IR radiation characteristics of rocket exhaust plumes under varying motor operating conditions

Qinglin NIU,Zhihong HE,Shikui DONG

School of Energy Science and Engineering,Harbin Institute of Technology,Harbin 150001,China

IR radiation characteristics of rocket exhaust plumes under varying motor operating conditions

Qinglin NIU,Zhihong HE,Shikui DONG*

School of Energy Science and Engineering,Harbin Institute of Technology,Harbin 150001,China

Available online 26 April 2017

*Corresponding author.

E-mail address:dongsk@hit.edu.cn(S.DONG).

Peer review under responsibility of Editorial Committee of CJA.

Production and hosting by Elsevier

http://dx.doi.org/10.1016/j.cja.2017.04.003

1000-9361©2017 Production and hosting by Elsevier Ltd.on behalf of Chinese Society of Aeronautics and Astronautics.This is an open access article under the CC BY-NC-ND license(http://creativecommons.org/licenses/by-nc-nd/4.0/).

The infrared(IR)irradiance signature from rocket motor exhaust plumes is closely related to motor type,propellant composition,burn time,rocket geometry,chamber parameters and flight conditions.In this paper,an infrared signature analysis tool(IRSAT)was developed to understand the spectral characteristics of exhaust plumes in detail.Through a finite volume technique,flow field properties were obtained through the solution of axisymmetric Navier-Stokes equations with the Reynolds-averaged approach.A refined 13-species,30-reaction chemistry scheme was used for combustion effects and ak-ε-Rtturbulence model for entrainment effects.Using flowfield properties as input data,the spectrum was integrated with a line of sight(LOS)method based on a single line group(SLG)model with Curtis-Godson approximation.The model correctly predicted spectral distribution in the wavelengths of 1.50–5.50 μm and had good agreement for its location with imaging spectrometer data.The IRSAT was then applied to discuss the effects of three operating conditions on IR signatures:(a)afterburning;(b)chamber pressure from ignition to cutoff;and(c)minor changes in the ratio of hydroxyl-terminated polybutadiene(HTPB)binder to ammonium perchlorate(AP)oxidizer in propellant.Results show that afterburning effects can increase the size and shape of radiance images with enhancement of radiation intensity up to 40%.Also,the total IR irradiance in different bands can be characterized by a non-dimensional chamber pressure trace in which the maximum discrepancy is less than 13%during ignition and engine cutoff.An increase of chamber pressure can lead to more distinct diamonds,whose distance intervals are extended,and the position of the first diamond moving backwards.In addition,an increase in HTPB/AP causes a significant jump in spectral intensity.The incremental rates of radiance intensity integrated in each band are linear with the increase of HTPB,and the growth rates of radiance intensities in some bands reach up to 50%as HTPB weight increases by 3%.

©2017 Production and hosting by Elsevier Ltd.on behalf of Chinese Society of Aeronautics and Astronautics.This is an open access article under the CC BY-NC-ND license(http://creativecommons.org/licenses/by-nc-nd/4.0/).

Afterburning exhaust plume;

Chemical reaction;

Ignition and cutoff;

Infrared radiation;

Solid rocket motor;

Propellant mixture ratio

1.Introduction

Rocket motor exhaust plumes are a dominant source of infrared radiation signatures in flight vehicles.In rocket motors,fuel-rich gases generated during in-chamber propellant combustion exit a nozzle and then interact with ambient air.Some oxygen is thus entrained into the plume,and the afterburning reaction constantly occurs in the mixing layer,which can translate into a great increase in temperature and radiation intensity for the plume.1In a specif i ed vibrational mode,the IR signature of plumes contain distinct spectral information from different radiating species,especially H2O in 2.7 μm region and CO2in 4.3 μm band.These two bands are the principal source of atmospheric absorption in observations of missile launches.2Therefore,the high-temperature plume emitted from rocket motors plays an important role in the operation of target detection,tracking,classification and identification(DTCI)as applied to missiles guiding techniques,3spacedbased sensing systems4and combustion diagnostics.5Consequently,rocket motors are required to be optimized properly so as to have low plume irradiance for survivability.

In the process of operating a motor,there are a world of influences that may affect the irradiance signatures of plumes formed between ignition and engine cutoff.These include such effects as those caused by variation in motor types,propellant formulations,burn times and flight conditions.To validate certain issues with real motors operating,static f i ring experiments have been conducted to measure the spectral characteristics of IR signatures for solid rocket motors(SRMs).Devir and Avital et al.6,7measured the IR irradiance signature of a small Ballistic Evaluation Motor(BEM)with no metal additives in its propellant.Blanc and Wang et al.8,9measured IR spectral characteristics of double-base propellant solid rocket motors.Kim et al.10experimented with IR radiance for standard and real rocket motors with nitrate ester plasticized polyether(NEPE)propellants that had different chamber pressures during combustion.For a solid rocket motor with aluminized propellant,Rialland et al.11measured IR signatures from an in-flight rocket plume,which implied aluminum particle properties and behavior in the plume were difficult to model,and the intensity in the particle spectral band in mid-long wavelength seemed to be very weak.As mentioned above,most experiments were only conducted to test the performance of motors or to verify numerical models.Therefore,due to a lack of detailed observations,it is essential to understand how to affect IR signatures for a variety of rocket motor operating parameters with the aid of numerical tools.

When an SRM ignites,the ignition overpressure(IOP),a strong transient pressure wave,is generated in-chamber,and an uplift pressure may also exist during engine cutoff.12A standardized SRM has a fixed nozzle area and stagnation temperature.When the chamber pressure rises,the nozzle pressure ratio(NPR)can increase as well.This gives a higher nozzle mass flow rate and alters the plume shock structure and IR images of exhaust plumes,which can be used to visualize shock cell patterns.13These unsteady pressures can highlight the spectral and directional characteristics of the exhaust plume attributed to an influence on distributions of species and temperature.14Generally,rocket combustion is optimized at an oxidizer-fuel(O/F)ratio considerably less than stoichiometric;some exhaust species thus burn when they mix with the air entering the mixing layer.15Afterburning of these rich-fuel gases is bound to strengthen the irradiance intensity of the plume.Since plume invisibility should be an inherent part of modern SRM design,it is essential to perform analyses on the effects of propellant compositions on emission signatures.Therefore,the internal chamber modeling of an SRM,as a pre-computation in the predictions of exhaust plumes,requires evaluation of combustion products using a thermo-chemical code,like the NASA CEA code.16As a matter of fact,a small amount of additives are often added to major propellant ingratiates and not considered in calculations,for example in Ref.9.This treatment of evaluating combustion products may have an influence on the IR irradiance signatures of plumes in the far field.

The objective of this work is to develop an efficient model for the prediction of exhaust plume IR spectral radiation characteristics within the wavelengths of 1.50–5.50 μm.In addition,it aims to study the effects of different motor operating parameters on the IR signature of solid rocket motors in terms of afterburning,chamber pressure and propellant ingredient changes.Using a Ballistic Evaluation Motor type-II(BEM-2)6as of the test platform for this research,numerical calculations were performed.This paper is organized as follows.Section 2 describes the physical models,which consist of turbulence,chemical afterburning and radiation models.Section 3 presents numerical methods used for the solutions of flow field and radiative transfer,as well as for validation of the code.Section 4 discusses the effects of three changes in operating conditions on solid rocket plumes and IR signatures:(a)afterburning for an under-expanded supersonic jet with and without chemical reactions;(b)ignition and cutoff with a variety of chamber pressures;and(c)propellant ingredients for minor changes in the ratio of HTPB binder to AP oxidizer.Section 5 provides conclusions from this discussion,followed by a reference list and acknowledgements.

2.Physical models

2.1.Governing equations

For investigations of high speed turbulent combustion jet flow,the axisymmetric form of the Navier-Stokes equation,which contain turbulence and species transport equations,is expressed as

with conservative vectorQ,convective variables(E,F,H),and viscous flux vectors(Ev,Fv,Hv)and source term vectorsS.tis the time term.xandrare the axial and radial coordinates,respectively.The detailed expanded form and relative parameters of these vectors were also given in Ref.15.Considering the low-altitude rocket exhaust plume as a hot,reacting,radiating and turbulent flow with an afterburning process and entrainment effect,the chemistry source termScand the radiation source termSrshould be introduced as the source term vectorsSin Eq.(1).There,the radiative transfer equation,for a rigorous solution,must be solved along several lines of sight(LOS)at each point in the flow field and at each computation step,but such a procedure is extremely costly.Nevertheless,Saladino and Farmer17stated that the radiation source within gaseous radiation is negligible compared to other source terms.The radiation/convection coupled model on an only gaseous species solid rocket motor plume,reported by Wang and Kim et al.,1,10has nearly the same infrared radiation intensity as the solution of the uncoupling model.6,18Therefore,the radiation heat transfer in rocket motor plumes,consisting of pure gas phase products,can be predicted with the flow-field calculation and without the fully coupled radiation model.Thus,flow field parameters can be obtained at the first step and then treated as input data to be introduced into the radiation calculation.

The variables in Eq.(1)were described in detail in previous work.15The chemistry source term in the energy equation above can be given as

whereWiandRiare the molecular weight and gas constant of theith species,andis the standard heat enthalpy of formation for theith species at a temperature ofT0.The total enthalpy of theith species at temperature ofTis expressed as

whereT0=298.15 K.

The specific heatcpiis expressed as piecewise 4th degree polynomial functions:

whereRis the universal gas constant,andZidenotes polynomial coefficients.

2.2.Turbulence model

Turbulence plays a significant role in plume behavior and,in particular,determining the scale of the plume and afterburning effect through the mixing layer between the hot exhaust plume and the surrounding atmosphere.The influence of turbulent fluctuations in the near-field region can be ignored and attributed to the supersonic feature of the plume,but the effects of the turbulence in the far field are obvious.Ref.7concluded that turbulence models(k- ε andk-ω)had 5–10%accuracy for the measured radiance,performing far better than the laminar model with up to 20%discrepancy.The level of turbulent kinetic energy basically affects the temperature and the OH concentration of the rocket exhaust plumes.19For underexpanded plumes,there are several more diamonds in the plume images of measured radiance than the calculated results as given in Ref.6,which most probably results from the decay of turbulence.Based on a two equation realizablek-ε model,20Goldberg developed a three-equationk-ε-Rtturbulence model21that added un-damped eddy viscosity(Rt)to account for non-equilibrium conditions and avoid free stream turbulence decay under shear-free flow conditions.Therefore,this turbulent model was selected to predict the exhaust plume so as to obtain a multi-diamond distribution that corresponds with flow-field observations.

2.3.Chemical afterburning model

The exhaust gases from a rocket motor consist of multiple species,the most important of which is an amount of fuel-rich gas that can cause afterburning in the mixing layer due to the entrainment of oxygen from ambient air.A system of reactions based on finite-rate chemistry is used to predict the afterburning effect as follows:

whereAis pre-exponential factor,nis the temperature exponent,andEais the activation energy.The rate constants for the reverse reactionskbare evaluated from the equilibrium constants.Thus theith species˙ωiis given as

where ρijis the density of theith reactant or product in thejth reaction.

Wang et al.1predicted the presence of afterburning in the exhaust plume using a reaction system of 7 species(O,H,OH,CO,CO2,H2O and O2)and 10 reactions,listed as 1–10 reactions in Table 1,but the predicted IR results seem to not be in good agreement with measurements.We consider that this discrepancy can be attributed to a kinetic mechanism that may be a significant influencing factor.For example,HCl,as a main species,was frozen.Ref.22also showed that about 90%of HCl molecules remained unreacted at an altitude of 0.5 km,and they were also neglected in Ref.6.However,the HCl species was considered reactive in Ref.18and another species,HO2,was given as well.HO2was considered to be associated with the entire reaction system,especially for the product of OH,which also was reported by Rapanotti.23Moreover,there exist many detailed reactions between ambient gas and products from the combustion chamber when hightemperature exhaust plumes eject into the air.Therefore,nitrogen and oxygen should have an influence on certain nitrogen oxides and intermediate products such as NO,N,O,H and OH.So,we referred to the N2/O2system given in Ref.24.Consequently,13 primary chemical species,O2,N2,H2,CO,CO2,H2O,HO2,HCl,N,NO,OH,H and O,are considered.Chemical kinetics were modeled by a thirty reaction mechanism:eleven exchange reactions and five recombination reactions.The first 10 reactions(reported in Ref.25)are related to fuel-rich gas from the nozzle exit plane within the H2/CO/O2system,and the last 6 reactions to the plume mixing with the ambient air within the N2/O2system.Furthermore,the reactions from 11 to 17 are related to the species HCl.The detailed data of the finite rate chemical reactions for afterburning are listed in Table 1.Rate coefficients are in units of m3/(kmol s)and m6/(kmol2s) for bimolecular and termolecular reactions,respectively.

The concentration of the third bodyMis expressed aswhere ρiis the density of theith reactant;kc，iis the third body coefficients of speciesi.For five recombination reactions from numbers 6 to 10 in Table 1,third-body coefficientskc，ifrom the CHEMKIN database26are listed in Table 2.Other unstated species can be of any chemical species,and their third body coefficients are equal to 1.0.

Table 1 Chemical reactions used to predict afterburning chemistry in rocket exhaust plumes.

2.4.Infrared radiation transfer model

The radiant intensity of the exhaust plume results from three effects:27(1)spectral emission lines determined by the composition and temperature of the gases;(2)broadband(Planck)radiation determined by the temperature of the gases;(3)spectral absorption of the radiance by the plume itself.In this work,the SLG model28reported in NASA-SP-3080 were used to compute the spectral intensities from a non-isothermal mixture of combustion gases.The SLG is a narrow band model that treats all lines within an interval as a single line.Therefore,the Curtis-Godson approximation29can be adopted to evaluate parameters in this band group in which all lines in a group have similar strengths.Details of this calculation procedure can be also found in Refs.28,30.

As shown in Fig.1,a sensor-plume viewing geometry is specif i ed in this paper.The observed direction is vertical to the plume axis at a viewing angle of 90°,and the position is placed at a close distance from the plume.The exhaust plume is divided into some sub-segments and a number of rays pass through the plume along the LOS of the sensor.In each segment,the radiation within a spectral band of the sensor is added to a running sum of the total radiation along the LOS.In the hot multi species rocket exhaust plume flow,the radiation transfer equation,determining the local spectral intensity of the radiation,is expressed by31:

where λ indicates the wavelength,Iλis the local spectral intensity,κλand σsλare the absorption and scattering coefficients,respectively.Iλbis the Planck blackbody function,and Φλis the spectral scattering phase function.sandsrepresent position and direction that can be integrated over 4π solid angle dΩi.

For non-aluminized propellant,all mixture species will remain in gas phase and particle scattering never occurs in exhaust plumes.In this case,the radiative transfer equation,introducing optical thickness as τλ= κλL，can be reduced to the following form:whereLis the path length,and it can be divided intoilayers.As shown in Fig.1,Liis the path length of theith layer in medium.

Table 2 Third body coefficients of partial species.

Effects of CO2and H2O molecules on the infrared signature are dominant compared to that of other species in the exhaust plumes.32Thus we focus on the gas emissions of CO2and H2O within spectral bands 1.50–5.50 μm.In this case,several different radiation modes contribute to this spectrum.Characteristic emission bands of four main species are listed in Table 3 with many modes overlapping each other.

In this study,three types of illustrations are used to describe the IR irradiance intensities:(1)the spectral irradiance intensity as a function of wavelength,which shows the intensity at the average spectral resolution of 5 cm-1in wave numbers;(2)the total intensity,which is the sum of the intensities integrated within specific spectral bands;(3)the IR image,which is the average intensity in each grid node with 1 cm×1 cm pixels.

3.Numerical method

3.1.Flow field calculation method

The steady-state solution is obtained from a time marching method with a finite volume method.All computations are performed on a structured grid with about 0.1 million elements,which verifies the grid-independence of the solution.The spatial discretization is a second-order accurate scheme where the diffusion flux is discretized centrally and convective flux applies the upwind-biased form.The standard wall function was used near the wall boundary.A higher-order discretization technique using a total variation diminishing(TVD)principle is implemented for inviscid flux vectors.Theturbulence level is set to 2%and the turbulence length scale to 0.001 m.

Table 3 Spectral regions of main species.

3.2.Radiation calculation method

To evaluate the local spectral intensity of the radiation in the flow field,the above equation has to be solved along several lines-of-sight for each point and each wavelength.The multicomponent gas absorption coefficients combined with the multi-temperature model were obtained through line-by-line method.33Spectra with a 5 cm-1resolution were calculated at each grid point along a LOS normal to the plume,as shown in Fig.1.A line passing through the shock-layer flow field was calculated in a straightforward manner with a layer-by-layer summation.LOS,when placing a known travel route in the flow,will terminate until the line departs from the flow field,which is equal to there being no interaction with the lines parallel to the observed direction.This method has been employed in previous work.34Assuming each layered medium is isotropic and isothermal,as shown in Fig.1,the radiative intensity along the LOS can be derived as:

where the superscriptidenotes theith layer,are directional spectral intensity and black body intensity respectively,andis the transmittance.Thus,the radiative intensity of a line through the flow covering wavelengths from λ1to λ2in any direction can be given as:

3.3.Computational grid generation and boundary conditions

To gain confidence with the numerical model,a validation test was performed on a small Ballistic Evaluation Motor type-II(BEM-2)from the Institute for Israel Military Industries Ltd.(IMI).6,7The propellant ingredients did not include metal additives and a one-phase gaseous plume could be created.The throat diameter of the type-II motor was 15 mm and the nozzle divergence angle was 15°.The nozzle exit diameter was 22.5 mm.The area ratio of the nozzle outlet to the throat was 2.25.An axial two-dimensional computational domain of 0.6 m×2.5 m with the assigned boundary conditions is shown in Fig.2(a).The nozzle inlet centre was set to be the origin of coordinates.Fig.2(b)shows the computational grid,which is a compromise between accuracy and computation time through a comparison of a finer grid and a basic grid.Thus,a non-uniform,orthogonal,cylindrical grid of 400×150 cells was used,with high resolution near all solid boundaries,toward which the grid was clustered and the dimensionless wall distance was found to be below 1.

The assigned boundary conditions are shown in Fig.2(a).A uniform temperature-pressure condition was applied to farfield boundaries of the computational domain(in black).Ambient pressure and temperature conditions were considered to be 101325 Pa and 288 K for ground test cases.A no-slip,no penetration wall boundary condition was imposed on the nozzle wall(in red).An axis symmetric condition(in green)was employed in the central line of the nozzle.Stagnation conditions were specif i ed at the nozzle inlet(in blue).

3.4.Validation of the infrared radiation code

These computational Fluid Dynamics(CFD)results,as input data,can be used for the calculation of radiance signatures.Fig.3 describes mole fraction distributions along the centerline of the plume.The major species,such as CO2,H2O,and CO,have little change in magnitude other than the species O2,but mole fractions of micro-scale products drastically change in the near field.Fig.4 illustrates the two gas species of CO2and H2O,which emit major IR irradiance in 1.50–5.50 μm regions over the 1 m downstream distance.As seen in Fig.4(a),the temperature contour shows the intrinsic core with several obvious shock cells and the mixing layer with afterburning due to the ambient air entrainment.Contours of CO2and H2O molar concentration in Fig.4(b)and(c)also appear in similar distributions,such as reflectsed shocks,and distances from sequential shock cells.

The experimental spectra of BEM-2 is the intrinsic radiation of the plume due to removal of the atmospheric absorption by spectroradiometer calibration at the same distance between the sensor and the plume.Therefore,atmospheric absorption is not considered in calculations.Based on the flow field of the plume,the infrared emission predicted by the present calculation model is obtained.A comparison of the IR radiation images between calculations and experiments in the range of 4.372–4.516 μm is given in Fig.5,it indicates that both ‘diamond” distributions and irradiance intensities of the calculated IR image are in a good agreement with the measured results.Fig.6 gives a comparison of the spectral profiles of the plume radiation covering 1.50–5.50 μm between measured and calculated results integrated over 0.8 m of the plume length,and shows good agreement with measurements as well.

4.Results

4.1.Effects of afterburning

It is well known that the afterburning process can significantly affect temperature and other thermo-gas-dynamic parameters of the plume.In fact,afterburning is an inevitable phenomenon in practical exhaust plumes that must be taken into account in their infrared signatures.This section focuses on understanding how afterburning effects contribute to IR irradiance of exhaust plumes by comparing reactive and nonreactive(frozen)cases.Using the BEM-2 as the object of investigation,a comparison of temperature in the axis line between reactive and frozen plumes for under-expanded supersonic multi-species flow is shown in Fig.7.The two curves overlap well in the region fromx=0 m tox=0.3 m(about 12 diameters of the nozzle exit).This region is defined as the jet core,illustrated in Fig.8,in which temperature is almost insensitive to chemical reactions in the internal flow region.On the axis of the plume,afterburning mainly exists in the mixing layer within the far field because the average temperature of afterburning plumes,attributed to the mixture of combustion gases and air,is about 200–300 K higher on average than the frozen plume after 0.5 m.As seen in Fig.7 temperature profiles,both have several peaks located at shock cells due to different pressures between the exhaust gas and surrounding air,and subsequent smooth drops.Note that the temperature difference between both plumes does not remain a fixed value,but decreases toward the downstream distance,and both trend toward ambient temperature in the far field.It is implied that the fuel-rich gases are consumed with the oxygen entrainment from cold air.

Fig.9 illustrates comparisons of the radial temperature distribution between the reactive plume and the frozen plume at different downstream distances.Clearly,great changes take place in the far field regions.In radial directions,temperature of the afterburning plume is apparently higher than the frozen plume near the axis of the jet and close to the same value in far field regions.A bimodal temperature distribution,as shown atx=0.2 m andx=0.4 m,exists in the near field.In the far field region,since the exhausted gases quickly mix with ambient air,the afterburning effect leads to a higher temperature than the non-reaction plumes,and temperature in this region obeys a Gaussian distribution,which is considered to be‘self-similar”.Furthermore,stable species,such as CO2and H2O,increase with unstable products consuming what can further react with oxygen,like H2and CO,as the ambient air entrains into plumes.Comparisons of main species fractions in the axis line between reactive plume and frozen plume are given in Fig.10.

Fig.11(a)–(c)plot contours of IR-spectral intensity in spectral bands of 2.70–2.95 μm,4.20–4.45 μm and 1.50–5.50 μm for frozen and reaction plumes.The afterburning effect extends the radiance scale and enhances irradiance intensity in different bands shown by IR images;for instance,the average length of the reaction plumes exceeds frozen plumes by 30%.Especially in the plume’s far field,afterburning leads to irradiance intensity enhancement and structure change,which is very different from the slender shape of frozen plumes.This phenomenon is on account of the afterburning effect from the outer boundary of the mixing layer to the boundary of the jet core.In these three bands mentioned above,the brightest diamond seems to occur at the second shock cell with high gas temperature,though not highest,and heavy molar concentrations of main species such as H2O and CO2.Subsequently,incomplete combustions of H2and CO gases participate in the oxidative reaction with ambient air and produce H2O and CO2in the near field of the plume.Compared with the non-reaction plume,afterburning can obviously increase the species concentrations of H2O and CO2,which are known as main emitters of IR intensity.2,10Nevertheless,the molar and mass fraction of each species,except for O2and N2,are always decreasing due to the entrainment of atmospheric air.In fact,the plume signature is mainly dominated by both the gas temperature and the number density of species.IR irradiance intensity decreases visibly under the integrated action of multiple factors in the far field downstream.

Fig.12 illustrates variations of the IR intensity rate on the center line of the exhaust plume.I0denotes the irradiance intensity in the centerline of the nozzle exit.IReactionandIFrozenrepresent the intensity in the axis of the plume for reaction and frozen cases,respectively.The IR irradiance caused by afterburning mainly occurs in transition and far field regions and its intensity is normalized within corresponding bands at the nozzle exit.Several distinct peaks indicate that these diamonds do intensify IR signatures located at the shock cells,and it can be explained in three regions as given in Fig.8.In the near field of the plume,the IR intensity of the reaction plume does not alter significantly compared with the frozen plume at a downstream distance of 0.2 m from the exit for the present case.In the transition region from 0.2 m to 0.6 m,IR emission rates of the reaction plume clearly increase with remarkable fluctuations in all bands.The maximal rate is up to 40%at a distance of 0.6 m,where the shock cell structure is not quite distinct,indicating shock cell structures may be a more dominant factor impacting emissions in this region.Subsequently,IR rates start to decrease toward downstream in the far-field region and reach zero in the end.As seen in Fig.12,the IR rate in the 2.70–2.95 μm band,attributed to production of H2O and CO2in the axis of the plume,and is higher than in band 4.20–4.45 μm by about 100%.

Fig.13 shows a comparison of IR spectral radiance between the reaction plume and the frozen plume within the wavelengths of 1.50–5.50 μm.The calculated spectral radiation intensity of the reaction plume is higher than that of the frozen plume,which indicates afterburning plays an important role in IR irradiance emission for main species and especially for H2O in 2.71–3.43 μm and CO2in 4.17–4.22 μm and 4.29–4.55 μm.Growing rates peak at 2.7 μm and 4.3 μm and are up to 89.5%and 121%,respectively.Moreover,spectral intensities integrated within the wavelengths of 2.70–2.95 μm,4.20–4.45 μm,and 1.50–5.50 μm are given in the histogram at the top left side.The total intensity of the reaction plume is higher than the frozen plume by 81.5%in band 1.50–5.50 μm,by 110%in band 2.70–2.95 μm and by 66.7%in band 4.20–4.45 μm.

4.2.Effects of ignition and cutoff on the plume signature

During the operation of solid rocket motors,engine ignition and cutoff can generate unsteady transient pressure waves in the combustion chamber.Almost every ignition,due to a large amount of gaseous combustion products being produced instantly by burning propellant,produce a pressure peak that is significantly higher than the steady state.At the end of combustion for some rocket motors,pressure spikes occur as well because of the increase in burning surface area from the crushing of grains.These distinct pressure-varying effects can result in spatial and time dependent pressure disturbances of the plume as well as give rise to short-term transients in the intensities of a rocket plume emission.For the comparative study of transient pressures for rocket motors,the pressure history of the BEM-2 is selected as a basic pressure case(Case A)and used along with two other synthetic pressure-time profiles(illustrated in Fig.14).Table 4 lists calculated points,corresponding times and pressures in the basic case.The extinguishing pressures are treated as Case B and Case C(in red and blue)as in Ref.10where similar pressure profiles were also shown according to the chamber pressure of standard and real rocket motors during combustion.

To obtain transient radiation characteristics of the exhaust plume during f i ring and extinguishing operations,a transient simulation scheme is used to obtain the plume fields of three cases.Seven pressure points are examined sequentially in one run with characteristic times:initial f i ring,first pressure spike,first pressure trough,an average steady condition,second trough during engine cutoff,second peak and late stage of extinction.Notably,the forth pressure point at 0.7 s,approximated to a quasi-steady pressure as also shown in Ref.7,is defined as a basic pressure.For a simple,although realistic computation,it is assumed that the chamber pressure has no impact on combustion products in the inlet.

Fig.15 gives IR images in bands of 2.70–2.95 μm and 4.20–4.45 μm.Comparisons of IR irradiance at seven characteristic times show that the increase in chamber pressure can lead to IR intensity enhancement and scale expansion toward downstream distances and radical directions.For instance,the IR irradiance intensity is higher than others and the size is longer than the basic case by about 20%at 0.1300 s.In this case,more distinct diamonds distribute in the centerline of the plume within 2.70–2.95 μm and 4.20–4.45 μm bands.By contrast with Fig.15(b),it is found that IR contours in spectral band 2.70–2.95 μm are more slender than in 4.20–4.45 μm band,as also shown in the above section.That is because the rising of the chamber pressure can increase gas velocity and static pressure in the nozzle exit plane,which will certainly lead to length extension and structure changes of the plume.Both Fig.15(a)and(b)clearly show that the distance intervals between diamonds in IR images are extended with the increase of chamber pressure,and the first diamond moves backwards.Overall,it is concluded that the change of chamber pressure,especially during engine ignition and engine cutoff,is of great importance for the IR radiance of the rocket exhaust plume.

A set of time-resolved IR spectra calculated within the wavelengths of 1.50–5.50 μm for the basic case are shown in Fig.16.As was already noted,plume irradiance differs according to the chamber pressure.Similar to Fig.15,the pressure peak has a higher IR irradiance compared to other cases at every wavelength during motor ignition.Specif i cally,the spectra emitted by main species(H2O and CO2)near mid-infrared region of 2.7 μm and 4.3 μm significantly increase at high chamber pressures.At 0.1300 s,the maximum intensity of the 2.7 μm band is up to 43.1 W/(sr·μm)and higher than the basic case by 40.7%.For the 4.2 μm band,they are 568.5 W/(sr·μm)and 33.4%,respectively.Compared with the basic pressure case,the plume intensity at peak pressure does not have many increments,less than 4%,during motor cutoff.Sequential IR spectra,calculated from the whole process of the BEM-2 f i ring,show that IR irradiance signatures are changeable when the unsteady transient chamber pressure occurs,especially in the intensive initial peak caused by a pellet ignition.Nevertheless,a comparative study is conducted just for Case A on IR irradiance that shows the chamber pressure is not higher than that for Case B during extinguishing operations.Fig.17 illustrates comparison of static temperature in the axis of plumes between cutoff pressure peaks.It is seen that the temperature increases and the corresponding peaks move backwards,attributed to changes in the size and shape of the plume,when the chamber pressure rises.

Total IR irradiance in three spectral bands show that the plume total irradiance differs according to the spectral bands in Fig.18.The total intensity in the 2.70–2.95 μm band is lower than that in the 4.20–4.45 μm band by about 60%,and the integrated radiance of the two bands accounts for more than half of the total IR irradiance in spectral band 1.50–5.50 μm.There is a similar distribution in total intensity for three narrow spectral bands.According to the analyses above,it is believed that the total IR irradiance can be characterized with the chamber pressure for a specific rocket motor.

Fig.19 shows the relationship between the total radiance in different bands and the chamber pressure.The pressure curves in the graph are normalized with the averaged pressure valueat the steady stage of the chamber pressure,which is equal to the pressure value at the time of 0.7 s.Spectral intensities integrated within different bands at 0.7 s are taken as reference values to nondimensionalize the corresponding radiance intensities at other computed points.In fact,more computed pressure points,including a homogeneous repartition within the pressure range excursion,are considered in predictions.It is found that other points also have a similar distribution as given in Fig.19,hence only seven representative points are selected that can fully reflects the pressure change information.It is noted that the dimensionless intensities at different times are in very good agreement with the corresponding dimensionless pressures.During ignition and engine cutoff,the maximum discrepancy between IR irradiance and criterion pressure profiles is less than 13%in band 2.70–2.95 μm,and the intensity integrated within the wavelengths of 4.20–4.45 μm is always in accordance with the reference pressure.Therefore,the total IR radiance can be characterized with the chamber pressure trace,which can be obtained by a premeasurement of a specific rocket motor.Therefore,a semiempirical formula for the plume infrared signature as a function of the chamber pressure can be expressed as:

Table 4 Selected computed points along the pressure trace inside the BEM-2 during operation.

where（p）is the total spectral intensity integrated within the band of λ1- λ2in the chamber pressurep.λ1and λ2are upper and lower limits on the band,respectively.p0denotes any pressure value along chamber pressure trace.

4.3.Effects of propellant ingredients

For non-aluminized solid rocket motors,propellant formulas consist of an oxidizer/binder and additives.Generally,the oxidizer and the binder are AP and HTPB,respectively.In practice,there are two aspects of treatment in propellants.First,an optimized oxidizer-fuel(O/F)ratio could be less than stoichiometric,so the ratio of HTPB/AP in the propellant mixture affects a variety of parameters in the chamber.Second,it is essential to obtain nozzle-exit properties through a nozzle performance code in the numerical computation of rocket exhaust plumes.For simplification,a small amount of ingredients are neglected and replaced with an equal amount of HTPB/AP.Therefore,the aim of this section is to determine whether a slight change of HTPB/AP content has a great impact on the spectral radiance of the plume.

The weight percentage of AP is taken as a variable without consideration of the grain size distribution,and HTPB is kept within the practical quantity of 9–13%.As with the BEM-2 from Ref.7,five group ingredients with AP oxidizer/HTPB binder/additives by the 0.75%increment of HTPB in weight are computed,and only three cases are listed in Table 5.In all cases,thermal properties of mixed gases from the chamber to the nozzle exit are computed by the Chemical Equilibrium with Applications(CEA)code,which was reported by Gordon and Mcbride.16Mole fractions of main gas phase species in the exit plane are listed in Table 5,and the great difference is fromthe species at the nozzle exit.The amount of fuel-rich gas species increases,as CO and H2,with the slight raising of HTPB.In contrast,the final stable products,such as CO2and H2O,decrease.Consequently,temperature and species distributions of the exhaust plume can be effected,to a certain extent,by properties in the nozzle exit plane and have an influence on the infrared emission spectrum.

Table 5 Calculation parameters for three AP/HTPB ratios.

Based on flow field parameters,the corresponding radiance maps for three cases are obtained in Fig.20.Fig.20(a)shows the spectral radiance in the spectral band of 2.70–2.95 μm.It is seen that an increment of 1.5%for HTPB,from Case 1 to Case 5 sequentially,has an influence on the spectral radiance of the plume.Fig.20(a)indicates the following differences in radiance contours:(1)The maximum intensity decreases and the radiance region extends as well.(2)The brightest diamonds move backward away from the nozzle exit and the distribution of other bright diamonds varies according to locations at shock cells.(3)Both the scale and shape of the lighter region increase slightly.Fig.20(b)illustrates the spectral emission within the wavelengths of 4.20–4.45 μm,whose diamond distributions and intensity levels are similar to the 2.70–2.95 μm band.In addition,the level of diamonds near the exit declines more obviously with each increment of HTPB.These phenomena are attributed to species and temperature distributions in the plume field,which are strongly dependent on exit parameters,ambient atmospheric conditions and chemistry schemes.As plotted in Fig.20(a)and(b),synthetic IR images show that radiance fields have a great difference in intensity and scale for H2O-2.7 μm band and CO2-4.3 μm band.Moreover,spectral irradiance profiles integrated over 1 m from the entire plume length,for three propellant ingredients mentioned above,are shown in Fig.21.The spectral intensity as a function of wavelengths ranges from 1.50 μm to 5.50 μm.As demonstrated in the figure,the three curves are highly similar,and the increment of the spectral intensity is about 20%,from Case 1 to Case 5.

In practice,the weight fraction of HTPB ranges from 9%to 13%.In this section,five computed points,at 0.75%increments of HTPB from 10%to 13%,are selected to analyze variations of radiance intensities within different bands.We assume the additive in the propellant is constant,and the formulation content varies between HTPB and AP to keep the total weight of both ingredients a fixed value as in Table 5.Radiance intensities in three bands(1.50–5.50 μm,2.70–2.95 μm,and 4.20–4.45 μm)with five selected HTPB increments(10.00%,10.75%,11.50%,12.25%and 13.00%)are calculated and presented in Fig.22.Taking the radiance intensities in the case of 10%HTPB as reference values,a sensitivity study of radiance intensity increments in three bands for each formulation are synthesized in a graph and presented in Fig.23.As can be seen from this figure,the increment rates of radiance intensity integrated in each band are linear with increase in HTPB,and the growth rates of radiance intensities in three bands are 2.70–2.95 μm band,1.50–5.50 μm band and 4.20–4.45 μm band from high to low and reach up to 50%,42%and 34%,respectively,as HTPB increases 3%in weight.As a consequence,the proportion of each component in the propellant should be as accurate as possible for predictions of IR radiation signatures.

5.Conclusions

A systemic and validated numerical tool was developed to compute the infrared radiative signatures of rocket plumes and to investigate IR spectral radiation characteristics within the wavelengths of 1.50–5.50 μm for operating motors in terms of afterburning,chamber pressure and propellant ingredient changes.In this construct,a refined 13-species,30-reaction chemistry scheme and ak-ε-Rtturbulence model were employed to predict flow field properties of the exhaust plume with the finite volume technique.The spectrum was integrated with an LOS method that depended on an SLG model with Curtis-Godson approximation.IR irradiance results calculated with this model show good agreement with experimental data in spectral intensities and IR maps.

Using the BEM-2 as a test platform for this research,the IRSAT was applied to discuss the following three effects on IR signatures under operating conditions:(a)afterburning effects;(b)chamber pressure effects during ignition and cutoff;and(c)minor changes in the ratio of HTPB binder to AP oxidizer in propellants.

The afterburning effects increased the size and shape of radiance images,which caused an increase of 30%in length,and 89.5%in intensity and 121%at peaks of 2.7 μm and 4.3 μm.The IR radiance caused by afterburning mainly occurred in transition and far field regions of the plume where IR emission rates increased with remarkable fluctuations across all bands up to a maximal rate of 40%.In the near field,the IR irradiance intensity did not change significantly compared with the frozen plume.

An increase in chamber pressure lead to an incremental increase in IR irradiance intensity and scale.There were more distinct diamonds whose distance intervals extended,and the position of the first diamond moved backwards.The total IR radiance was characterized by a chamber pressure trace,which could be obtained by a pre-measurement of a specific rocket motor.During ignition and engine cutoff,the maximum discrepancy between the IR irradiance and the criterion pressure profiles was less than 13%in the band of 2.70–2.95 μm and always was in accordance with the reference pressure within the wavelengths of 4.20–4.45 μm.

For a rocket motor with AP oxidizer/HTPB binder/additives,the incremental rates of radiant intensity integrated in each band were linear as the HTPB increased,and the growth rates of radiance intensities in three bands were 2.70–2.95 μm band,1.50–5.50 μm band and 4.20–4.45 μm band from high to low and reached up to 50%,42%and 34%,respectively,as HTPB increased 3%in weight.The increase of HTPB/AP lead to a decrease of the maximum intensity in images but an increase of the total intensity in bands.The brightest diamond moved backward away from the nozzle exit,but both size and shape of the lighter region increased slightly.In addition,the intensity of diamonds near the exit declined more obviously with the increment of HTPB.In future work,it is necessary to study the influence of above three factors,afterburning,chamber pressure fluctuation and HTPB rate,on the IR radiance signatures at different flight altitudes,speeds(Mach numbers),angles of attack and observation angles of sensors.

Acknowledgement

This study was supported by the National Natural Science Foundation of China(No.51576054).

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18 April 2016;revised 19 October 2016;accepted 22 December 2016