwaves through visible spectra of molecules in the gas phase;absorption cross-sections for molecules having dense spectral features.The pressure broadening of spectral lines with normalized line shape is given as following function:

where ν is wave number; νηη′ is spectral line transition frequency;γ is the half width;δ represents the pressure induced line shift;T and p are the temperature and pressure of gases,respectively;prefis the reference pressure.

The monochromatic absorption coefficient κ（ν，T，p）((mol·cm-2)-1)at wave number ν(cm-1)due to this transition is then given by

where S（T）is the intensity of spectral line.

According to the weighted-sum-of -grey-gases(WSGG)model,spectral absorption coefficient of the mixing gases is the sum of weighted absorption coefficients of all gases according to volumefractions Fn.There fore,the spectral absorption coefficient for plume gases can be calculated as

For calculation of radiative properties of particles,particle diameter and the complex refractive index m=n+ik are needed.According to CFD simulation result of flow fields,8 groups of Al2O3particle diameter are considered:4,6,8,10,12,14,16 and 18 μm.Reed and Calia had proposed formulas for the complex refractive indices of Al2O3,which will be used in this work.13

The radiative properties of a single Al2O3particle,like scattering cross section Cs,attenuation cross section Ce,scattering factor Qs,and attenuation factor Qeare computed based on Mie scattering theory.11Products of Qs,Qewith cross section area of a particle will give scattering coefficient κeλand attenuation coefficient κeλof the particle.

where anand bnare scattering coefficients in Mie scattering and Χ is the particle size parameter.

where Ψnand ξnare Bessel functions which are infinite series,and can be computed with recurrence scheme; Ψ′nand ξ′nare the derivatives of Ψnand ξn.Computation of the scattering phase function Φλ（θ）of a single Al2O3particle is given as

where g1and g2are amplitude functions which are also computed with an,bnand scattering angular functions.

To calculate radiative properties of Al2O3particle clouds,a separate and independent effect is assumed.Then,the total radiative properties of particle clouds can be computed as the numerical summation of all particles.

3.3.Radiation intensity of solid rocket plume

In computing radiative heat transfer from plume to the rocket motor base,or evaluating radiation from the entire plume volume,radiation intensity is usually concerned.Radiation intensity in one direction is the integral directed radiance on the whole bounding surface of a plume’s hot core.If focused on the plume radiation of a certain waveband,like peak spectrum of gas radiation,numerical integration is also need on the wavelength.

4.Results and discussion

4.1.Verification case

For verification of the theoretical model and code for plume radiation of solid rocket motors proposed in this work,plume radiance of the three stage rocket motor Star-27 at 114 km is first computed and compared with corresponding results of Burt and Boyd.22The Monte Carlo method has been used to compute the global radiance of the plume in 2.2 μm in work of Burt and Boyd.Emissivity of high temperature particles was computed with an empirical formula of Reed and Calia.12

where ελis the emissivity and Rpis the radius of particles.

The radiative properties of gases were computed with an ellipse statistical Bhatnagar–Gross–Krook model.The calculation results from the work of Burt and Boyd22and of this code.are shown in Figs.4 and 5,respectively.By comparing the two figures,it’s found that values of plume radiance in this work agree well with that of Burt and Boyd;the evolutionary characteristics of plume radiance in length and radius of the two are very similar.

Fig.4 Calculated radiance with Monte-Carlo method by Burt and Boyd.22

Fig.5 Global radiance computed with code of the work in this paper.

4.2.Plume radiation of reduced scaled rocket model and sililarity analysis

To fully investigate the similarity between plume radiation of reduced-scale rocket models and a full-sized solid rocket motor,radiance of the Trident D5 motors in wavelength 2–6 μm with scale ratios(r)from 0.1 to 1.0 are calculated,and effects of gases and Al2O3particles have been compared.The radiance contours at normal direction to the plume axis in 2.7 μm and 4.2 μm are shown in Figs.6 and 7,respectively.Sub-figures in the left column are results in cases considering sole gas radiation,and those in the right column are results considering gas and particle radiation.

The following can be found from Fig.6:With increasing model rocket size,length and radius of area with high plume radiance increase with almost the same geometric ratio.Shapes of radiance contours for different scale ratios show good similarity of flow fields.However,value of radiance varies significantly for different scaled plumes,being higher for larger plumes.Plume radiance is not only determined by flow parameters,like temperature,molefraction of gas,and density of Al2O3particles,but also by optical thickness of the plume.A larger size plume with similar flow field undoubtedly has greater optical thickness,and so has a higher radiance.The central tail area of each plume has the highest radiance due to secondary combustion of CO and a bigger optical thickness of the cross section.Considering the radiation contribution of Al2O3particles,radiance of plumes will increase to about 2.5 times that of sole gas radiation.Compared with the smooth outer surface of the high light stripes in radiance contours of sole gas radiation,there are multi waves on the boundary of the high light stripe when considering gas and Al2O3particle radiation due to discontinuity in density of Al2O3particles in the plume.

To reflect on differences between plume radiance at 4.2 μm and 2.7 μm,Fig.7 only shows results of plumes from the fullsize rocket motor and a 0.5 scale model.Compared with Fig.6,it can be found that length of the high light stripe in the radiance contour of 4.2 μm is longer than that of 2.7 μm.The reason is that particle radiation decreases at 4.2 μm and gas radiation takes the leading role as this is the peak spectrum of CO2and CO radiation.Gas temperature and mole fraction of CO2and CO is high in the long central area at latter part of the plume.Another difference between radiance contours of the two wavelengths is that ratio of plume radiance forgas and particle radiation to that of sole gas radiation is only 1.7 at 4.2 μm,which is much smaller than the 2.5 at 2.7 μm.

To investigate similarity rules for the radiation intensity of entire plume volumes in different scales,ratios of radiation intensity between plumes from the full-size rocket motor and reduced scale-models in wavelengths 2.7 μm and 4.2 μm have been calculated and illustrated in Fig.8.The horizontal ordinate r in the figures means the scale ratio of rocket geometry,and the vertical ordinate I/I0means the ratio of a reduced scale plume’s radiation I intensity to that of the full-size plume.Results of investigation for θ= π/6,π/3,π/2,2π/3 and 5π/6,with φ = π/2 are indicated.The other three lines correspond to the 1.5,2.0 and 2.5 power functions of geometricscale ratios.It can be seen in Fig.8 that the ratio of radiation intensity I/I0increases with a higher growth rate than the 2 power of r for the two wavelengths at all the five elevation angles.Growth rules of I/I0for the five elevation angles vary significantly at wavelength 2.7 μm,and get close to the 2 power of r for θ is π/6,2π/3 and 5π/6,but are closer to the 2.5 power of r when θ is 5π/6 and π/2.Because radiation of Al2O3particles at 2.7 μm is very strong,effects of increasing optical thickness with increasing plume volume is most remarkable at directions with a larger θ,and is smaller at other directions.In wavelength 4.2 μm,growth rules of I/I0for the five elevation angles come close to the 2 power for scale ratio,and differences between growth rules of I/I0of the five elevation angles are much smaller than that in wavelength 2.7 μm.Radiation of Al2O3particles in 4.2 μm is comparatively smaller than that of CO and CO2.There is an upper limitation of optical thickness for gas radiation that increases with absorption coefficient of the gas.Gas radiation will increase with optical thickness ifits value is smaller than the upper limit,while remaining constant for a larger optical thickness.The upper limitation of optical thickness is smaller in wavelength 4.2 μm,which is even smaller than the optical thickness of the plume at all five directions.So growth rules of I/I0for different θ apparently doesnot change in wavelength 4.2 μm.

To investigate radiance variation with axial position on the outer surface of a plume’s hot core,the averaged area radiance in the normal direction of the plume axis for the full sized Trident D5 motor and four reduced-scale models at 2.7 μm and 4.2 μm wavelengths are shown in Fig.9.The horizontal ordinate X in Fig.9 means the non-dimensional axial ordinates,which is ratio of the axial coordinate with the length of the plume.Results both considering and ignoring particle radiation beside the gas radiation are presented.It’s shown that at 2.7 μm,averaged area radiance in the normal direction increases with X consistently in both cases for the five scaled plumes.At wavelength 4.2 μm,averaged area radiance in the normal direction also increases consistently with X for plumes when scale ratio r is 0.2 or 0.4 while showing vibration changes around the level of X when r is 0.6,0.8 or 1.0.As the radiation of particles assumes the main role in plume radiance at 2.7 μm,this grows with increasing cross section and optical thickness for a larger X in the plume.While radiation of CO2and CO have the main role in plume radiation at 4.2 μm with receded particle radiation,this only grows with increasing X and cross section for a small plume volume.Averaged area radiance of a plume will not increase with X when optical thickness of gases becomes higher than the upper limit value,resulting in vibration change in averaged area radiance around a level.

Fig.6 Plume radiance of reduce-scale and full-sized rocket motorsat normal direction in 2.7 μm.

Fig.7 Plume radiance at normal direction in 4.2 μm of reduced-scale and full-size rocket motors.

Fig.8 Ratio of radiation intensity in the reduced-scale and full-size rocket plumes.

Spectral radiation intensity of the entire plume volume at different directions is an important parameter for target identification,which is also computed in this work.Fig.10 shows variation of plume radiation intensity Iλwith θ at wavelengths 2.7 μm and 4.2 μm from the hot core of the full-sized plume.Results considering the radiation of sole gas and gas with particles are comparatively given.Three featured findings can be concluded from the figure.One is the parabolic curved distribution of radiation intensity with θ,which is caused by variation of projecting area on the outer surface of a plume’s hot core.The second finding is the quite different quotas of particle radiation in compound gas and particle radiation at 2.7 μm and 4.2 μm,which accounts for about 60%of compound radiation intensity at 2.7 μm,but only accounts for 10%at 4.2 μm.As the temperature of most Al2O3particles is higher than 2500 K,the peak radiation wavelength is 1.15 μm.Radiation of Al2O3particles decreases with increasing wavelength very quickly,making its quota much higher at 2.7 μm than 4.2 μm.The last finding is the slight asymmetry of radiation intensity in front hemisphere(θ ＞ π/2)and rear hemisphere(θ ＜ π/2).It is higher in front hemisphere,which is also caused by the differences of projected area on the surface of a plume’s hot core in front and rear hemispheres.

In viewing infrared spectral characteristics for plume radiation of the full-sized Trident D5 motor,the relationship of spectral radiation intensity with wavelength at direction θ = π/2 has been plotted in Fig.11;Results of both sole gas and gas with particles are given.There are two peak wavebands of radiation intensity,2.7–3.0 μm and 4.2–4.6 μm.The former waveband is a feature of the radiative spectrum of H2O,and the latter is that of CO2and CO.Aside from the two peak wavebands,spectral radiation intensity in 2–6 μm decreases with increasing wavelength.Since the Al2O3particles are the leading component of plume radiation in short wave infrared bands,radiation will decrease with wavelength in waveband.

5.Conclusions

Infrared radiation in 2–6 μm waveband for plumes of the fullsized Trident D5 motor and 9 reduced-size models with scale ratios from 0.1 to 0.9 have been computed in ground test conditions,and similarity rules of plume radiation have been investigated.Complete flow data inside the rocket motor and of the plume have been simulated with a CFD code under same inlet conditions.The 3D direction and spectral radiance of plumes have been computed with the developed FVM radiance code.

Fig.11 Spectral radiation intensity at plume θ = π/2 from full sized rocket motor.

Research shows that contours of plume radiance for rocket models of different scale ratios with comparable geometry and flow parameters are similar,but values of radiance for larger scale plumes are higher.The central tail part of a plume has the highest radiance in plume contours due to secondary combustion of CO.Radiation of Al2O3particles makes the radiance of plumes increase to about 2.5 times that of sole gas radiation at 2.7 μm,and 1.7 times at 4.2 μm.

Al2O3particles are the major radiation component in the rocket plume,having radiation much larger than gases at most wavelength in 2–6 μm.Ratios of plume radiation intensity between reduced-scale models and full-sized Trident D5 motor are higher than the 2 power of scale ratio,and becomes closer to the 2 power for θ = π/6,2π/3 and 5π/6,but closer to the 2.5 power for θ = π/3 and π/2.Averaged area radiance on plume surfaces consistently increase with axial length at wavelength 2.7 μm for the full-sized Trident D5 motor and reduced-size models,showing vibration changes around its level at wavelength 4.2 μm when r=0.6,0.8 and 1.0.Radiation intensity of the entire plume volume shows a parabolic curved distribution with elevation angle θ,which is slightly higher in thefront hemisphere.Spectral radiation intensity in 2–6 μm of the fullsized Trident D5 plume at normal direction decreases with wavelength,except in the two peak wavebands 2.7–3.0 μm and 4.2–4.6 μm where radiation intensity grows with radiation of CO and CO2.

Acknowledgements

This study was co-supported by the National Natural Science Foundation of China(Nos.51376065 and 51176052),and Guangdong Key Scientific Project(No.2013B010405004).

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Zhang Xiaoying received her B.S.,M.S.and Ph.D.degrees in thermal and power engineering from Beihang University in 1996,1999 and 2002 respectively.She then became a teacher at South China University of Technology from 2002 to 2014.She later transferred to work in the Sino-French Institute of Nuclear Engineering and Technology,Sun Yat-sen University.Her main research interest is the numerical simulation of infrared radiation for rocket plumes.

23 January 2015;revised 10 August 2015;accepted 11 May 2016

Available online 22 June 2016

Infrared radiation;

Plume;

Reduced-scale model;

Similarity;

Solid rocket motor

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E-mail address:zxiaoying@mail.sysu.edu.cn(X.Zhang).

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http://dx.doi.org/10.1016/j.cja.2016.06.005

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