The development of a new model to simulate the dispersion of rocket exhaust clouds

Accepted Manuscript The development of a new model to simulate the dispersion of rocket exhaust clouds

Erick Giovani Sperandio Nascimento, Davidson Martins Moreira, Taciana Toledo de Almeida Albuquerque

PII: DOI: Reference:

S1270-9638(16)31186-5 http://dx.doi.org/10.1016/j.ast.2017.06.034 AESCTE 4090

To appear in:

Aerospace Science and Technology

Received date: Revised date: Accepted date:

2 December 2016 11 June 2017 27 June 2017

Please cite this article in press as: E.G. Sperandio Nascimento et al., The development of a new model to simulate the dispersion of rocket exhaust clouds, Aerosp. Sci. Technol. (2017), http://dx.doi.org/10.1016/j.ast.2017.06.034

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THE DEVELOPMENT OF A NEW MODEL TO SIMULATE THE DISPERSION OF ROCKET EXHAUST CLOUDS Erick Giovani Sperandio Nascimento1, Davidson Martins Moreira1,2*, Taciana Toledo de Almeida Albuquerque1,3

1

Federal University of Espírito Santo - Vitoria - Brazil 2

3

SENAI CIMATEC - Salvador - Brazil

Federal University of Minas Gerais - Belo Horizonte - Brazil *

Corresponding author: [email protected]

ABSTRACT This study presents the development of a new model named MSRED, which was designed to simulate the formation, rise, expansion, stabilisation and dispersion of rocket exhaust clouds for short-range assessment, using a three-dimensional semi-analytical solution of the advection-diffusion equation based on the ADMM method. For long-range modelling, the MSRED was built to generate a ready-to-use initial conditions file to be input to the CMAQ model, as it represents the state-of-the-art in regional and chemical transport air quality modelling. Simulations and analysis were carried out in order to evaluate the application of this integrated modelling system for different rocket launch cases and atmospheric conditions, for the Alcantara Launching Center (ALC, the Brazilian gate to the space) region. This hybrid, modern and multidisciplinary system is the basis of a modelling framework that will be employed at ALC for pre- and post-launching simulations of the environmental effects of rocket operations.

1. INTRODUCTION

1

Due to the thrust produced by the burning of solid or liquid fuel, gases (toxic or nontoxic) are released into the atmosphere during a rocket launch and subsequently transported and dispersed by the wind. In the main rocket and space vehicle launching areas worldwide (e.g., the Kennedy Space Center in the United States, or the Guiana Space Centre in French Guiana), mathematical algorithms are executed to analyse the trajectory of these gases prior to the launch. These computer models are an abstraction of a process that involves one or more functions designed to simplify the description of a certain natural process. They may be restricted by factors such as the limitations of the solution and mathematical approximation, the scope and availability of data, and the inherent complexity that can be tolerated in the data analysis and reduction process. Various studies, such as those by Denison et al. (1994), Brady et al. (1997), Bennett et al. (1997), Bernhardt et al. (2011), Koch et al. (2013), Voigt et al. (2013), and Bauer et al. (2013), addressed the impact of rocket exhaust pollutants on the stratosphere, without focusing on their impact on the region of the atmospheric boundary layer (ABL), especially during and immediately after the rocket is launched. Evaluating the impact of these pollutants on the ozone layer, as a large amount of HCl and alumina is emitted during the burning of the propellant, has gained widespread appeal. Alumina particles can provide a surface for the heterogeneous conversion of HCl into other chlorinated compounds, which serve an important role in the depletion of the ozone layer (Pitts and Finlayson-Pitts, 2000). This study is focused on the conceptual, mathematical, and computational modelling of the dispersion and transport of effluents derived from clouds of rocket exhaust into the lower troposphere to obtain a viable description of this phenomenon, which is characterised by turbulent diffusion. Some approaches use computational fluid dynamics (CFD) techniques for modelling the formation of the exhaust plume; however, the computational cost of this methodology is very high, which prevents its use in the operating environment (Bauer et al.,

2

2013; Koch et al., 2013). Other researchers use an approach based on Lagrangian models (Bardina and Rajkumar, 2003; Bardina and Thirumalainambi, 2004 and 2005; Rajasekhar et al., 2011) to model toxic gases, whereas others use Gaussian approaches. Some of these models include the Rocket Exhaust Effluent Diffusion Model (REEDM) (Bjorklund et al., 1982), which was operationally employed by the National Aeronautics and Space Administration (NASA) to evaluate the impact of rocket exhaust clouds; the Open Burn/Open Detonation Dispersion Model (OBODM) (Bjorklund et al., 1998), which does not focus on modelling the impact of the rocket exhaust cloud, but was designed to assess the impact of open-air explosions using the mechanism in the REEDM as a basis; the Stratified Atmosphere Rocket Release Impact Model (SARRIM) (Cencetti et al., 2011), which is employed by the Service Environnement et Sauvegarde Sol at the Centre National d'Études Spatiales (CNES) — France's space agency — in the evaluation of the environmental impact of rocket effluent emissions at the Kourou spaceport in French Guiana; the PlumeTracker (Wells et al., 2013), which seeks to simulate the elevation, transport, stabilisation, and subsequent deposition and precipitation of particles from the ground cloud generated by the rocket launches; and the Modelo Simulador da Dispersão de Efluentes de Foguetes (MSDEF, in Portuguese) (Moreira et al., 2011), which utilises the same physical aspects as the REEDM but with differences in the meteorological layers, the condition of continuity of flow and concentration (more realistic vertical profiles), different turbulence parameterisations (diffusion coefficients and dispersion parameters), and a semi-analytical solution of the advection-diffusion equation in the horizontal and vertical directions by applying the Gaussian dispersion hypothesis in the y direction, considering the current knowledge of the physics of the ABL. Nascimento et al. (2014) presented the first effort for representing exhaust clouds from rocket launches using the Community Multi-Scale Air Quality (CMAQ) modelling system for the Alcantara Launching Center (ALC) region. Nascimento et al.

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(2015a, 2015b) developed a project that focused on applying the WRF model with large eddy simulation (WRF-LES) for real cases to generate meteorological input data for the MSDEF model, with an emphasis on atmospheric turbulence simulations. In the works of Bainy (2015) and Voese (2017), the problem of the dispersion of gases is simplified and solved using an analytical solution by the application of the Generalized Integral Laplace Transform Technique (GILTT). Iriart and Fisch (2016) used the WRF model coupled to its chemical module (WRF-CHEM) to simulate the dispersion of the pollutants emitted by the satellite launcher vehicle (or Veículo Lançador de Satélites, VLS, in Portuguese) launched from the ALC, performing simulations for different meteorological conditions in the ALC for the year of 2008, for the pollutant CO. They considered that all the emissions from the rocket occur at the surface level, using a domain with 20x20 grid cells of 1km resolution. Schuch and Fisch (2017) developed a work derived from Iriart and Fisch (2016), using the WRF-CHEM but implementing a distribution mechanism of the emissions due to the rocket launching along the vertical layers, evaluating the impact for other pollutants rather than only CO, namely: HCl, alumina and CO2, however without considering the long range impact of the chemical transport of HCl, as this is the most chemically reactive and hazardous among these pollutants. Although each approach has its advantages in representing the physics involved in this process, an additional step is needed in the construction of a hybrid computational tool that is capable of incorporating the state of the art in meteorological modelling and the transport and dispersion of rocket exhaust pollutants into the atmosphere. In this context, hybrid approaches that incorporate various tools for the simulation and evaluation of the impact of rocket launches on the atmosphere are being developed and used in the main launch centres worldwide. These approaches involve meteorological modelling, followed by the simulation of both the formation of the cloud of toxic gases at the time the rocket is launched and their

4

subsequent dispersion and transport during and after stabilisation within a relatively short time range (from a few minutes to a few hours), consecutively combined with modelling the chemical transport of the toxic gas cloud for long-range evaluation over a longer time range in the lower troposphere. These hybrid approaches are more complete and appropriate for determining the impact of the toxic effluents of rocket exhaust. Thus, this work presents the development of a short-range model that advances on a novel semi-analytical three-dimensional solution of the advection-diffusion equation and on the representation of the cloud formed during rocket launches by considering the release time of the exhaust pollutants, using a nonstationary solution. It has been built to read meteorological input data from WRF and to prepare the pollutant concentration field for long-range modelling in CMAQ. Also, this work presents the study and simulation of the meteorology and the dispersion and chemical transport of rocket exhaust pollutants in the region of the ALC, Maranhão state, Brazil, by employing this hybrid system for the assessment of the impact of normal launches on the atmosphere. To address the objective, the paper is organised as follows: Section 2 provides the methodology, including the conceptual and mathematical descriptions of the model; in Section 3, are showed the numerical results; and in Section 4, are provided the conclusions.

2. METHODOLOGY Based on the current state of the art in this research area, this study sought to develop a new model for the short-range evaluation of the dispersion of rocket effluents and the integration with meteorological and chemical transport of pollutants modelling systems to create a framework that can be used by the Brazilian Space Agency at the ALC. Thus, the Model for Simulating Rocket Effluent Dispersion (MSRED) was created and developed in this study to continue the initial efforts that produced the MSDEF model. 5

To provide the MSRED model with the information necessary for its execution, some meteorological variables need to be provided to the model, for example, vertical temperature profiles, wind direction and speed at ground level and at different levels in the atmosphere, height of the boundary layer, Monin-Obukhov length, friction velocity and convective velocity. These variables are obtained via observational measurements in the regions of interest, for example, the campaigns conducted in the region of the ALC. However, this process involves a relatively high financial cost, as it requires the availability of machinery and highly specialised human resources. Thus, an effort was made in this project to provide this information necessary for the MSRED through the application of a meteorological model to this case. The WRF model (Skamarock and Klemp, 2008), which had been developed by a consortium of American institutions formed by the National Center for Atmospheric Research (NCAR) — the National Oceanic and Atmospheric Administration, represented by the National Centres for Environmental Prediction (NCEP) and the Forecast Systems Laboratory (FSL); the Air Force Weather Agency (AFWA); the Naval Research Laboratory; the University of Oklahoma; and the Federal Aviation Administration (FAA) — was selected. It is a three-dimensional atmospheric modelling system applicable to both meteorological research and numerical weather forecasting. It offers various options for simulating physical atmospheric processes and can be run on a variety of computing platforms. The WRF model is suitable for an extensive range of applications at scales that range from a few dozen metres to a global level, with the following notable applications: modelling for meteorological investigation, weather forecasting by numerical solution in real time, idealised simulation of atmospheric events, study and development of data assimilation processes, and coupling with other modelling systems, such as air quality models. In the case of the latter, various systems for modelling air quality use meteorological and terrain data

6

generated by simulations performed using the WRF model. Highlights include the American Meteorological Society-Environmental Protection Agency Regulatory Model (AERMOD), the California Puff (CALPUFF) model, and the CMAQ model. The WRF itself has a module responsible for modelling air quality, which is denoted WRF-Chem, and it simulates the chemical processes of dispersion, transport, and mixing of gases and particles that simultaneously occur in the atmosphere with meteorological modelling. The WRF is the state of the art in atmospheric science. It is extensively employed throughout the world, both for academic and operational purposes, and is being continuously improved by the scientific community (available in: http://www2.mmm.ucar.edu/wrf/users). With the objective of studying and simulating the process for the chemical transport of rocket effluent into the atmosphere, for the long-range evaluation of the environmental impact at a regional scale, an effort was made to assess the existing air quality models that can be applied in this context. Thus, the CMAQ model (Byun and Schere, 2006), which was developed by the US Environmental Protection Agency (USEPA) by its Atmospheric Science Modeling Division and is maintained by the University of North Carolina (UNC), was chosen, as it is a three-dimensional modelling system that simultaneously models multiple atmospheric pollutants, including tropospheric ozone, particulate matter, and a variety of toxic gases, and assists both regulatory agencies and polluting companies in the assessment of air quality to determine the best air quality management scenarios for impacted communities and governments. The system includes components responsible for pollutant emissions, meteorology, and chemical, transport, and depositional processes. Given that it represents the state of the art in air quality modelling, it has been extensively distributed around the world and has an active scientific community that maintains it and develops constant evolutions to reduce the uncertainties in the simulations (available in: https://www.cmascenter.org). It also has a module that couples to the WRF meteorological model to enable interactions between

7

the atmospheric pollutants and the meteorological variables. This model is the official model of the USEPA, which conducts daily simulations of tropospheric ozone concentrations and other pollutants across the US to evaluate air quality in the country and recommends the CMAQ model for multi-scale studies of air quality. Especially in the case of the CMAQ model, its current version (version 5.1) has a module that specifically addresses the chemical reactions of the gaseous compounds and aerosols formed from the emissions of chlorinated compounds (e.g., HCl), which comprise a large portion of the rocket effluents — an aspect that makes the CMAQ even more interesting compared with other models, such as the CALPUFF or WRF-Chem. Thus, one of the main innovations is to apply the CMAQ model to the case of effluent emissions due to rocket launches.

2.1 Conceptual description of the model The concepts of “ground cloud” and “contrail cloud” are illustrated in Figure 1 using the launch of Titan IV at Cape Canaveral as an example. For an atmospheric dispersion analysis of the rocket emissions, which can affect receptors on the ground, the simulation of emissions from the launching of a vehicle, starting from the ground and to a maximum height of approximately 3000 m, has been standard practice in the US (Cape Canaveral and Vandenberg Air Force Base). For any modelling application or simulation of normal or aborted launches in the assessment of air quality, the correct representation of the formation of rocket exhaust clouds is essential.

Figure 1 One hypothesis that the model makes about the nature and behaviour of the cloud released by a rocket is that it can be initially defined as one single cloud that grows and moves but remains as one cloud during its rise phase. This concept is illustrated in Figure 2; 8

the model is designed to obtain concentrations in the direction of the prevailing wind, starting from the position in the stabilised cloud. This approach is the same approach employed in the REEDM and MSDEF models.

Figure 2

In relation to the discretisation of the atmospheric boundary layer (ABL) and the representation of the source term, the MSRED is based on the technique described by Moreira et al. (2011) with several improvements. The model associates the initial formation of the cloud in a spherical shape with normal launches and a cylindrical shape with aborted or test launches or launches that involve explosions. The determination of the stabilisation height of the exhaust cloud for normal launches and the plume generated for launch failures is an important factor in the calculation of the concentration, as the maximum concentration calculated on the Earth’s surface is generally inversely proportional to the cube of the stabilisation height (Bjorklund et al., 1982). In the case of normal vehicle launches with solid fuel, the launch time and the residence time in the first hundred metres are relatively short. The exhaust cloud is therefore compressed by the heated gas emitted during a period of approximately ten to fifteen seconds. Experiments with the data collected by NASA indicate that the rise of the exhaust cloud in these circumstances is calculated more appropriately using an instantaneous cloud rise model. In the case of an aborted launch or a launch that involves an explosion, the best option is the continuous plume rise model. In both cases, the models are based on the work originally described by Briggs (1969) for calculating the plume rise, with derivations subsequently described by Dumbauld et al. (1973) and Bjorklund et al. (1982) for calculating the instantaneous cloud rise and, more recently, with improvements developed in the work of Moreira et al. (2011) and incorporated into the MSDEF model. In 9

this study, new improvements were developed based on the work of Moreira et al. (2011) to seek a better representation of the source term (which is the exhaust cloud), notably with regard to the incorporation of specific formulations for calculating cloud rise in different atmospheric stability conditions, the use of more realistic meteorological parameters derived from the output of the WRF meteorological model for different height levels, and the calculation of the vertical gradient of the virtual potential temperature, as well as the stabilisation height. Once the cloud is defined and has attained the condition of thermal stability with the atmosphere, the cloud is partitioned into “disks”. The positioning of each disk with respect to the origin (launch platform) is determined based on various cloud parameters, such as the stabilisation height, radius, and time for each atmospheric stability condition, via a sequence of meteorological layers defined using the levels and meteorological variables available in the output of the WRF model. The concept of partitioning the stabilised cloud is illustrated in Figure 3.

Figure 3

The exhaust cloud, once stabilized, may overpass the ABL height. In this case, for the computation of the concentration, two distinct regions are considered: the first, delimited at the bottom by the terrestrial surface, and at the top by the ABL; and the second, ranging from the ABL to the height of 3,000 m (as suggested by Bjorklund et al., 1982). In this second region, it is assumed that the pollutants are not transported above 3,000 m and the gases coming from this layer do not penetrate in its basis (top of the ABL). However, for particles, it is assumed that always occurs penetration due to the gravitational process.

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2.2 Mathematical description of the model The advection-diffusion equation of air pollution in the atmosphere is a declaration of conservation of the suspended matter. The turbulent concentration flows are assumed to be proportional to the mean concentration gradient, which is known as the Fick theory. This assumption, combined with the continuity equation, generates the advection-diffusion equation (Blackadar, 1997):

∂c ∂c ∂c ∂ § ∂c · ∂ § ∂c · ∂ § ∂c · ∂c + u + v + ( w − v g ) = ¨ K x ¸ + ¨¨ K y ¸¸ + ¨ K z ¸ − λc − Λc ∂x ∂y ∂z ∂x © ∂x ¹ ∂y © ∂y ¹ ∂z © ∂z ¹ ∂t (1)

for 0 < z < h, 0 < y < Ly and x > 0, where c denotes the mean concentration; h is the height of the atmospheric boundary layer; Ly is very distant from the source; Kx, Ky, Kz, and u, v, w are the Cartesian components of the turbulent diffusion and the wind, respectively; vg is the gravitational deposition; Ȝ is the physical-chemical decay coefficient; and ȁ is the removal by rain coefficient. The x-axis of the Cartesian coordinate system is aligned with the wind direction, the yaxis is oriented perpendicular to the wind direction, and the z-axis is aligned in the vertical direction. To solve equation (1), the mean lateral wind component is assumed to be zero (v = 0). The initial and boundary conditions are defined as: at the start of the pollutant release, the region of the dispersion is assumed to be not polluted:

c( x, y, z,0) = 0

at t = 0

11

(2)

and an emission source with a constant rate Q is assumed,

c( 0, y , z , t)=

Q [η (t) - η (t - t r )]δ ( y - y o )δ ( z − H s ) u(z)

at x = 0

(3)

in which į is the Dirac delta function, Hs is the height of the source, Ș is the Heaviside function and tr is the duration of the release (Bianconi and Tamponi, 1993). The pollutants are also subject to the boundary conditions:

Kz

∂c =0 ∂z

at z = h

(4a)

z = z0

(4b)

and

Kz

∂c =V c ∂z d

at

where Vd is the deposition velocity and z0 is the roughness length (at

z = z0 ,

K z = K 0 = constant ). In the y direction, the following conditions exist:

∂c =0 ∂y

at y = 0, L y

12

(5)

The wind speed u and Kx, Ky, Kz are assumed to only depend on the variable z, with w and vg constant. At this point, the technique described by Moreira et al. (2005a; 2006), which is known as the Advection-Diffusion Multilayer Model (ADMM) method, is taken as the basis. It is a semi-analytical solution based on the discretisation of the atmospheric boundary layer into sublayers, in which the advection-diffusion equation is solved using the Laplace transform technique. Thus, a stepwise approximation is made, which is subsequently applied to problem (1) via the discretisation of the height h into sublayers to calculate the mean values of Kx, Ky, Kz, and u for each sublayer. This procedure transforms the domain of the problem (1) into a multilayer system in the z direction. This approach is very generic, as it can be applied when these parameters represent an arbitrary continuous function of the variable z. At this point, equation (1) can be rewritten as a set of advective-diffusive problems with the parameters kept constant for a given sublayer:

∂cn ∂c ∂c ∂ 2c ∂ 2c ∂ 2c + un n + (w − vg ) n = K xn 2n + K yn 2n + K zn 2n − λcn − Λcn ∂t ∂x ∂z ∂x ∂y ∂z

(6)

for n = 1:N, where N denotes the number of sublayers and cn represents the concentration in the nth sublayer. Additionally, two extra boundary conditions related to the interactions that occur at the interfaces of the sublayers (in addition to the conditions already defined for z = 0 and z = h) must be defined:

n = 1, 2,...(N-1)

cn = cn +1

13

(7a)

Kn

∂c ∂cn = K n+1 n+1 ∂z ∂z

n = 1, 2,...(N-1)

(7b)

These conditions need to be considered to unambiguously determine the 2N arbitrary constants that appear in the solution for the set of problems of equation (6). Starting from this point, the Generalised Integral Transform Technique (GITT) (Cotta, 1993) can be applied in the y direction. The GITT is a hybrid method that has been employed to solve a diverse class of problems, particularly in the area of heat transfer and fluid dynamics. The formal application of the GITT method begins with the selection of the problem of the associated eigenvalues (also known in the literature as the auxiliary problem) and their respective boundary conditions:

ψ i" (y) + λ i2ψ i ( y ) = 0

for

0 < y < Ly

(8a)

ψ i' ( y ) = 0

for

y = 0, Ly

(8b)

The solution is ȥi = cos(Ȝiy), where Ȝi represents the positive roots of the expression sin(ȜiLy) = 0. Thus, Ȝ0 = 0 and Ȝi = iʌ/Ly. The functions ȥi (y) and Ȝi, known as eigenvectors and eigenvalues, respectively, are associated with the Sturm-Liouville problem and satisfy the following orthonormality condition:

­ 0, m ≠ n ½ 1 ψ ( z )ψ n ( z )dv = ® ¾ 1/2 ³ m N Nn v ¯ 1, m = n ¿ 1/2 m

14

(9)

in which Nm is given by:

N m = ³ψ m2 ( z )dv

(10)

v

According to the GITT formalism, the first step is to expand the variable c(x,y,z,t) in the following manner:

∞

cni ( x, z, t )ψ i ( y )

i =0

N1/2 i

cn ( x, y, z, t ) = ¦

(11)

Substituting equation (11) into equation (6), the following equation is obtained by assuming K xn = K x ; K yn = K y ; K zn = K z :

∞

¦

∂cni ( x, z , t ) ψ i ( y ) 1/ 2 i

∂t

i =0

∞

K xn ¦

N

∞

+ un ¦

∞

+ K zn ¦ i =0

∂x 2

N1/2 i

∂z

1/2 i

N

N

∞

+ ( w − vg )¦ i =0

∞

ψ i" ( y )

i =0

N1/2 i

+ K yn ¦ cni ( x, z , t )

∂ 2 cni ( x, z , t ) ψ i ( y ) 2

1/ 2 i

∂x

i =0

∂ 2 cni ( x, z , t ) ψ i ( y )

i =0

∂cni ( x, z , t ) ψ i ( y )

+

∞

ψ i ( y)

i =0

N1/i 2

− (λ + Λ )¦ cni ( x, z , t )

∂cni ( x, z , t ) ψ i ( y ) ∂z

N1/2 i

=

(12)

in which ' and '' represent the first-order derivative and second-order derivative, respectively. L

The next step is to apply the operator

³ 0

ψ j ( y) N1/2 j

dy to equation (12) and use equation (8a)

to observe thatψ i" = − λ i2ψ i . Using the orthonormality property, equation (12) can be rewritten as follows: 15

∂cn i ( x , z , t ) Kx

+ un

∂t ∂ 2 cn i ( x , z , t ) ∂x 2

∂ cn i ( x , z , t ) + Kz

+ ( w − vg )

∂x ∂ 2 cn i ( x , z , t ) ∂z 2

∂ cn i ( x , z , t ) ∂z

=

(13)

− ( λ + Λ + K y λ ) cn i ( x , z , t ) 2 i

For the source condition (3), we have:

L

∞

¦u c

n ni

i =0

(0, z, t ) ³ 0

L

ȥi ȥ j

dy = ³ 1/2 N1/2 i Nj 0

Q [η (t)-η (t-t r )] į ( y - yo )į ( z - H s )ȥ j N1/2 j

dy

(14)

Thus, developing the integrals, the following equation is obtained:

cn (0, z, t ) =

Q [η (t)-η (t-t r )]δ ( z − H s )ψ i ( yo ) un N1/2 i

(15)

Now, applying the Laplace transform in equation (13), the following equation is obtained:

  2 2  d 2 cni ( s, z , p ) ( w − vg ) dcni ( s, z , p) ( p + λ + Λ + sun − K x s + K y λi )cni ( s, z , p) − − = dz 2 Kz dz Kz ( K x s − un )cni (0, z , p ) Kz (16)

16

 where c ( s, z, p) = L {c ( x, z, t ); x → s; t → p} , with the initial condition:

 c (s, z,0) = 0

at t = 0

(17)

the source condition,

cni (0 ,z , p) =

Q 1 − e − ptr ψ i ( yo ) ( ) 1/2 δ ( z − H s ) un p Ni

at

x=0

(18)

and the boundary conditions:

 dc ( s, z, p) Kz =0 dz

at z = h

(19a)

and

 dc ( s, z, p)  Kz = Vd c ( s, z, p) dz

at z = z0

(19b)

 − Bcni ( s, z , p ) = − DQδ ( z − H s )

(20)

resulting in,

 d 2 cni ( s, z , p ) dz

2

−A

 dcni ( s, z , p ) dz

17

where

A=

w − vg Kz

; B=

( p + λ + Λ + sun − K x s 2 + K y λi2 ) Kz

; and D =

(1 − e − ptr ) (un − K x s ) ψ i ( yo ) p un K z N1/i 2

Equation (20) has the well-known solution:

(1 − e  cni ( s, z, p) = G1e( R1 + R2 ) z + G2e( R1 − R2 ) z + p

− ptr

)Q R3

(e

( R1 − R2 )( z − H s )

− e( R1 + R2 )( z − H s )

)

(21) where

R1 =

§ K s· 1/2 A N 1/2 K z B1/ 2 ª¬ A2 + 4 B º¼ ; and β = ¨¨1 − x ¸¸ ; R2 = ; R3 = i un ¹ 2 ψ i ( y0 ) β 2 ©

Subsequently, the concentration is obtained by the application of the numerical  inversion of the transformed concentration cn i by the Gaussian quadrature scheme:

M1

cni ( x, z , t ) = ¦ j =1

pj § − tr t 1 e − ¨¨ © ( p j t)

pj t

M2

aj ¦ k =1

pk ak ª¬G1e( R1 + R2 ) z + G2 e( R1 − R2 ) z + x

º · » ¸¸ ¹ Q e( R1 − R2 )( z − H s ) − e( R1 + R2 )( z − H s ) H ( z − H ) » s » R3 » » ¼

(

)

18

(22)

where

R1 =

1 ( w − vg ) 2 Kz

§ pj · p ¨ + λ + Λ + k u n β + K y λi2 ¸ 1 x ¸ R2 = ¨ t ¸ 2¨ Kz ¨ ¸ © ¹

N 1/2 K R3 = i z ψ i ( y0 ) β

1

2

1/2

ª§ w − vg · 2 º § pj pk 2· «¨ ¸ + 4 ¨ + λ + Λ + un β + K y λ j ¸ » Kz ¹ x © t ¹ ¼» ¬«© §

p ·

β = ¨¨1 − k ¸¸ Pe ¹ ©

with M1 representing the number of points of the Gaussian quadrature applied to the variable t, M2 the number of points of the Gaussian quadrature applied to the variable x, H(z – Hs) is the Heaviside function, and Pe = u n x K x the Peclet number, which essentially represents the ratio between advective and diffusive transport (Moreira et al., 2005b). The constants aj, ak, pj, and pk are the weights and roots of the Gaussian quadrature scheme, which are tabulated in the book of Stroud and Secrest (1966), where j and k are the quadrature points. Using the inverse form, the following equation is obtained:

19

ȥ i ( y ) ­ M 1 p j M 2 pk a j ¦ ak ª¬G1e( R1 + R2 ) z + G2 e( R1 − R2 ) z + 1/ 2 ® ¦ i =0 N i ¯ j =1 t k =1 x ∞

cn ( x, y, z , t ) = ¦ pj § − tr t − 1 e ¨¨ © ( p j t)

º½ · »° ¸¸ ¹ Q e( R1 − R2 )( z − H s ) − e( R1 + R2 )( z − H s ) H ( z − H ) » ° s »¾ R3 »° »° ¼¿

(

(23)

)

This equation is subsequently truncated into a sufficiently large number of terms of the sum of the series to obtain the final solution of the problem (6). From this solution, the solution to the three-dimensional advection-diffusion equation is obtained for a vertically inhomogeneous atmospheric boundary layer. Note that this solution is semi-analytical, as no approximation is made throughout the derivation process, with the exception of the stepwise approximation of the diffusion coefficient and longitudinal wind speed, the numerical Laplace inversion of the transformed concentration, and the truncation of the series of the GITT solution. After determining the stabilisation time and the source (which are the multiple layers formed by the cloud partitioning), the final concentration of the pollutant at a certain level will be the contribution of all the sources:

n

C ( x , y , z , t ) = ¦ ci ( x, y , z , t ) ,

i = 1,2,3,…, n

(24)

i

where n represents the nth source due to the partitioning of the exhaust cloud of pollutants released by the rocket during the stabilisation time.

2.3 Design and encoding of the MSRED model 20

The system was designed to integrate with the WRF and CMAQ models. Each aspect of its design was conceived in a manner that would ensure the perfect coupling between the different models by a well-defined execution chain and a system design based on three layers: the presentation layer, the persistence layer, and the business layer. The basic structure of the MSRED model’s execution chain is shown in Figure 4. The model was constructed using the FORTRAN language, the netCDF (Unidata, 2015) and Models-3/EDSS Input/Output Applications Programming Interface (I/O API) libraries for the coupling with the WRF and CMAQ models, and the OpenMPI library (Gabriel et al., 2004) for its parallel execution, enabling its use in an operating environment that makes computing resources available for the execution of parallel processing. It utilizes the Meteorology-Chemistry Interface Processor (MCIP) (Otte and Pleim, 2010) to prepare the meteorological output from WRF in compliance with CMAQ data convention. The MSRED model uses the meteorological layers defined in the WRF modelling for the discretization of the ABL.

Figure 4

2.4 Parameterisations of the atmospheric turbulence In principle, the diffusion of a cloud can be mathematically simulated. The problem of simulating the dispersion of a pollutant released into the atmosphere primarily becomes the determination of the appropriate diffusion coefficient. Generally, this problem has been addressed by the definition of classes of meteorological conditions (e.g., “stable”, “neutral”, and “unstable”) and by the establishment of empirical measures of the turbulent diffusion coefficient for each condition. However, if the meteorological measurements are adequate, these empirical measurements may be related to detailed characteristics of the atmosphere. 21

In the resolution of atmospheric diffusion problems, choosing a turbulence parameterisation is a key aspect of modelling the dispersion of pollutants. The accuracy of each model is significantly dependent on the calculation of the turbulent parameters; it is related to the current understanding of the atmospheric boundary layer (Mangia et al., 2002). Given that the proposed solution for the advection-diffusion equation is threedimensional, the horizontal (Kx), lateral (Ky), and vertical (Kz) diffusion coefficients are necessary. In this study, they were determined in accordance with Degrazia et al. (2000) for stable, unstable, and neutral atmospheric conditions.

3. NUMERICAL RESULTS This section presents the results for the modelling of the dispersion and chemical transport of exhaust clouds of pollutants from normal rocket launches, for different atmospheric stability conditions, using the MSRED model for the short-range evaluation and the CMAQ model for the long-range evaluation.

3.1 Models configurations The case study concerns a four-day simulation from March 18, 2013 to March 22, 2013 using the WRF model (version 3.6) for generating meteorological data, with Global Forecast System Final Analysis (GFS FNL) data as the input for the region of the ALC. The ALC is located in the city of Alcântara, on the coast of the state of Maranhão, Brazil (refer to Figure 5). It has geographical coordinates of 2°24’ S and 44°24’ W, is 32 km from the capital São Luís and has an altitude between 40 m and 50 m. Brazilian rockets (satellites and/or scientific experiments) are launched at the ALC via the VLS and/or sounding rockets, such as the VSB30.

22

Figure 5

Five domains were configured, with a horizontal resolution of 8.1 km, 2.7 km, 900 m, 300 m, and 100 m at 70 vertical levels. Figure 6 shows the location and distribution of the domains; domain 5, which has the finest resolution, is so small in relation to the others that its location is signalled only by the number five.

Figure 6

Three meteorological scenarios were selected within the period modelled by the WRF, which would represent the different atmospheric stability conditions. For each scenario, the impact of a hypothetical launch of a rocket with the same characteristics as the VLS (refer to Table 1) could be assessed in a normal situation. Given that observational data are neither available for pollutant concentrations collected at the ALC from rocket launch events nor available in the literature, qualitative analyses and evaluations are conducted in relation to the use of the MSRED model and its coupling with the CMAQ model based on the available literature.

Table 1

Table 2, whose data were obtained from the execution report of the MSRED, presents the meteorological information extracted from the modelling with the WRF, which characterised each scenario and its respective condition of atmospheric stability, where the time is expressed as Greenwich Mean Time, u* represents the friction velocity (m/s), L is the 23

Monin-Obukhov length (m), w* is the convective velocity (m/s), zi is the height of the atmospheric boundary layer (m), which is h in the model, and uv1 and ud1 are the speed (m/s) and the direction (º), respectively, of the average wind at the surface layer (~10 m). These variables refer to the grid cell (43,43) of domain 3 (resolution of 900 m), where the ALC is located. Domain 3 was chosen for executing the modelling due to its adequate size and resolution for assessing the impact of the long-range chemical transport of the exhaust cloud on the towns and cities surrounding the ALC region. The ABL was discretized using the meteorological vertical layers defined in the WRF modelling, each one with approximately 50 m, except the first layer with 17 m, and the second with 25 m.

Table 2

3.2 Analysis of the modelling results In order to evaluate the meteorological modelling performance, a comparative analysis was conducted between the model output and radiosonde sounding data collected in the launch site (12:00 GMT, March 18, 2013). Figure 7(a) shows a comparison for wind speed parameter. In general, it can be noted that the model showed the same behavior as the upper air observed data. The wind direction parameter, shown by Figure 7(b), presented winds mostly blowing from East and Northeast. The values found in model output were very close to those measured. Figure 7(c) shows the air temperature comparison plot as a function of height. It is also worth mentioning the proximity of the behavior of both data sets, showing parity in temperature values in relation to height, following the trend of the curve in which the temperature decreases with height.

Figure 7 24

Table 3 presents information concerning the stabilisation height (hc), stabilisation radius (rc), stabilisation time (t*), and distance covered until the stabilisation of the pollutant exhaust cloud (¨xc) for each atmospheric condition and type of launch. In the case of normal launches, a difference in the stabilisation height of the exhaust cloud is observed when comparing the stable conditions with the neutral/unstable conditions. This difference is attributed to the improvement in the mathematical modelling of the exhaust cloud formation proposed in this study, which highlights the importance of a formulation that considers the different atmospheric stability conditions. In stable conditions, the cloud rise tends to be considerably reduced, which produces shorter heights than in convective or neutral cases (Seinfeld and Pandis, 2006). Tables 4 and 5 present the parameterizations and simulation set up for this case for WRF and CMAQ models, respectively.

Table 3

Table 4

Table 5

Figure 8 shows a graphical analysis of the vertical distribution of the percentage volume of each partition in relation to the total volume of the exhaust cloud for each atmospheric condition for the normal launch case. The cloud has a spherical shape and is 25

smaller in the stable case than in the unstable and neutral cases. Each scenario has the same amount of mass released by the rocket; however, the formed cloud has a greater or lesser volume depending on the atmospheric stability condition. The details of the formulation of the formation of the cloud (including its shape) for each stability conditions are presented in the work of Nascimento (2016).

Figure 8

Figure 9 shows the same graphical analysis of the vertical distribution of the percentage volume of each partition in relation to the total volume of the exhaust cloud for each atmospheric condition for the aborted launch case. In this case, the cloud has a cylindrical shape, as shown in the figures. In both graphical analyses of each case (normal and aborted launch), the behaviour of the vertical distribution of the partitions is consistent with the mathematical modelling in this study for the formation of the exhaust cloud. The cloud’s shapes for each condition are very similar because they use the same formulation (see Nascimento, 2016), varying only due to the meteorological parameters, such as the wind speed, stability parameter and air temperature.

Figure 9

At this point it is important to mention that does not exist contaminant concentration data from rocket exhaust in order to make comparisons with numerical simulations in the literature. Nevertheless, the ADMM methodology used for obtaining the MSRED model has been tested in several experiments available in the literature, such as Kinkaid (Moreira et al., 2004), Copenhagen (Moreira et al., 2005a; 2005b), Prairie Grass (Moreira et al., 2005c; 26

Moreira et al., 2006; Moreira et al., 2014) and Hanford (Moreira et al., 2010), which generates confidence in this qualitative analysis. The following figures show the scenarios of the modelling with MSRED and CMAQ for the pollutant HCl (March 18, 2013). The impact of the pollutant HCl was analysed due to its high degree of danger and impact on ambient air. HCl is a colourless gas with an irritating and pungent odour that is perceptible at or above concentrations of approximately 0.8 ppm (Lide, 2003); it is corrosive to the eyes, skin, and mucous membranes. In humans, acute exposure to HCL within a short period of time can cause coughing, hoarseness, inflammation and ulceration of the respiratory tract, chest pain, and pulmonary oedema (USEPA, 1993; 1999). The MSRED model was executed to generate concentration scenarios for the pollutant HCl at the surface level, with a 20 min interval for the normal launch case for each atmospheric condition. These scenarios were employed by the model to generate the mean for the first hour after the launch, which generated the initial conditions input for the CMAQ for the long-range modelling of the impact of the exhaust cloud. After the execution of the MSRED, the CMAQ model was executed, and a scenario for the mean concentration of HCl at the surface level was generated with a 20-minute interval (Figure 10). In the presented scenario, after 1 hour and 20 minutes (at 17:20 h GMT), the exhaust cloud travelled approximately 15 km from the launch centre, which is consistent with the surface wind speed at the time of the launch, which, according to Table 2, is 2.9 m/s for this case. At this time, the HCl concentrations are lower than the HCl concentrations at the beginning of the second hour, which is expected, as the pollutant undergoes physical and chemical processes over time that tend to decrease the concentration. However, they begin to increase, starting from the 17:40 h GMT scenario and remain higher until the penultimate frame, which occurs after two hours. This result is attributed to the three-dimensional 27

character of the solution implemented in the MSRED and its coupling with the CMAQ, as the MSRED calculates the three-dimensional concentration field for input into the photochemical model based on the emissions from the partitions of the cloud distributed in the various vertical layers, which are also modelled three-dimensionally by the CMAQ model. Due to the atmospheric turbulence and the deposition, diffusion, and advection processes, the mass of the pollutant present in the upper layers will eventually be transported to the surface layer, which increases the concentration values of the pollutant in this layer.

Figure 10

The analysis of this scenario shows the importance of the hybrid approach for an integrated evaluation of the impact of the large cloud of pollutant exhaust from rocket launches on the ambient air, both for the appropriate modelling of the cloud formation and of the short scale of time and space in which the phenomenon occurs, and for the modelling of the long-range chemical transport, to evaluate the impact on receptors located at greater distances (higher than 20km). Figure 11 shows the mean 20-minute HCl concentration scenario modelled by the CMAQ, using the initial conditions generated by the MSRED for a hypothetical normal launch in stable atmospheric conditions. In the same manner as the convective case, the concentrations increase over time; however, the surface-level concentrations are much higher than in the previous case, as the exhaust cloud is lower, less vertically distributed than in the convective scenario and, therefore, denser. Also, there is less inherent turbulence in a stable condition, which renders the dispersion of contaminants in the atmosphere difficult.

Figure 11

28

The three-dimensional long-range modelling of the chemical transport with the CMAQ model demonstrated that the HCl concentrations in stable conditions significantly increased to levels that are very dangerous to human health, with a potential impact on cities such as Lagoa do Mato and Bequimão, 40 km and 48 km far, respectively, which are located southwest and west of the ALC. In the case of normal launching in neutral conditions, the scenario for modelling the chemical transport with the CMAQ did not indicate significant concentrations of HCl at the surface level (Figure 12), which indicates that this scenario generated the lowest concentration values for the pollutant HCl of the three normal launch scenarios.

Figure 12

4. CONCLUSIONS This study presented a current topic in the research field of atmospheric sciences related to the development of a computer model for simulating the dispersion of gases released by rockets at the ALC. As stated in the introduction, there is currently no atmospheric modelling system capable of simulating the impact of the large exhaust cloud formed during the launching of rockets in the ALC region. A few modelling systems are available that can handle the case of rocket launches, but they are either not available for use by the scientific community or are unsuitable for use at the ALC. The use of hybrid approaches for assessing the impact of rocket exhaust clouds at different temporal and spatial scales, which are capable of merging meteorological modelling with short-range dispersion modelling and long-range modelling for the chemical transport of the contaminants emitted during rocket launches, is necessary. 29

Due to the unique nature of rocket emissions and the gaps that exist in this area of the atmospheric sciences, the development of a new mathematical-computational model capable of simulating such an impact at temporal and spatial scales smaller than those addressed by typical approaches for modelling air quality is critical. This new model was designed to integrate with other atmospheric models that have the ability to simulate both the input meteorological scenario and the chemical transport of contaminants for long-range evaluation to create the basis for a framework or modelling system that is suitable for use at the ALC. As they represent the state of the art in their fields of activity, the WRF model was chosen for meteorological modelling, and the CMAQ model was chosen for chemical transport modelling. The new model — MSRED — was specially designed and developed to incorporate the state of the art in atmospheric sciences and computing. It was designed based on the work of Moreira et al. (2011), who developed the MSDEF, with various improvements. The threedimensional solution of the advection-diffusion equation was developed using a semianalytical approach to a inhomogeneous atmospheric boundary layer, in which the atmospheric turbulence profiles can be described in three dimensions using the turbulent diffusivity coefficients of the K-theory, without a high computational cost and with a reduction in the rounding errors compared with the three-dimensional numerical methods for solving this equation. Scenarios were presented that resulted from the application of the meteorological modelling with the WRF model and its coupling with the MSRED model, as well as shortrange modelling of the dispersion of the exhaust cloud with the MSRED model and its coupling with the CMAQ model for long-range evaluation. As no data are available for the concentration of pollutants due to rocket launch events at the ALC, only a qualitative evaluation of the results from modelling with MSRED and CMAQ was possible. The 30

analyses of the modelled scenarios demonstrated the importance of evaluating the impact of the contaminants emitted during different scenarios for rocket launches and atmospheric conditions, particularly in relation to the inhabited regions that surround the ALC. Based on the results and the proposed and developed method, the objectives of this work were successfully achieved. An experimental campaign in the ALC region is planned for the near future to assess the concentration field of pollutants released by rockets, which would enable the comparison of the modelling proposed in this study with observed data.

Acknowledgements The authors would like to thank the Brazilian National Council for Scientific and Technological Development (Conselho Nacional de Desenvolvimento Científico e Tecnológico – CNPq) and the Brazilian Federal Agency for the Support and Evaluation of Graduate Education (Coordenação de Aperfeiçoamento de Pessoal de Nível Superior – CAPES) for financial support.

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Unidata. The netCDF Library. Boulder, CO: UCAR/Unidata Program Center, EUA. DOI: doi:10.5065/D6H70CW6, 2015. U.S. Department of Health and Human Services. Hazardous Substances Data Bank (HSDB, online database). National Toxicology Information Program, National Library of Medicine, Bethesda, MD, EUA, 1993. U.S. Environmental Protection Agency. Integrated Risk Information System (IRIS) on Hydrogen Chloride. National Center for Environmental Assessment, Office of Research and Development, Washington, DC, EUA, 1999. Voese, J., 2017. Uma aproximação analítica tridimensional para um problema de dispersão de efluentes de foguetes em uma nuvem estabilizada. Dissertação (Mestrado em Modelagem matemática). Programa de pós-graduação em Modelagem Matemática, Universidade Federal de Pelotas, Pelotas – RS. Voigt, C., Schumann, U., Graf, K. and Gottschaldt, K.D., 2013. Impact of rocket exhaust plumes on atmospheric composition and climate ʊ an overview. EUCASS Proceedings Series – Advances in AeroSpace Sciences 4, 657-670. Wells, J.E., Black, D.L. and Taylor, C.L., 2013. Development and Validation of a Computational Model for Predicting the Behavior of Plumes from Large Solid Rocket Motors. ATK Internal Conference, April 24-25, 2013, Ogden, UT, USA.

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Table 1. Relationship of the emission rate and the effective heat of the propellant for each type of launch (Moreira, 2010).

Information

Normal Launch Aborted Launch 5.2 × 105

Emission rate Q (g/s)

Effective heat H (cal/g) contained in the fuel 1.6 × 103

1

1.36 × 105 103

Table 2. Meteorological information of each modelling scenario.

Atmospheric

Date and time

Local date and

u*

L

w*

zi

uv1

ud1

Condition

(GMT)

time (GMT-3)

(m/s)

(m)

(m/s)

(m)

(m/s)

(º)

Stable

18/03/2013

18/03/2016 06:00 h

0.4

100.0

0.0

874.8

3.5

74.0

18/03/2016 13:00 h

0.6

-30.3

2.5

773.5

2.9

62.8

18/03/2016 19:00 h

0.6

180.0

0.0

733.0

4.0

63.6

09:00 h Unstable

18/03/2013 16:00 h

Neutral

18/03/2013 22:00 h

1

Table 3. Information about the formation of the pollutant exhaust cloud for each atmospheric condition and launch type.

Atmospheric Condition Launch Type hc (m) rc (m)

t* (s)

¨xc (m)

Stable

Normal

349.4

223.1 168.7

583.0

Stable

Aborted

909.3

417.7 180.6

624.1

Unstable

Normal

867.8

552.8 146.1

430.5

Unstable

Aborted

695.0

311.1 111.5

328.7

Neutral

Normal

811.5

517.0 167.2

663.1

Neutral

Aborted

858.5

392.6 177.5

704.1

1

Table 4: Physics options used for WRF.

Option mp_physics ra_lw_physics ra_sw_physics sf_sfclay_physics sf_surface_physics bl_pbl_physics cu_physics

Domain 1 2 1 1 1 2 5 1

Domain 2 2 1 1 1 2 5 0

Domain 3 2 1 1 1 2 5 0

Domain 4 2 1 1 1 2 0 0

Domain 5 2 1 1 1 2 0 0

Table 5: List of the options used in CMAQ.

Property Gas Chemistry Aerosol Chemistry Advection Vertical Diffusion Solver Cloud Module

Selected Option cb05tucl_ae6_aq aero6 vyamo acm2 ebi_cb05tucl cloud_acm_ae6

Figure 1. Illustration of the “ground-cloud” and “contrail-cloud” parts of the emission from the Titan IV rocket, which is associated with normal launching (Nyman, 2009).

1

Figure 2. Conceptual illustration of the formation of the cloud (source), “cloud-rise”, and atmospheric dispersion of the cloud (Nyman, 2009).

1

Figure 3. Partitioning of the stabilised cloud into “disks” (Nyman, 2009). 1

METEOROLOGICAL MODELLING - Meteorological parameters (wind direction and speed, boundary layer height, air temperature and pressure, etc.) - Information on the modelling grid (position, size, resolution) - Vertical levels

WRF

EXECUTION OPTIONS FOR THE USER MCIP

MODELLING OF THE DISPERSION AND SHORT-RANGE IMPACT MSRED

Instantaneous 3D concentration

Mean hourly 3D concentration

Execution report

MODELLING OF THE CHEMICAL TRANSPORT AND THE LONG-RANGE IMPACT WITH THE CMAQ SMOKE (anthropogenic emissions)

Initial conditions by the MSRED

BCON (boundary conditions)

CCTM (chemical transport)

3D concentration

Figure 4. Flowchart that illustrates the execution chain of the modelling system. 1

Alcantara Launch Center

Figure 5. Location of the ALC in Alcantara, Maranhão, Brazil. 1

Figure 6. Location and distribution of the domains configured in the modelling with WRF-LES.

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Figure 7. Comparison between the results from WRF-LES with radiosonde sounding data collected in the ALC (12:00h GMT): (a) Wind speed vertical profile; (b) Wind direction vertical profile; (c) Air temperature vertical profile.

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5 10 Volume (%)

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5 10 Volume (%)

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Figure 8. Percentage volume of each partition in relation to the total volume of the exhaust cloud for the normal launch case and the (a) stable, (b) unstable, and (c) neutral atmospheric conditions.

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Height (m)

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Figure 9. Percentage volume of each partition in relation to the total volume of the exhaust cloud for the aborted launch case and the (a) stable, (b) unstable, and (c) neutral atmospheric conditions.

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Figure 10. Mean 20-minute concentration scenario for the pollutant HCl, modelled by the CMAQ for the normal launch case with unstable conditions, using the initial conditions generated by the MSRED model, from 17:20 until 19:00 GMT.

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Figure 11. Mean 20-minute concentration scenario for the pollutant HCl, modelled by the CMAQ for the normal launch case with stable conditions, using the initial conditions generated by the MSRED model, from 10:20 until 12:00 GMT. 3

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Figure 12. Mean 20-minute concentration scenario for the pollutant HCl, modelled by the CMAQ for the normal launch case with neutral conditions, using the initial conditions generated by the MSRED model, from 23:20 until 01:00 GMT. 3