dynamics of sonic hydrogen jet injection and mixing

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Dynamics of Sonic Hydrogen Jet Injection and Mixing

Inside Scramjet CombustorZ. A. Rana

a, B. Thornber

a & D. Drikakis

a

a Dept. of Fluid Mechanics & Computational Sciences, School of Engineering, Cranfield

University, Bedfordshire, MK43 0AL, UK

Published online: 19 Nov 2014.

To cite this article: Z. A. Rana, B. Thornber & D. Drikakis (2013) Dynamics of Sonic Hydrogen Jet Injection andMixing Inside Scramjet Combustor, Engineering Applications of Computational Fluid Mechanics, 7:1, 13-39, DOI:

10.1080/19942060.2013.11015451

To link to this article: http://dx.doi.org/10.1080/19942060.2013.11015451

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Engineering Applications of Computational Fluid Mechanics Vol. 7, No. 1, pp. 13 – 39 (2013)

Received: 1 Jan. 2012; Revised: 25 Aug. 2012; Accepted: 4 Sep. 2012

13

DYNAMICS OF SONIC HYDROGEN JET INJECTION AND MIXING

INSIDE SCRAMJET COMBUSTOR

Z.A. Rana *, B. Thornber and D. Drikakis

Dept. of Fluid Mechanics & Computational Sciences, School of Engineering, Cranfield University, Bedfordshire, MK43 0AL, UK.

* E-Mail: [email protected] (Corresponding Author)

ABSTRACT: This paper presents the application of a Finite Volume Godunov-type implicit large eddy simulation

method to study fuel injection into the combustion chamber of HyShot-II scramjet engine without chemical

reaction/combustion in order to understand the fuel injection and air-fuel (hydrogen) mixing. The study is carried out

in two parts; part one presents analysis of 2D HyShot-II geometry (without fuel injection) incorporating high

temperature gas formulation which is validated against the NASA Thermally-Perfect-Gas code in order to obtain the

combustion chamber inlet conditions. These combustor initial conditions are then utilized in part two for 3D

combustion chamber simulations with hydrogen injection but cold flow where a digital filter based turbulent inflow

boundary condition has been utilized. The purpose of the study is to understand the flow physics, hydrogen jet penetration and air & fuel mixing inside the HyShot-II combustor which is vital at the design stages. Various flow

features are investigated such as the Mach number, velocity, pressure distributions, temperature, turbulent kinetic

energy, Reynolds stresses and the effect of counter rotating vortices on mixing. The results of full geometry

simulations are compared with computational results from the German Aerospace Centre, DLR, whereas due to

unavailability of any data for hydrogen cold flow the validity of the results is based upon a similar validation case

presented earlier (Rana et al., 2011b).

Keywords: hydrogen injection, compressible turbulent flows, scrmajet combustor, implicit LES

1. INTRODUCTION

Hypersonic Air-breathing Propulsion (HAP)devices, such as scramjet (supersonic combustionramjet) engines, are required for efficienthypersonic propulsion. A scramjet employssupersonic combustion, typically above Mach 2,in order to generate thrust for propulsion. HAPsystems eliminate the requirement to carryoxygen on-board the flight as the device wouldscoop oxygen from the atmosphere as it goesalong resulting in huge savings in terms of weightand possibly size. But this is not as simple as itsounds. HAP systems such as scramjets have no

thrust at all while standing still. Research hascontinued in this area with a view to develop aSingle-Stage-To-Orbit (SSTO) propulsion systemthat can operate from zero runway speed tohypersonic cruise (above Mach 5), and athypersonic velocities the scramjet would start producing the necessary thrust.Escher (2001) proposed seven operating modes ofa supercharged ejector scramjet (SESJ) combined

cycle engine. In this study Escher examined bothSSTO and Two-Stage-To-Orbit (TSTO)applications for this engine. Hiraiwa et al. (2008)

presented their study of a scramjet and rocket-

ramjet combined cycle engine which included both wind tunnel experiments and CFD

evaluation of the combined cycle engine. Theexperiments were carried out at HIEST (HighEnthalpy Shock Tunnel) and RJTF (Ramjet TestFacility) at the Kakuda space center, Japan. Mach6 conditions were tested using a subscale modelof the engine. The engine was designed to operateat ejector-jet mode at low speed (start from zerovelocity), then Ramjet mode activated atsupersonic speeds. To achieve hypersonic speedsthe scramjet and rocket modes were activated.The work presented achieved a net thrust in lowerMach numbers and tests are underway for higher

Mach numbers.HyShot is a major scramjet research project thatwas started by the University of Queensland(Australia) to obtain pressure measurements insupersonic combustion chamber. Currently it hasdeveloped into a multi-national project withsponsorships from various organizations fromAustralia, UK, USA, Japan, South Korea and

Germany including several defense organizations.The main objective is to develop an

understanding of supersonic combustion and itsapplication for passenger aircraft, for the projects

such as LAPCAT (Long-Term Advanced


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Engineering Applications of Computational Fluid Mechanics Vol. 7, No. 1 (2013)

14

Propulsion Concepts and Technologies). TheHyShot-II scramjet was flight tested in 2002 andit successfully achieved supersonic combustion atMach 7.8 at an altitude between 23 km and 35km. The fuel used for this flight test washydrogen and flight test data was collected forfuel-off and fuel-on conditions inside twoseparate combustion chambers.Apart from actual test flights of the HyShot-IIscramjet engine wind tunnel studies were carriedout using the T4 Shock Tunnel at the Universityof Queensland by Paull et al. (2004); Stalker et al.(2005). This work was further developed usingthe High Enthalpy Shock Tunnel Gottingen,HEG, of the German Aerospace Centre, DLR.HEG is capable of testing a complete scramjetwith internal combustion and external

aerodynamics. It can generate a pulse of gas to anozzle at stagnation pressure of up to 200 MPa

and stagnation Enthalpy of up to 24 MJ/kg. Afterthe successful test flight of the HyShot-IIscramjet, ground based testing was carried out toanalyze the data from flight test. For this purposetwo test conditions were developed for nominal

flight altitudes of 32.5 km and 27.1 km which isthe range of altitude where the flight test(HyShot- II) achieved supersonic combustion anddata was collected. The idea behind is to developa methodology for ground based testing of

scramjet engines for further developments as inGardner and Hannemann (2004); Hannemann

(2003); Eitelberg (1994); Gardner et al (2004). Amost recent study of the scramjet wind tunnel testwas presented by Schramm et al. (2008). In thisground based test of the HyShot-II model at theDLR, the HEG tunnel was used and the actual

flight test conditions were duplicated for theground test for measurement of surface pressure,heat transfer and high speed flow visualizationinside the HyShot-II combustion chamber.Several configurations have been considered for

the fuel injection inside a scramjet includinginclined as in Ferrante et al (2011) and transverse

which is applied in the HyShot-II configuration.The success of a scramjet engine largely dependsupon the mixing of fuel, entering into thecombustion chamber, with the air stream atsupersonic velocities. The residence time of airinside the combustion chamber is very short (inthe range of 2-4 ms), therefore, it is extremelyimportant to design the combustion chamber forefficient mixing of fuel and air. Because of theshort residence time and extreme conditionsinside the combustion chamber, it is very difficultto visualize the flow. CFD is playing a vital rolein the development of hypersonic flow

understanding and technology development forHAP devices; especially flow visualization, flow physics at such extreme conditions andextrapolation to flight conditions. CFD analysis isalso being carried out on the HyShot-II at variousinstitutions and the results are compared withflight test and wind tunnel test data. All the effortshave highlighted the extreme difficulty associatedwith capturing even just the turbulent non-reacting flow inside the combustor where two jetstreams meet. Most of these studies have been performed either without fuel injection or withfuel injection for combustion which requires hugecomputational resources. The need at the designstage is to understand the flow physics ofhydrogen injection into the supersonic air flowinside the HyShot-II combustor that can be

performed quickly and accurately to provide flow predictions for the scramjet combustor.

For transverse fuel injection, as in the HyShot-IIscramjet, the flow is generally termed as jetinjection in supersonic cross-flow (JISC).Understanding the physics of mixing in JISC isvery important in order to get improvements in

air-fuel mixing and successful combustion toachieve useful thrust from a scramjet engine.Gruber et al (1995) carried out an experimentalstudy of transverse jet mixing. The free-streamconditions used in his experiment were Mach 2

and the jet entered into the free-stream at sonicvelocity. They presented a structure of bow shock

and horse-shoe vortex being generated as the jetentered the free-stream. Ben-Yakar et al (2006)also carried out a similar experimental study ofthe same phenomenon and presented his results in2006 at a free-stream Mach number of 3.3 and

sonic jet. They compared two different fuelsentering the free-stream, namely hydrogen andethylene, to observe large variations in injectionvelocities due to the difference in molecularweights of two fuels. These differences led to

“substantial variation in the jet shear layer growthrate and the mixing properties Ben-Yakar et al.

(2006)”. Later on Kawai and Lele (2010) presented a CFD study of this phenomenon usingclassical LES approach using a localized artificialdiffusivity (LAD) method based upon a technique by Cook (2004) which adds the grid-dependentartificial fluid transport coefficients to the physical transport coefficients. More recentlyRana et al. (2011b) used Implicit Large EddySimulation (ILES) technique along with a digitalfilter based turbulent inflow boundary conditionto study JISC phenomenon for the experiment bySantiago and Dutton (1997) and providedinstantaneous analysis for the instabilities around


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the jet plume and how they help promote themixing. They also demonstrated computationalefficiency obtained using the methodology.Further studies of similar interest have been presented by Aziz et al. (2008), Wasewar andSarathi (2008) and Liu and Wang (2011).The work presented in this article utilizes thesame ILES approach using high resolutionmethods to study the flow of a transverse sonichydrogen jet injected into the free-streamturbulent supersonic (Mach number 2.5) flow ofair. The supersonic turbulent boundary layer inthe combustion chamber is implemented using thedigital filter based turbulent boundary condition.First, the full Hyshot-II geometry in twodimensions is analyzed using the hightemperature gas formulation with variable ratio of

specific heats (γ) to obtain the correct shockstructures in and around the scramjet and inside

the combustion chamber. Using this analysis, the properties of the flow entering the combustionchamber are obtained. These are then applied to athree-dimensional analysis of the full combustionchamber analysis where velocity, pressure

distributions, turbulent kinetic energy (TKE),Reynolds shear-stresses (RS) along with jet penetration and flow mixing are analyzed. Section2 briefly describes the computational frameworkand Section 3 presents the HyShot-II scramjet and

combustion chamber geometries along with thecomputational domains and initial condition of

the flow used in these simulations. Section 4 presents the full HyShot-II analysis along with theinitial conditions obtained for combustor analysis.The Section 5 presents the results and discussionfor three-dimensional combustor analysis, and

finally, Section 6 presents a conclusion for thearticle.

2. COMPUTATIONAL FRAMEWORK

The governing equations for a Newtonian fluidflow i.e., Navier-Stokes (NS) equations are

employed in this study which can be written as:

+ ∇ ∙ (u) = 0 ,(u) + ∇ ∙ (uu) = -∇∙S , (1) + ∇ ∙ (u) = -∇∙(S ∙ u) - ∇∙q where ρ, e, u, q and S are the density, total energy per unit volume, the velocity components, the

heat flux and stress tensor respectively. The NSequations are solved using the method of lineswhere the inviscid fluxes are solved in each

direction and viscous fluxes are solved using acentral difference method. The equation in onedimension can be re-written in vector form inCartesian space as follows:

U

+F

= 0 (2)

where, U and F are vectors of conserved

variables and inviscid fluxes and ar e:

U =

; F =

2 + +

(3)

where, ρ is density, (u,v,w) are the components of

velocity, E is total energy and p is pressure.

2.1 Perfect gas formulation

The total energy (E) in Eq. (3) is the sum ofinternal energy (e) and kinetic energy (K.E.):

= + .. = ( + 0.5(2+2+2)) (4)

For a perfect gas, the above system of equations isclosed using an equation of state as below:

=

=

−1

(5)

where R is the gas constant, T is temperature andγ is the ratio of specific heats.

2.2 Thermally perfect gas formulation

High temperature effects make the air deviatefrom perfect gas behavior. The internal energy (e)comprises four different modes, which are exciteddepending upon temperature. At temperatures below 300 K, the internal energy includes the

translation and rotational modes of energy, but athigher temperatures the vibrational mode of

energy is also excited. At extreme temperaturesabove 9000 K ionization starts and thus theelectronic energy mode is excited. In this case it becomes important to account for all theappropriate energy modes as below as in

Anderson (2006) and Hirschel (2005):

= + + + (6)The equation of state in Eq. (5) holds for a perfectgas either calorifically and thermally perfect or just thermally perfect where vibrational mode is

excited. For a calorifically and thermally perfectgas, Eq. (5) gives the internal energy as follows:

+ = (−1) (7)


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Eq. (7) includes only the translational androtational modes of energy and thus cannot beconsidered as total internal energy in a high speedflow. To calculate the total internal energy of athermally perfect gas the vibrational energy modemust be accounted for, which is described as below:

= ( −1)2 (8)

Hirschel (2005) has defined the values of θ fordifferent molecules. NACA Report (1953) definesthe value of θ for air as 5500R and is useful ifdifferent mass fractions are not used. This gives

the total internal energy of the flow of a thermally perfect gas as below:

=

(−1)

+

( −1)2 (9)

For a thermally perfect gas the specific heats atconstant volume and pressure cannot beconsidered constant and become a function oftemperature. Thus the ratio of specific heats also becomes a function of temperature. To determine

the temperature fluctuations, the followingequation is solved iteratively for T:

= − ( −1)2

−1 (10)

The iterative process to solve Eq. (10) requires areasonable initial guess to start off the iterationsand converges after approximately 5 iterations.As the ratio of specific heats is a function oftemperature, the relations provided in NACA-Report (1953) for thermally perfect gas are usedto determine the value of the ratio of specificheats.

2.3 Numerical methods

The computational code used in this work is

CNS3D (Drikakis and Tsangaris, 1993) whichutilizes the Finite Volume Godunov type methodto solve the governing equations of Newtonianflow. The initial values of the solution vector arespecified at the start of the simulations. The code

solves Riemann problem to calculate the inter-cellfluxes using HLLC Riemann solver (Toro, 2009)which assumes a three-wave structure of theRiemann problem solution, allowing for twointermediate states enclosed by the two fastestwaves. It has successfully been used to simulate avariety of flows in conjunction with the CNS3D

code, for example Drikakis (2003) and Rana et al.(2009a, b and 2011a, b).

Higher order spatial accuracy is obtained byemploying a fifth-order accurate MUSCL(Monotone Upstream-centered Schemes forConservation Laws) Scheme with modification tothe velocity vector as in Thornber et al. (2008).This modification adds another stage to thereconstruction process but ensures uniformdissipation of the kinetic energy to extend thevalidity of the Godunov type method to nearlyzero Mach number, whilst still preserving themonotonicity. Thornber et al. (2008)demonstrated that with this modification theleading-order kinetic energy dissipation is proportional to u3 /∆x, which is similar to that proposed by Kolmogorov for homogenousdecaying turbulence and validated this approachfor a deep cavity aero-acoustics and ship

airwakes. This dissipation rate plays the role of animplicit subgrid scale (SGS) model in the

numerical scheme. As no explicit SGS model isemployed in the code, this class of high resolutionscheme is termed as implicit large eddysimulation (ILES). Finally, time integration isachieved by using a three stage 2nd order accurate

strong-stability-preserving Runge-Kutta scheme.

2.4 Turbulent inflow boundary condition

A novel yet simple technique based upon digitalfilter for the generation of turbulence inflow datais used which is useful when only limitedturbulence data is available. The techniqueintroduced by Klein et al. (2003) assumed aGaussian form for the homogeneous turbulencecorrelation. Xie and Castro (2008) modified thetechnique by employing an exponentialcorrelation instead of Gaussian form. Thismodification has been utilized by Touber andSandham (2009) for the LES of turbulent shock-induced separation bubble. A simpler approach todigital filter based turbulent data generation

method has been implemented in CNS3D andvalidated by Rana et al. (2011b) for a case wherea sonic jet is injected into a supersonic turbulentfree-stream flow of Mach number 1.6 along withsupersonic turbulent boundary layer (STBL).Rana et al. (2011a) further investigated theaccuracy and computational efficiency of the

method by comparing it to random white noise based turbulent boundary condition. The samemethod has been utilized here to the study ofhydrogen injection into a Mach 2.5 free-stream ofair inside the HyShot-II combustion chamber in

this paper.


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3. COMPUTATIONAL DOMAIN AND

INITIALIZATION

A schematic drawing of the HyShot-II scramjet isshown in Fig. 1. It has three major parts; the inletramp, combustion chamber (combustor) andexhaust. The inlet ramp is 18° half angle wedgewith a span of 100 mm. The combustor is 9.8 mmin height and 75 mm in span with an overalllength of around 300 mm. Between the inlet rampand the combustor is a floor and two side bleeds.The purpose of the bleed is to spill the boundaryand entropy layers as well as to disgorge theshock generated by front edge of the cowl. Themain purpose of this is to make the flow insidethe combustor as smooth as possible and free ofdiscontinuities. The cowl of the HyShot-II has an

angle of 18°

on the top side. The bottom wall alsohas an angle of 16.5° at the bottom face as shownin the Fig. 1. The wall thicknesses of the inletramp, the cowl and the bottom wall are 20 mm,20 mm and 17 mm, respectively. Finally, theexhaust nozzle is simply of a divergent typenozzle.Fig. 2 presents the computational domain alongwith the boundary conditions selected for the two-dimensional analysis of the HyShot-II geometry.A structured grid technique is utilized. Table 1 presents the two grid resolutions studied for this

geometry. As explained earlier, the objective tostudy the two- dimensional full geometry is toobtain the combustion chamber inlet conditions,therefore, the non-dimensional wall distance (z+)is not very critical to this part of the study and iskept at 50 for both grids. Table 2 presents theinitial conditions utilized for the two-dimensionalanalysis by Karl et al. (2008).

The combustion chamber plan view is shown inFig. 3. Four equidistant injection holes are locatedat 58 mm from the front edge of the bottom wall

of combustor. These are holes of 2 mm diameter

to allow for the fuel (hydrogen) to be injected intothe combustor. From the two-dimensionalanalysis, the combustor inlet conditions areobtained at the x=355 mm position as shown inthe Fig. 3. Then the combustor is studied in three-dimensions and the domain selected for analysisis shown in green in Fig. 3. It consists of one fuelinjection hole which is in the center of the

domain. This arrangement is similar to those presented in the experimental studies of the sonic jet mixing with a supersonic flow stream in Ben-

Yakar et al. (2006), Gruber et al. (1995), VanLerberghe et al. (2000), Kawai and Lele (2010)

and Rana et al. (2011b), making comparison process simple. Similar to the JISC case in Rana

Fig. 1 Schematic diagram of HyShot-II scramjet.

Fig. 2 Computation flow field and boundary

conditions for HyShot-II simulation.

Table 1 Two grid resolutions used to study two-

dimensional HyShot-II geometry in order to

obtain combustor inlet conditions.

Grid Resolution

Coarse 0.13 × 106 (300 x 440)

Fine 0.53 ×106 (600 x 880)

Table 2 Averaged inflow condition for 2D Intake forflow field analysis (Karl et al., 2008).

Property Value

Angle of Attack 3.56 (degr ees)

Mach Number 7.40013

Static Pressure 1812.53 (Pa)

Temperature 242.44 (K)

Density 0.025962 (kg/ m3)

Reynolds Number 3.8E6 (m−1)

N2 Mass Fraction 7.48784E-1

N Mass Fraction 3.85178E-10

NO Mass Fraction 2.40283E-2

O2 Mass Fraction 2.27054E-1

O Mass Fraction 1.34457E-4

et al. (2011b), the Reynolds number used for thecomputations is 50,000 based upon the free-stream Mach number and the diameter (D) of theinjection port such that:

= ∞∞∞ = 5.0 × 104 (11)


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Fig. 3 Plan view of combustion chamber; 3D

domain is shown in green to cover complete

combustion chamber and includes 25 mm ofexhaust nozzle.

Fig. 4 Computational domain for combustion

chamber (CC) simulations.

Table 3 Computational meshes used for simulation of

HyShot-II combustor using ILES and digital

filters based turbulent inflow data generator.

Grid Nx Ny Nz Total

(×106 )

Ly Lz z+

Coarse 509 101 101 5.2 0.5 0.2 10

Medium 765 121 111 10.2 0.5 0.2 10

Fine 1176 141 121 20.1 0.5 0.2 10

which is six times smaller compared to theexperiment to allow for a reasonable resolution ofthe computational domain for ILES.The computational domain for the combustionchamber simulations is shown in Fig. 4 with the boundary conditions utilized, where thedimensions are normalized by the height of thecombustor. This conversion makes the x=355 mm

position equal to X/D= -26.5 and brings the X/D=0 at the center of the injection holes, making theanalysis process simpler. Three grid resolutions

are employed for the combustor analysis andTable 3 presents the details for these (where Nrepresents resolution and L represent length scalesin each direction). Due to the lack of data

available for comparison, the validity of theresults is based upon previous simulations, Ranaet al. (2011b), using the same algorithms andmethodology. The grids for the combustionchamber simulations utilized the similar non-

dimensional lengths as used in the previous study.The fine grid simulations were carried out usingnearly 7500 CPU hours on Cranfield UniversityHPC cluster “Astral” (dual-core CPU with aclock-rate of 3 GHz).

4. HYSHOT-II ANALYSIS

Two dimensional computations of the fullgeometry are performed using the initialconditions presented in Table 2 and the hightemperature gas formulation which allows forvariable ratio of specific heats (γ) for thermally perfect gas. The aim of this two dimensional work

is to understand the shock structures inside thecombustor and to obtain the initial conditions forthe three dimensional combustor simulations (at

x=355 mm or X/D= -26.5 location). Fig. 5a showsthe full geometry domain flow field along with

the shock generated at the leading tip of the inlet

ramp and Fig. 5b represents a close-up view ofthe combustion chamber inlet position showing

another shock generated at the cowl which isdisgorged through the bleed hole along with the

boundary layer generated at the inlet ramp.Another weak shock develops at the bottom wallof the combustion chamber which enters thechamber and creates a shock train inside byreflecting from top and bottom walls of the

combustion chamber. Fig. 5d shows a shock traintravelling inside the combustion chamber but asthe shock is very weak it slightly changes the

flow properties inside the chamber.Fig. 6 presents the pressure distribution on the

inlet ramp and inside the combustion chamber ofHyShot-II scramjet without any fuel injection. For

both grid levels results are in good accordancewith the experimental data by Schramm et al.(2008), but are slightly offset from the CFD dataon the inlet ramp in Fig. 6a. Pressure distributionsinside the combustion chamber are compared with

previous CFD by Karl et al. (2008) andexperimental data in Figs. 6b and c on the top and bottom walls of the combustion chamber. On bothlocations the ILES data are in excellent agreementwith the experimental and CFD data towards the

start and middle of the combustion chamber, but


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Fig. 5 Internal and external shock formations around the HyShot-II scramjet engine: (a) Two dimensional full

geometry analysis; (b) Close-up view of shock formations at bleed section and combustion chamber entranceshowing a shock generated by bottom wall and entering into combustion chamber; (c) Mach number contours

at combustion chamber entrance; and (d) Shock train travelling inside combustion chamber.

Fig. 6 Normalized pressure distributions, (a) at inlet ramp, and inside combustion chamber without fuel injection, (b)lower wall and (c) upper wall of combustion chamber.


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Fig.7 Combustion chamber inlet profiles for various flow features obtained at X = 355 mm position (or, X/D = -

26.5) as shown in Fig. 5(a & c)). These profiles are used as inflow conditions for the three dimensionalcombustion chamber simulations, (a) Velocity profile; (b) Pressure profile; and (c) Temperature profile.

some discrepancy can be observed in the datatowards the end of the combustion chamber, stillit captures same number of shockwaves travellinginside it shown by the peaks in the pressure

distributions.The combustion chamber flow properties arecaptured at X=355 mm (or X/D= -26.5) as shownin Fig. 7 which are used as initial conditions forthree dimensional combustion chamber

simulations along with hydrogen fuel injection.Both grid level data are presented for the velocity

profiles, temperature and pressure distributions atthe X/D= -26.5D location. Slight discrepancy inthe data can be observed for the coarse grid level but the fine grid level is a nice match to the previous CFD data obtained at DLR (Germany).

The shock-train travelling inside the combustionchamber can be observed by the jump in the three profiles. These data are used along with thesediscontinuities in the profiles in order to simulatethe combustion chamber with the shock train, as itis anticipated that this shock train helps trigger themixing process when the fuel is injected into the

combustion chamber.

5. COMBUSTION CHAMBER ANALYSIS

The flow of hydrogen inside the combustion

chamber is sonic with standard density,temperature and pressure as per condition used inDLR (Schramm et al., 2008; Karl et al., 2008). Acircular (hydrogen) jet transverse to the free-stream turbulent supersonic air flow is generally

termed jet injection into a supersonic cross-flow.Typical features of JISC are lambda, bow and barrel shocks, Mach disc, horseshoe vortices andcounter-rotating vortices (CRVs). Rana et al.(2011b) demonstrated that without the supersonic

turbulent boundary layer (STBL) in the incoming

flow upstream the jet injection the lambda shockin front of the bow shock cannot be capturedcorrectly. Therefore, the STBL in the incomingflow has been simulated using a digital filter based synthetic turbulence inflow data generator

(Klein et al., 2003; Xie and Castro, 2008; Touberand Sandham, 2009) which has been validatedfor a similar JISC case (Rana et al., 2011b) atMach 1.6 where the results have been comparedwith the previous LES (Kawai and Lele, 2010)

and experimental data (Santiago and Dutton ,1997; Everett et al., 1998; Van Lerberghe et al. ,

2000). As no experimental or CFD data areavailable in order to compare the results ofhydrogen injection into the HyShot-II combustionchamber without combustion, the results presented in this article base their validity upon

the earlier validation cases.Fig. 8 presents time-averaged three-dimensionalflow structures of hydrogen injection in theHyShot-II combustion chamber using the Q-criterion. When the circular jet of fuel is injected,

it generates a horseshoe vortex upstream of the jetinjection port and a pair of CRVs which runsdownstream the jet plume. Fig. 8 shows that theseCRVs have distorted after X/D= 15~20 which isan interesting finding and will be discussed later.

Also shown is the bow shock being reflected fromthe top wall of the combustion chamber andcreating a train of bow shocks downstream. Fromaround X/D ~ 20 the flow does not show anyclear structures and is a very complex mix ofvarious flow features which are interacting witheach other and enhancing the flow mixing. Theflow development in the combustion chamber isdiscussed below. Fig. 9 shows the time-averagedthree-dimensional Mach contours at various


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Fig. 8 Time averaged three dimensional flow structure using Q-criterion showing various JISC flow structures inside

HyShot-II combustion chamber.

Fig. 9 Three dimensional Mach contours showing

flow development as hydrogen jet is injected

inside HyShot-II combustion chamber.

Fig. 10 Time history of instantaneous pressure

signature within upstream recirculation region

for non-dimensional time between 120 and

150.

locations showing averaged flow development asthe hydrogen jet is injected inside the combustion

chamber.

5.1 Instantaneous flow

Before discussing various time-averaged flowfeatures and flow mixing, in this section,instantaneous flow has been analyzed tounderstand the flow development inside thecombustion chamber. Fig. 10 shows theinstantaneous pressure signature at a point withinthe upstream recirculation zone (X/D, Y/D, Z/D)= (-0.8, 0, 0.25) for a non-dimensional time (τ ) between 120 and 150 for all three grid levels. Thisis the point where the instantaneous flow featuressuch as KH (Kelvin-Helmholtz) instabilitiesoriginate as the supersonic inflow hits the jet

plume. As discussed (Rana et al., 2011b) thefluctuations in the pressure signature occurs withthe KH instabilities. For all grid levels similarlevels of pressure peaks are observed in Fig. 10.Fig. 11 presents instantaneous snapshots of the jetfluid volume fraction on the mid plane (Y/D= 0)for the three grid levels where the gridimprovement effects are clearly visible by thecapture of small scale coherent structures at the“fine” grid level.Fig. 12 presents the instantaneous flowdevelopment at another non-dimensional time (τ =148.57) at various locations on the “fine” gridlevel. On the wall-normal mid plane (Y/D= 0) theflow mixing occurs instantaneously as soon as the


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Fig. 11 Instantaneous snapshots of jet fluid volume fraction at t = 120.21 on mid plane (Y/D = 0) for three grid levels.

Fig.12 Instantaneous views of jet fluid volume fraction presenting flow development inside HyShot-II combustion

chamber at t = 148.57 on mid plane (Y/D = 0) and wall-normal planes (X/D = 1, 3, 5 15 and 90) for “fine”grid.


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Fig. 13 Energy spectra at various locations upstream and downstream of jet plume. The “p” represents the point

locations as (X/D,Y/D,Z/D) for each point.

jet of hydrogen is injected into the mainstreamflow. Traces of hydrogen can be visualizedentrained in the upstream recirculation zone

which can be helpful in early combustion ofhydrogen. On the spanwise wall-normal planes atvarious locations (X/D= 1, 3, 5, 15 and 90) theflow mixing is developing gradually. Initiallymaximum fuel concentration is in the path of the

jet plume, where the CRVs can be seenoriginating. Gradually as the flow develops thehydrogen volume fraction is filling in the space

around the CRVs as the CRVs trigger thespanwise fluid mixing. It has been establishedearlier by Karl et al. (2008) that the inflow for fullgeometry of HyShot-II and the combustionchamber is highly two-dimensional, but as soon


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as the hydrogen jet is injected and the mixing process starts, the flow becomes highly three-dimensional as shown in Figs. 12b to f.Energy spectra at various upstream anddownstream locations are presented in Fig. 13against the Strouhal number (St) for the three gridlevels. The spectra have been obtained using FFT(Fast Fourier Transform) and sample data have been obtained at each time step. Two points, p1and p2, are selected in the incoming STBL on theupstream of the jet plume, two points, p3 and p4,are around the jet plume where the KHinstabilities are being generated, point p5 is the inthe downstream location close to the jet plumeand finally the point p6 is downstream away fromthe jet plume, all on the mid plane (Y/D = 0) for

all grid levels. The spectra at the points p1 and p2

present reasonable generation of energy with theSTBL but as the flow is dominated by the viscousforces close to the wall excessive dissipation can be observed as well. The points p3 and p4 arewithin the shear layer flow areas and demonstratereasonable match to an ideal energy spectrum.Overall, the energy spectra at all the pointsdemonstrate the trends in accordance with theKolmogorov’s k

-5/3 trend showing clear

production regions in the highest wavenumberrange (or low Strouhal number), clear inertialsubrange for medium wavenumbers and

prominent dissipation range. Similar findingshave also been reported in the references

(Drikakis et al., 2007; Grinstein et al., 2011).

5.2 Jet penetration

In this, and the following, sections the time-averaged flow inside the combustion chamber isanalyzed. The time-averaged data presented herehas been obtained for a non-dimensional time (τ ~160) by averaging 2000 instantaneous equi-timestep files. The trajectory of maximum jet

concentration has been obtained by using acorrelation, Equation (12), proposed byAbramovich (1963), which has also been used byOrth and Funk (1967) in their experiments to

study the jet penetration in supersonic flow wherethey demonstrated that the Equation (12) agrees“reasonably well with the experimental values forX/D ≤ 8.

=

0.434 0.333

(12)

where P represents the dynamic pressure and the

subscripts j and c represent the jet and cross-flow,respectively. Fig. 14 presents the jet trajectory ascalculated using Equation (12) on the wall-normal

Fig.14 Jet penetration shown as curve for trajectoryof maximum hydrogen concentration on wall-

normal mid plane (Y/D=0).

Fig. 15 Time averaged Mach number and hydrogen

volume fraction (passive scalar) inside

combustion chamber at wall-normal mid

plane (Y/D = 0) along with streamlines.

mid plane (Z/D= 0). It can be noticed that thetrajectory is a nice curve from the jet orifice tillthe Mach disc and after the Mach disc it isrunning in almost a straight path parallel to the bottom wall of the combustion chamber. Thestraight path in the trajectory can be due to low

jet-to-cross-flow momentum flux ratio (Schetzand Billig, 1966) (J ~ 0.3). This low value of Jforces the jet plume to bend in the direction offlow and does not allow much penetration of the

jet plume which results in the jet trajectory beingalmost horizontal and closer to the bottom plate ofthe combustor.


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5.3 Velocity field

Figs. 15 and 16 show time-averaged Mach

number and hydrogen volume fraction (passivescalar) contours inside the combustion chamber atdifferent locations along with the streamlines to

understand the flow. Figs. 15a and b are thecontour plots on the wall normal mid plane (Y/D

= 0). As the fuel is injected it acts as a barrier tothe free-stream flow and resulting major flowfeatures can be identified like the lambda, bowand barrel shocks on the mid plane. The lambda

shock interacts with the incoming STBL ataround X/D ~ 4 location. The fuel jet immediatelyturns into the free-stream flow direction. There isa large recirculation zone in front of the fuel port

which entrains some fuel inside it. Provided thetemperature is high enough and appropriateignition time of hydrogen, this entrained fuel inthe recirculation zone could lead to earlycombustion which is important as the residence

time of fuel inside the combustion chamber is ofthe order of 2-4 ms.

Fig. 16 Time averaged Mach number and hydrogen volume fraction (passive scalar) inside the combustion chamber at

cross-flow planes (X/D = 1, 3, 5, 15 and 90) along with streamlines (contour legend same as shown in Fig.

15).


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Fig. 17 Normalized stream-wise velocity profiles at various locations on wall-normal mid plane (Y/D = 0).

Downstream of the jet injection two regions can be clearly seen for the fuel and air separately inFig. 15b which emphasize the point that the jetexpansion is restricted in this area and two fluidsmix only in the lower half of the combustionchamber. This is the region where a pair of CRVsis developing and resulting in enhancedlongitudinal and spanwise mixing of the twofluids. The feature of these CRVs that enhancesthe fluid mixing is the counter-rotation which

“stirs” the two fluid together and creates a largerarea of mixing on the top and sides of CRVs. Fig.16 shows the contours plots on the wall-normalcross-view planes (X/D= 1, 3, 5, 15 and 90)demonstrating the development of the CRVs.Initially, the time-averaged flow is highlysymmetrical and the two CRVs start immediatelyafter the hydrogen jet injection as shown in Fig.16a at X/D=1 location.


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Fig. 18 Normalized wall-normal velocity profiles at various locations on wall-normal mid plane (Y/D = 0).

Figs. 16c to e show the growth of the CRVs atfurther downstream locations. At these locationsthe reflected shocks from the top and bottomwalls of the combustion chamber interact with the

CRVs to disrupt and weakens them. This alsocauses the CRVs to distort considerably as shownin Fig. 16g at location X/D= 15. A pair of trailingCRVs (TCRVs) also emerges at location X/D = 5, below the major CRVs, which has grown in size

at location X/D= 15. All these CRVs act to

enhance the mixing mechanism closer to jetinjection which is demonstrated by the jet passive

scalar contours at the respective locations. Furtherdownstream the combustion chamber at location

X/D = 90, we do not see clear CRVs or trailingCRVs.Figs. 17 and 18 show the streamwise and wall-

normal velocities on the wall-normal mid plane(Y/D= 0) at various locations throughout the

combustion chamber downstream of the hydrogen


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Fig. 19 Hydrogen volume fraction (H2 V.F.) profiles at various locations on wall-normal mid plane (Y/D = 0); (Linelegend same as in Fig. 18).

jet injection. From the Mach number contours inFig. 15a we understand that there is arecirculation zone downstream of the jet injection.This has been validated by the streamwisevelocity profile at location X/D= 1 in Fig. 17a aswell. At location X/D= 3 the recirculation zone is

not visible but there are kinks in the streamwisevelocity profiles due to the CRVs. Similarly, Fig.18 shows changes in the wall-normal velocity

profiles at the corresponding locations. It isobserved from these profiles that the CRVs arestronger closer to the jet injection port, furtherdownstream they are increasing in size and alsogaining height with the jet trajectory, but arelosing wall-normal velocities. The streamwise

velocity profiles are becoming more symmetricsimilar to a channel type flow. The CRVs aremainly acting in the region between X/D= 1 to


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Fig. 20 Normalized longitudinal pressure profiles on bottom wall of combustion chamber after hydrogen injection at

various locations on wall (Y/D = 0, 1, 2, 3 and 4).

X/D~ 15, after which they disappear and the flow becomes highly symmetrical especially from X/D= 20 and onwards.Fig. 19 shows the hydrogen volume fraction atvarious locations on the wall-normal mid plane(Y/D= 0). It can be seen that the hydrogen

concentration is maximum closer to the injection port but it occupies less area whereas it decreases

away from injection point but occupies more area.The auto-ignition temperature of hydrogen in airis nearly 800 K and it forms a flammable mixture

when the concentration of hydrogen gas is 4-74%in air. It is clearly seen that the hydrogenconcentration on the wall-normal mid plane (Y/D= 0) is well within the limits of a flammablemixture and as the temperature inside the HyShot-II combustion chamber is above 1000 K, thismixture would begin to burn depending upon theauto-ignition time to hydrogen in this particular case. The contour plots of hydrogen concentrationin Figs. 16b, d, f, h and j indicate similar phenomenon that spreads throughout thecombustion chamber further downstream.

5.4 Pressure distributions

Time-averaged pressure distributions have been plotted in the Figs. 20 and 21 inside thecombustion chamber on the bottom and top walls,respectively. Comparing these figures to the pressure distributions plot (without fuel injection)

in Fig. 6 it is noted that the pressure on the top

and bottom walls inside the combustion chamberhas increased, but at the same time the intensity ofthe shock waves travelling inside the combustionchamber is decreased especially towards the end

of the combustion chamber. This is due to the factthat the shocks interact with the pair of CRVs inthe region between X/D= 0 to X/D= 20 whichweakens the shocks and breaks up the CRVs aswell. It is also noticed that close to the injection port, the pressure distribution is smooth on the bottom wall but it is fluctuating on the top wall onthe mid line plane (Y/D= 0), which is due to the

bow shock hitting the top wall of the combustionchamber. Away from the mid plane at locationY/D= 3, close to the injection port the pressure


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Fig. 21 Normalized longitudinal pressure profiles on top wall of combustion chamber after hydrogen injection at

various locations on wall (Y/D = 0, 1, 2, 3 and 4).

Fig. 22 Time averaged turbulent kinetic energy andReynolds shear-stress contours inside

combustion chamber at wall-normal mid

plane (Y/D = 0) along with streamlines.

distribution fluctuates on the bottom wall due tothe horseshoe vortex covering a wide area but it issmooth on the top wall as it is not affected by the bow shock far away from the mid line plane.

5.5 Turbulent kinetic energy and Reynolds

stresses

The contours of time-averaged turbulent kinetic

energy (TKE) are calculated as:

= ′ ′ + ′ ′ + ′ ′ 2∞2 (13)

and the Reynolds shear-stress as

= ′ ′ ⁄ (∞2 ) (14)where both are non-dimensionalised by the free-stream velocity, are presented in Figs. 22 and 23at various locations in the flow field. Fig. 22

presents TKE and RS at the wall-normal mid plane (Y/D= 0). There are three high TKE zonesclearly visible; one is in the upstream region inthe recirculation zone and the others downstreamof the jet injection port. The higher TKE region


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Fig. 23 Time averaged turbulent kinetic energy and Reynolds shear-stress contours inside combustion chamber at

cross-flow planes (X/D = 1, 3, 5, 15 and 90) along with streamlines (contour legend same as shown in Fig.

22).

upstream of the jet plume corresponds to therecirculation region upstream and generation ofthe KH instabilities in this region. The high TKEregion downstream of the jet plume is related tothe fluctuations in the leeward side of the jet

plume. It can also be noted that TKE dissipationincreases very rapidly after X/D= 5 position.

At the same time, there are two high RS regions,one upstream and the other downstream of the jetinjection port but both of them are in opposite

directions. The negative RS region upstream ofthe jet injection port corresponds to high activityin the jet shear layer region where the mixing

starts. This is due to the Kelvin-Helmholtz typeinstabilities generating in the jet shear layer

region which are shown earlier in Section 5.1.Fig. 23 shows TKE and RS at the wall-normal

cross-view planes (X/D= 1, 3, 5, 15 and 90)where very strong RS are visible in the region ofCRVs indicating strong vortex generation and


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Fig. 24 Turbulent kinetic energy (TKE) profiles at various locations on wall-normal mid plane (Y/D = 0); (Line

legend same as in Fig. 18).

away from jet plume RS decreases. The TKEcontours plots indicate that maximum TKEregion is close to the jet injection port and awayfrom it TKE dissipates very quickly; at locationX/D= 5 there is much less TKE visible and atlocation X/D= 90 some TKE is present only in theturbulent boundary layer region.The RS plots in Fig. 23 show that strong RS (butin opposite directions) are present in the pair ofCRVs region which dissipates gradually at

locations X/D= 15. This is because in this articlethe RS is presented for the streamwise and thespanwise velocity components as opposed to thestreamwise and wall-normal velocity componentsin Rana et al. (2011b). Similar to the TKE, thereis very little RS present at far away locationdownstream of the jet injection at X/D= 90. Thisanalysis indicates that maximum mixing takes place in the jet shear layer and just downstream ofthe jet injection ports, and the flow is fully


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Fig. 25 Reynolds shear-stress (RS) profiles at various locations on the wall-normal mid plane (Y/D = 0); (Line legend

same as in Fig. 18).

developed at around X/D ~ 20 after which most ofthe chemical reaction would take placethroughout the rest of the combustion chamberlength. Long combustion chamber and small auto-ignition time of hydrogen can help combustion process but it would depend upon the residencetime of the flow inside the combustion chambermainly.

Figs. 24 and 25 show quantitative plots of theTKE and RS at the Y/D= 0 plane at various X/Dlocations, verifying the finding discussed above.

Note that the TKE and RS plot at location X/D= 5are very different from those at location X/D= 90.Based upon this discussion the whole length ofthe HyShot-II combustion chamber can bedivided into three separate regions. First regionfrom the injection port up to X/D= 5 locationwhere maximum mixing is taking place. Thesecond region is up to location X/D ~ 20 where

the flow has released most of its TKE and finallythe rest of the length of the combustion chamberwhere full combustion would take place.


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Fig. 26 Time averaged temperature and RMS contours of fluctuations in hydrogen volume fraction (passive scalar)

inside combustion chamber at wall-normal mid plane (Y/D = 0) along with streamlines.

Fig. 27 Time averaged temperature and RMS contours of fluctuations in hydrogen volume fraction (passive scalar)inside combustion chamber at crossflow planes (X/D = 1, 3, 5, 15 and 90) along with streamlines (contour

legend same as shown in Fig. 26).


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Fig. 28 RMS of fluctuations in hydrogen volume fraction (passive scalar) profiles at various locations on wall-normal

mid plane (Y/D = 0); (Line legend same as in Fig. 18).

5.6 Temperature profiles and flow mixing

Figs. 26 and 27 represent the contour plots of thetemperature and the root mean square (RMS) offluctuations in the hydrogen volume fraction atvarious locations in the flow field. These contour plots illustrate the major mixing zones inside the

combustion chamber and indicative temperaturesin these areas. Again, it is noted from Figs. 26band 27b that the majority of the mixing is

occurring in the windward side of the hydrogen jet plume. Temperature contours at these

locations indicate that this region is well withinthe auto-ignition temperature range and thuscombustion process would start immediately in

these areas. It can also be observed from Figs. 26a

and b that there is some hydrogen and air mixingin the upstream recirculation zone. This is the boundary layer region where the temperature is


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Fig. 29 Temperature profiles at various locations on wall-normal mid plane (Y/D = 0).

very high as indicated by the temperaturecontours. Therefore, it is understood that earlycombustion would start in the upstreamrecirculation zone, which is very helpfulconsidering short residence time of air-fuelmixture inside the combustor.Figs. 28 and 29 present quantitative results of the

RMS of the fluctuations in the hydrogen volumefraction and the temperature profiles on the wallnormal mid plane (Y/D= 0) at various locations.

Downstream from the jet plume, the mixing areais increasing gradually and the temperatureremains well above the auto-ignition temperature.It can be noted that the jet shear layer is an area ofmaximum activity. This is the area where the KHinstabilities are generated as discussed earlier.Some mixing is also occurring in the boundary

layer area just downstream of the jet injection portwhich is the leeward side of the jet plume. Adetailed analysis in this area has been presented


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Fig. 30 Percentage of hydrogen-air mixture within

flammability range on wall-normal mid plane

(Y/D = 0). In the close-up view the dashed

blue line shows the location of the injectionhole.

Fig. 31 Schematic diagram of HyShot-II scramjet.

Rana et al. (2011b) where slight fluctuation in theleeward side of barrel shock results in somemixing in this area. Considering that thetemperature is high enough in the this area and

the boundary layer region, combustion all aroundthe jet plume is expected as soon as the hydrogenis injected inside the combustion.Far downstream the jet plume, the mixing area

expands in size covering almost the entire slice inFigs. 27d, f, h and j which is also demonstrated bythe RMS plots in Fig. 28 showing reducing RMS but an increase of the area it occupies. As notmuch activity (TKE, RS etc.,) has been identifiedin this area, this will be the area where full

combustion/chemical reactions should be taking place for the entire length of the combustion

chamber. It can be deduced from the analysis thatfor the HyShot-II scramjet, the length of thecombustion chamber and the spanwise distance between the injection ports allows for proper

mixing of hydrogen and air inside the combustionchamber. Fig. 30 shows the percentage of air-fuelmixture within the flammability range on the

wall-normal mid plane (Y/D= 0). It can be seen inFig. 30 that the hydrogen entrained in the

upstream recirculation zone is within theflammability range and would help start early

ignition. The extent to how complete thecombustion process would be depends upon theresidence time of the air-fuel mixture inside the

combustion chamber and requires chemicalanalysis in details. Based upon the Fig. 30 and the

analysis of the HyShot-II combustion chamber,the chamber can be divided into three sections asin Fig. 31. Part one is from upstream recirculation

zone to X/D ~ 5 where most of the mixing isoccurring and high TKE and RS regions are

found which is also the region where CRVs andthe shocks act to enhance the mixing mechanism.

Second part can be up to X/D ~ 30 where the

major flow features dissipate away and lastly thethird part is the rest of the combustion chamber

where full mixing has achieved and full andthorough combustion should be observed. This

methodology of analyzing cold fuel flow inside acombustion chamber can be implemented at thedesign stage of a scramjet combustion chamber.

6. CONCLUSIONS

In this paper a complex multi-species flowoutside and inside the HyShot-II scramjet engine

has been analyzed. The supersonic turbulent boundary layer has been generated using a digital

filter based turbulent inflow data generationmethod which has been validated for a similar

case previously. The emphasis of this study wasthe fuel injection, penetration and mixing insidethe HyShot-II combustion chamber without anychemical reactions in order to understand the flowfeatures and properties. As no experimental or

CFD result are available to compare the data, thevalidity of the results for the combustionchamber are based upon the results presented

earlier, where exactly same methodology has beenimplemented and the results were compared with

the experimental and previous LES data.Important findings of the analysis are itemized below:

The internal and external flow around theHyShot-II scramjet consists of very complexshock structures and the air can be described asa thermally perfect gas because of the increasein the temperature of the air as it is compressedagainst the inlet ramp. The bleed region just

ahead of the combustor helps disgorge the boundary layer and shocks and clean thecombustor inflow, but there is a weak shock


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train running inside the combustor which isgenerated at the front edge of the bottom wallof combustor.

The jet penetration greatly depends upon the

jet-to-crossflow momentum flux ratio. As for

the sonic hydrogen injection case, this is verylow and the jet plume is distorted by the high

momentum of the incoming supersonicturbulent boundary layer giving a jet trajectory

close to horizontal.

Hydrogen is entrained in the recirculationregion upstream the jet plume and because thetemperature in this region is well above theauto-ignition temperature of hydrogen-airmixture, combustion would start in theupstream region of jet plume.

A pair of counter rotating vortices is generated just after the jet injection, but due to theinteraction with the shock train inside thecombustor the CRVs are distorted and afterX/D ~ 20 it is not clear if coherent counter

rotating vortices are present in the flow.

Around the jet plume the area of maximum

mixing is the leading edge of the jet shearlayer. The interaction of counter rotatingvortices with the shocks enhances the mixing process for hydrogen and air in the downstream

of jet plume. Maximum turbulent kinetic energy and

Reynolds shear-stresses are present in theregion closer to the jet plume (upstream anddownstream). Downstream the jet atapproximately X/D= 5 the TKE and RS start todissipate very quickly.

ACKNOWLEDGEMENTS

The simulations presented in this article have

been carried out on Cranfield University’s Astral supercomputer. The authors would like toacknowledge the financial support for this project

from EPSRC under the Doctoral TrainingAccounts (DTA) scheme.

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dynamics of sonic hydrogen jet injection and mixing

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