hydrogen/air supersonic combustion for future hypersonic vehicles

i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n en e r g y 3 6 ( 2 0 1 1 ) 1 1 9 6 9e1 1 9 8 4

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Hydrogen/air supersonic combustion for future hypersonicvehicles

D. Cecere a,*, A. Ingenito b, E. Giacomazzi a, L. Romagnosi a, C. Bruno b

a Sustainable Combustion Laboratory, ENEA, Rome, ItalybUniversity of Rome Sapienza, Rome, Italy

a r t i c l e i n f o

Article history:

Received 3 March 2011

Received in revised form

6 June 2011

Accepted 7 June 2011

Available online 18 July 2011

Keywords:

Supersonic combustion

Large Eddy simulation

Hydrogen combustion

* Corresponding author.E-mail address: [email protected] (D

0360-3199/$ e see front matter Copyright ªdoi:10.1016/j.ijhydene.2011.06.051

a b s t r a c t

In this work, supersonic hydrogen combustion in the Hyshot II scramjet engine is inves-

tigated. In particular, fundamental physics of mixing, combustion and vorticity generation

as well as the interaction between shock waves, boundary layer and heat release are

analyzed by means of 3D Large Eddy Simulations (LES) using detailed chemistry. Results

show very complex structures due to the interaction between the four sonic H2 crossflow

injections and the airstream flowing at M ¼ 2.79. A bow shock forms ahead of each H2

injector: the interaction between bow shocks and boundary layers leads to separation

zones where H2 recirculates. In these recirculation zones, OH radicals are produced, indi-

cating that a flame already starts upstream of the injectors and downstream of the flow

separation. The formation of barrel shocks due to the H2 expansion and recompressions is

also predicted. Comparison of pressure distribution along the wall centreline at 1.3 ms

shows agreement with experimental results, mostly in the first part of the combustor,

where the grid is very fine. The combustion is very fast and efficient: only 12.35% of

hydrogen is found unburned at the combustor exit. This confirms that burning hydrogen is

efficient and feasible also in supersonic flows and therefore it is a good candidate for

hypersonic airbreathing applications.

Copyright ª 2011, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights

reserved.

1. Introduction Tinlet ¼ TNð1þ ðg� 1=2ÞM2ÞxTN � 12:55 ¼ 2761 K. At these

The challenge of hypersonic vehicles for long-range passenger

transportation or for space applications requires the devel-

opment of efficient propulsion systems. In the hypersonic

flight regime, a supersonic combustion ramjet, i.e. a scramjet

(SCRJ), is preferred to a classical ramjet [1], in fact, at these

flight speeds, decelerating air to M < 1 increases significantly

the total pressure drop and flow temperatures within the

combustor. Assuming, in fact, a flight Mach of 7.6 and an

altitude of 28,000 m (TN ¼ 220 K, PN ¼ 4 kPa), the static

temperature at the combustor inlet is approximately given by

. Cecere).2011, Hydrogen Energy P

temperatures, material issues and chemical dissociation

effects are presented [2,3]. In a SCRJ, the air flow captured by

the inlet is decelerated but still stays supersonic (M w 2e4).

Since in a scramjet the residence time is very short (w1ms)

mixing of reactants, ignition, flame holding, and completion

of combustion are critical issues [4]. Therefore, it is necessary

to investigate the physical mechanisms together with high

reaction rate fuels that affect the mixing and combustion

efficiency in scramjet engines.

Theoretical work by these authors [5] has shown that

mixing can be accelerated by increasing streamwise vorticity:

ublications, LLC. Published by Elsevier Ltd. All rights reserved.

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http://dx.doi.org/10.1016/j.ijhydene.2011.06.051



Nomenclature

u* wall friction velocity

yþ wall units distance

t time, s

d H2 injection diameter, m

r density, kg m�3

ui i-th velocity component, m s�1

S stress tensor, kg m�1 s�2

Yn mass fraction of species n, e

U total energy, J kg�1

ksgs subgrid kinetic energy, m2 s�2

qi i-th heat flux component, J m�2 s�1

Vi,n i-th diffusion velocity component of n-th species,

m s�1

Jn n-th chemical species diffusive mass flux,

kg m�2 s�1

_un production/destruction rate of n-th species,

kg m�3 s�1

p pressure, Pa

Wn n-th species molecular weight, kgmol�1

Ru universal gas constant, ¼8.314, J mol�1 K�1

T temperature, K

Ns number of chemical species

H specific enthalpy, sum of formation and sensible,

J kg�1

m dynamic molecular viscosity, kg m�1 s�1

n kinematic viscosity, m2 s�1

mt turbulent viscosity, kg m�1 s�1

s viscous stress tensor, kg m�1 s�2

Dn n-th species mass diffusion, m2 s�1

Dt,n turbulent mass diffusivity of n-th species, m2 s�1

K thermal conductivity coefficient, J m�1 K�1 s�1

h Kolmogorov dissipative length scale, m

D filter size or grid spacing, m

u vorticity, s�1

u0 velocity fluctuation, m s�1

M Mach number, ¼U/a, e

xi i-th grid component, meðÞ Favre filtering

ðÞ Reynolds filtering

i n t e rn a t i o n a l j o u r n a l o f h y d r o g e n en e r g y 3 6 ( 2 0 1 1 ) 1 1 9 6 9e1 1 9 8 411970

this can be obtained by favouring the formation of pressure

and density gradients, e.g., by means of different injector

designs, such as transverse injectors [6], swirl injectors [7,8],

strut injectors [9], wall injectors [10], swept ramp injectors [11].

In order to have an efficient combustion within a finite engine

length, a fuel with very fast kinetics is required. Hydrogen

gives the highest heat release with the shortest kinetic time. It

is also clearly superior as coolant for operation at high flight

speeds and at combustor high temperatures [3]. Hydrogen is

already used as fuel in space propulsion due to its high energy

release when burning with oxygen (119.6 MJ/kg compared

with that of common and long chain hydrocarbons

w43 MJ/kg), and for its high reactivity [12] (see Table 1).

Its lowmolecular weight makes it the fuel with the higher-

specific impulse (ISP),w450 s: technically speaking, thismeans

that burning 1 kg/s of hydrogenwith oxygen produces a thrust

Table 1 e Fuels properties.

H2

Molecular Weight 2.016

Heat of combustion (low) [kJ g�1] 120

Liquid density [g cm�3] 0.071*

Boiling point, at 1 atm [K] 20.27

ISP fuel/O2 vacuum [s] 450

Heat capacity [J g�1 K�1] 9.69

Heat of vaporation [J g�1] 446

Diffusion vel. in NTP air [m s�1] �2.00

Flammability limits in air, vol % 4.0 to 75.0

Min. ignition energy in air [mJ] 0.02

Autoignition temp. [K] 858

Burning vel in NTP air [cm s�1] 265 to 325

Min. ignition energy in air [mJ] 0.02

Flame Temp. in air ðf ¼ 1Þ, [K] 2318

* At normal boiling point; NTP ¼ normal temperature and pressure.

Source: G. Brewer et al. (1981) [13], R. McCarty et al. (1981), ASTMD-1655-80

of 450 kgforce. Other positive features are the wide flamma-

bility limits (4e74% by volume in air) and the high diffusivity.

There are some drawbacks when using hydrogen as fuel in

aerospace vehicles: at standard pressure and temperature, H2

has a density of only 0.09 kg/m3 compared to the density of

gasoline, 750 kg/m3, or JP-8, 800 kg/m3. This is why hydrogen is

typically stored under cryogenic conditions. In addition,

hydrogen production is still very expensivewhen compared to

that of conventional hydrocarbons. Despite these limitations,

the hydrogen is the best candidate for aerospace propulsion

and future hypersonic airbreathing launchers and trans-

atmospheric aircrafts [13e15]. Recently, much work has

promoted hydrogen as a fuel also in the public transportation

industry thanks to its advantage over hydrocarbon-based

fuels like JP-8 or gasoline, since it does not produce any

harmful pollutants like carbonmonoxide (CO), carbon dioxide

CH4 Jet-A JP-4

16.04 w168 w132

50.0 42.8 42.8

0.423* w0.811 w0.774

112 440 to 539 333 to 519

300 290 270

3.50 1.98 2.04

510 360 344

�0.51 <0.71 <0.71

5.3 to 15.0 0.6 to 4.7 0.8 to 5.8

0.29 0.25 0.25

813 >500 >500

37 to 45 18 381

0.29 0.25 0.25

2148 2200 2200

a Jet-A, Mil-T-5624L, EXXON (1973), J. Kuchta (1973), H. Barnett (1956).



Table 2 e Combustor inlet flow conditions.

Air inlet Fuel inlet

Pressure [Pa] 82,210 307340

Mach no. 2.79 1

Density [kg/m3] 0.2358 0.3020

Temperature [K] 1229 250

Sound speed [m/s] 682.9 1204.4

Flow velocity [m/s] 1905.291 1204.4

i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n en e r g y 3 6 ( 2 0 1 1 ) 1 1 9 6 9e1 1 9 8 4 11971

(CO2), or particulate matter during the combustion process

[12]. This said, production of NOx emissions when burning

hydrogen with air is still an issue to be investigated, although

the short residence time in supersonic combustors suggests

low NOx production.

Scramjet combustion experiments are very complicated,

and only few limited run-time facilities are available. One of

the recent successful hydrogen-fuelled scramjets flight test is

the X-43A launched on 27March 2004 [16]. The X-43A is part of

NASA’s Hyper-X program to develop new airbreathing pro-

pulsion systems for use in hypersonic flight [17]. In 2002 the

Australian HyShot program successfully showed the feasi-

bility of hydrogen-fuelled scramjet combustion [18]; more

hypersonic vehicles have been tested (Hyfire, on March 2010

and X-51A on May 26, 2010). EU is also funding a project

(“LAPCAT II”) [19] to study the feasibility of a long-range

hypersonic commercial transport using hydrogen as fuel: thus

understanding how to improve hydrogen combustion under

supersonic conditions is critical to transform research into

technology.

Due to experimental difficulties in measuring complex

high-speed unsteady flowfields, the most convenient way to

understand unsteady features of supersonic mixing and

combustion lies in the use of computational fluid dynamics. In

this context, a 3D LES of the HyShot II combustor has been

carried out to investigate the physics of supersonic combus-

tion and the potential and performance of hydrogen as fuel.

The complexity of physics involved makes the problem of

Fig. 1 e Hyshot schematic; portion of the co

considerable interest also from a numerical point of view. To

the author’s knowledge, beside the present article there is

only another numerical work providing a Large Eddy Simula-

tion of the Hyshot II combustor, although at different condi-

tions (altitude of 35 km and 3.8� angle-of-attack) [20]. The

introduction of detailed chemistry (scheme of Warnatz

including 9 species and 38 reactions to account for radicals

formation [21]) results in more expensive computer run times

and storage requirements. High velocity and density gradi-

ents, and high hydrogen diffusivity also poses some numer-

ical critical issues. To solve them, a specific hybrid method is

adopted in this work to capture shocks without introducing

numerical oscillations and, to resolve turbulent structures

away from discontinuities with low dissipation.

2. The numerical simulations of HyShot IISCRJ combustor

The goal of the HyShot research program at the University of

Queensland was to demonstrate the feasibility of igniting and

maintaining supersonic combustion under realistic flight

conditions, and to compare results with similar shock tunnel

experiments. The HyShot launches used a two stage Terrier-

Orion Mk70 rocket to boost the payload and the empty Orion

motor to an apogee of approximately 330 km; as the spent

motor and its attached payload falls back to Earth, the vehicle

is then accelerated. The trajectory is designed so that between

23 km and 35 km the flightMach number is 7.6. It is during this

part of the trajectory that the measurements of supersonic

combustion are made. In the present work, numerical results

are validated with ground test experimental results repro-

ducing the flight conditions at 28 km andM¼ 7.6 and 0� angle-of-attack [22] (see Table 2); the global equivalence ratio is

0.426. Fig. 1 shows in blue the portion of the combustor

simulated in the present work.

The model used for the pre-flight ground tests (Fig. 1),

consists of a rectangular air intake 30.5 cm long and 10.0 cm

wide, a combustor 30.0 cm long and 7.5 cm wide and 0.98 cm

mbustion chamber simulated in blue.




high, a thrust plate 20.0 cm long � 7.5 cm wide. This model

was designed to generate similar combustor entrance condi-

tions to flight at Mach 7.6, while using an existing Mach 6.5

shock tunnel nozzle. This dictated the use of an experimental

model with a 17 wedge intake (compared to 18 in the flight

payload) and shock tunnel nozzle exit conditions with higher

freestreampressure than flight. The 30.0 cm length combustor

and fuel injectors were identical to those used in flight, except

that fuel injection took place 4.0 cm downstream of the

combustor entrance (compared to 5.8 cm in flight), and the

ground test model had larger number of combustor pressure

taps. In fact, the combustor hosts 16 pressure transducers

starting from 9.0 cm downstream of the combustor leading

edge. Distance betweennearby pressure transducers is 1.3 cm.

A final difference between the ground and flight hardwarewas

that the nozzle expansion was situated on the bodyside of the

combustor for ground test (compared to the cowlside for the

flight hardware). The thrust plate is at 12 with respect to the

airstream path and is equipped with 11 pressure transducers

1.1 cm downstream of the combustor exit. The gaseous

hydrogen is injected in crossflowwith respect to the incoming

air by means of four 0.2 cm diameter holes located 0.4 cm

downstream of the combustor inner surface leading edge.

In order to simulate properly the flow velocity at the

combustor entrance and to avoid simulating a shock wave

departing from the bottom of the combustor a realistic

velocity profile has been imposed at the combustor inlet, as

the well-developed boundary layer must be accounted for.

This profile has been obtained by Won et al. [23], and includes

also the effect of the intake.

2.1. Transport equations

In LES each turbulent field variable is decomposed into

a resolved and a subgrid-scale part. In this work, the spatial

filtering operation is implicitly defined by the local grid cell

size. Variables per unit volume are treated using Reynolds

decomposition, while Favre (densityweighted) decomposition

is used to describe quantities per mass unit. The instanta-

neous small-scale fluctuations are removed by the filter, but

their statistical effects remain inside the unclosed terms

representing the influence of the subgrid scales on the

resolved ones. Gaseous combustion is governed by a set of

transport equations expressing the conservation of mass,

momentum and energy, and by a thermodynamic equation of

state describing the gas behaviour. For a mixture of Ns ideal

gases in local thermodynamic equilibrium but chemical

nonequilibrium, the corresponding filtered field equations

(extended NaviereStokes equations) are:

� Transport Equation of Mass

vr

vtþ vr~ui

vxi¼ 0: (1)

� Transport Equation of Momentum

v�r~uj

�vt

þv�r~ui~uj þ pdij

�vx

¼ v~sijvx

þvssgsij

vx(2)

i i i

� Transport Equation of Total Energy (internal þ mechanical,

E þ K)

v�r ~U�

vtþv�r~ui

~U þ r~ui þ qi � ~ujsij þHsgsi � s

sgsi

�vxi

¼ 0 (3)

� Transport Equation of the Ns Species Mass Fraction

v�r~Yn

�þv�r~uj

~Yn

�¼ v

"rðD þ D Þ v

~Yn

#þ r~_u (4)

vt vxi vxin t;n

vxin

� Thermodynamic Equation of State

p ¼ rXNs

i¼1

~Yi

WiRu

~T (5)

These equations must be coupled with the constitutive

equations which describe the molecular transport.

In the above equations, t is the time variable, r the density,

uj the velocities, sij the viscous stress tensor, ~U the total filtered

energy per unit of mass, that is sum of the filtered internal

energy, ~e, the resolved kinetic energy, 1=2guiuj, and the subgrid

one, 1=2ðeuiui � euieuiÞ, qi is the heat flux, p the pressure, T the

temperature. The stress tensor and the heat flux are

respectively:

Tij ¼ 2m

�eSij � 13eSkkdij

�(6)

qi ¼ �kv�~T�

vxiþ r

XNs

n¼1

ehneYneVi;n þ

XNs

n¼1

qsgsi;n (7)

where Dn is the nth-species diffusion coefficient, Wn the nth-

species molecular weight, Yn the mass fraction, _un is the

production/destruction rate of species n, diffusing at velocity

Vi,n and resulting in a diffusive mass flux Jn. Finally, Ru is the

universal gas constant.

Summation of all species transport Equation (4) yields the

total mass conservation Equation (1). Therefore, the Ns species

transport Equation (4) and the mass conservation Equation (1)

are linearly dependent and one of them is redundant. Further-

more, to be consistent with mass conservation, the diffusion

fluxes (Jn ¼ rYnVn) and chemical source termsmust satisfy

XNs

n¼1

Jn ¼ 0 andXNs

n¼1

_un ¼ 0: (8)

In particular, the constraint on the summation of chemical

source terms derives from mass conservation for each of the

Ns chemical reactions of a chemical mechanism.

2.2. Turbulent combustion closure

All the unclosed subgrid terms in Equations (1)e(5) are

modelled using the Fractal Model FM; its details are in Refs.

[24,25,26]. FM is an “eddy viscosity” subgrid model, turning

itself off in the laminar regions of the flow. The self-similar

turbulent energy/vortex cascade, from the local filter size D

down to the local dissipative scale h, is modelled in each




computational cell bymeans of a fractal (recursive) technique,

i.e.,

ED

sDzNh$

Eh

sh/

u3D

DzNh$nh

u2h

h2; (9)

where E is the energy per unit mass, sD the Eddy turnover time

at scaleD (zD/U0D,U

0D being the velocity fluctuation at scaleD),

Nn the number of dissipative scales h locally generated, sh the

dissipative time (sh ¼ h2/nh), and nh the kinematic viscosity at

scale h. Details about estimatingNn are given in Ref. [24]. Based

on this cascade the scale h is estimated as Ref. [26]

h ¼ N1=4h $

�nh

nD

�3=4

$D

Re3=4t

: (10)

The subscripts D and h represent the filtered values in the

cell and the subgrid values, respectively. It is observed that in

reacting zones nD and nh differ since chemical reactions are

assumed to take place at the scale h, and thus the state of

Fig. 2 e Three views of an instantaneous Mach number flowfie

parallel plane Y [ 0.0078 m (c).

these scales will be different from the “filtered” state of the

cell. The ratio (nh/nD)3/4 can be of order 10.

Equation (10) indicates that h grows with increasing

temperature because nh grows with temperature: the FM

adapts itself to local flow conditions. In regions where D/hw 1

the local spatial filter D equals the dissipative scale, that can

be resolved without any modelling (the FM turns itself off).

This typically happens in the hottest flow regions.

Wherever D/h > 1, the FM models subgrid turbulent

stresses by means of an “eddy viscosity” mt [25],

mt ¼ p�1$mD$

��D

h

�2

�1

�; (11)

that yields automatically mt ¼ 0 when D/h ¼ 1 (e.g., in laminar

regions, and in particular at walls).

In this expression D/h is related to the Reynolds number

based on the local filter size and a velocity fluctuation

U0D ¼ ð2=3ksgsÞ1=2. In order to evaluate the turbulent viscosity

ld at X [ 0.0281 m (a), at Z [ 0.04 m (b), and at the wall-




the FM model needs the instantaneous value of the subgrid

kinetic energy in each computational cell. The form of the

transport equation for the subgrid kinetic energy Ksgs, defined

as ksgs ¼ 12ðeu2

i � ~u2

i Þ is:

v�rksgs

vt

þv�r~uik

sgs�

vxi¼ �rce

�ksgs3=2

Dþ ssgsij

v�~uj

�vxi

þv

�ðmþ mtÞ

v�ksgs

vxi

�vxi

þv

mt~R

Prt

v~T

vxi

!vxi

(12)

where the terms on the right hand side are respectively the

dissipation of subgrid kinetic energy, the subgrid stress work,

the modelled diffusion due to subgrid fluctuations in kinetic

energy, and the ksgs diffusion due to subgrid pressure fluctu-

ations modelled adopting an eddy viscosity assumption. The

coefficient Ce is assumed constant (and set to 0.916); the

pressure dilatation correlation in the subgrid kinetic energy

equation is neglected in this work. Once the turbulent

viscosity is known the subgrid stresses sijsgs may be modelled

as:

ssgsij ¼ þ2mt

�~Sij � 1

3~Skkdij

�� 23rksgsdij (13)

and following [27]

Hsgsi þ sij ¼ � mt

Prt

v ~Hvxi

� ðmþ mtÞv�ksgs

vxi� ~ujs

sgsij (14)

Combustion chemistry at or close to dissipation scales is

treated by the FM bymeans of a Perfectly Stirred Reactor (PSR),

with a residence time assumed equal to the local “eddy

turnover time” s* of the dissipative scales (this idea goes back

to the Eddy Dissipation Concept [28,29]). The volume fraction

Fig. 3 e (a) Instantaneous snapshot of temperature at X [ 2.81 c

streamwise velocity at X [ 2.81 cm with streamlines; (c) time av

and Y [ 0.97 cm.

g* occupied by these dissipative structures (fine scales) in each

computational cell is estimated by means of the local filter D

(i.e., the size of the fractal seed), the local dissipative scale h

(i.e., the fractal measurement unit) and the local fractal

dimension D3:

g�f

�D

h

�D3�3

: (15)

The fractal dimension is given by D3 ¼ 1þ ln Nh=ln ðD=hÞ.The local filter size is obtained as the cube-root of the local

grid volume, D ¼ ðDxDyDzÞ1=3. More details about g* and D3

estimation are in Refs. [25,26].

Once the volume fraction of the reacting “fine structures” is

known, the local chemical heat release is naturally modelled

as a subgrid effect based on the EDC model [29]. The Favre

filtered source terms are eui ¼ g�u�i in the Ns species equations,

and ~_Q ¼PNi¼1 g

�u�i Hi in the energy equation, where Hi is the

total enthalpy (sum of standard formation and sensible

enthalpies) of the i-th species. The instantaneous production/

destruction rate of the species i inside the reactor, ui*, is given

by the Arrhenius expressions of the particular chemical

mechanism adopted. ui* depends on the state of the reactor,

defined by its concentrations Yi*, temperature T* and pressure

p*. These are estimated assuming that during each time-step

1. The pressure p* is constant and equal to the filtered pres-

sure ~p in the cell;

2. The reactants are perfectly mixed inside the reactor, whose

mass is constant;

3. The local “fine structures” are modelled as a steady

Perfectly Stirred Reactor, closed and adiabatic;

4. the characteristic time of the subgrid reactor is equal to the

“eddy turnover time” of the dissipative vortices h [24].

m with isolines of pressure; (b) instantaneous snapshot of

eraged profile of pressure and temperature at X [ 2.81 cm




With the previous assumptions, species and energy

balance equations written for this subgrid PSR reactor are

solved at each computational cell to obtain T* and Yi*.

Where D/h � 1 the local scale D is dissipative; no modelling

is required, g* ¼ 1 and the local filtered and subgrid quantities

coincide.

2.3. Molecular properties

Molecular transports not taken into account in the resolved

equations are: Dufour and Soret effects, cross-diffusion,

pressure gradient diffusion, and diffusion by means of body

force. Preferential diffusion is considered and the species

diffusive mass flux is modelled by means of the Hirschfelder

and Curtiss treatment [30].

All molecular properties for individual chemical species,

except their binary mass diffusivities, are calculated a priori

by using the software library provided by Prof. Ern (EGlib)

[31,32]. In particular, kinetic theory is used for dynamic

viscosity ([33], pp. 23e29) and thermal conductivity ([33], pp.

274e278). The values calculated are then stored in a look-up

table, from 200 to 5000 K in 100 K steps. Values for interme-

diate temperatures are calculated at run-time by linear

Fig. 4 e Schematic of a transverse injection into a supersonic flow

a slice of Uy velocity field at X [ 2.81 cm and a counter-rotating v

at the plane X [ 2.81 cm and a horseshoe vortex are in (c).

interpolation. The mixture-eaverage properties are esti-

mated at run-time. In particular, the simulations used in this

work implement Wilke’s formula with Bird’s correction for

viscosity [34] ([35], p. 14), and Mathur’s expression for

thermal conductivity [36] ([35], p. 15). The effective diffusion

coefficients, Di, of species i into the mixture are estimated by

means of assumed individual Schmidt numbers, Sci, calcu-

lated as the median of the Sci vs T distributions for non-

premixed flames [37].

2.4. Numerical method

The spatially filtered NaviereStokes equations are solved by

means of a finite difference method on a Cartesian not

uniform grid in a collocated cell-centred variable arrange-

ment, together with an explicit, fully compressible solver. In

writing the numerical scheme, the focus was on the numer-

ical approximation of the derivatives in the advection terms at

the resolved scales. Due to the low hydrogen density, the

interface H2/air fluxes are evaluated by a hybrid method

capable of capturing shocks without introducing numerical

unphysical oscillations in regions where high gradients are

present and, at the same time, capable of resolving with low

[47] (a). Sideviews near a hydrogen injection hole showing

ortex pair in (b); the iso-surface YH2[0:1, a slice of pressure




dissipation turbulent structures away from discontinuities.

Convective fluxes in Equations (1)e(4) and (12) have been

calculated by means of a shock capturing or a low dissipation

scheme, accordingly to a sensor based on the density and

pressure fields [27].

In the shock capturing scheme the reconstruction of the

Riemann problem at the cell interface is performed by means

of a WENO 35 scheme. The interface fluxes from the recon-

structed states have been obtained by implementing the

approximate hybrid HLLC/HLLE Riemann solver [38]. In the

region where the flow is smooth the convective derivative are

determined by means of a fourth-order central finite differ-

ence scheme [39]. Time-integration is performed by means of

the fully explicit third-order accurate TVD Runge-Kutta

scheme of Shu and Osher [40]. For numerical stability the

time-step was about 10�9 s. The N.-S. equations are thus fully

coupled.

At the inlet, all quantities are prescribed, except density in

the subsonic regions, by means of characteristics inflow

boundary conditions. Partially non-reflecting boundary

conditions have been implemented (following the NSCBC

technique [41,42]) to reduce numerical reflection of acoustic

waves back into the computational domain where subsonic

regions are present. Because of the short testing time, all walls

are assumed adiabatic. In the present LES simulation the fuel

hole geometry are treated bymeans of an Immersed Boundary

technique (IB) [43]. The fitness function implemented in the

genetic algorithm used in the domain decomposition, aims to

balance the computational cost among the processors, and to

minimize the amount of data transferred across processors

boundaries. The S-HeaRT parallel code, written in FORTRAN

95 and the standardized MPI to implement parallel commu-

nication, can be run on different platforms (e.g., clusters of

single or multiple-core machines, SMP machines and so on).

This LES ran on the ENEACRESCOplatform, consisting of up to

2048 cores [44], showing excellent scalability on multiple

architectures.

Fig. 5 e Instantaneous (a) and averaged (b) mass fraction

fields for H2, H2O, OH, at the plane X [ 2.81 cm.

Instantaneous (c) and averaged (d) mass fraction fields for

H2, H2O, OH, at the plane Z [ 4.0 cm.

3. Numerical results

In this section, results of the 3D LES of the HyShot II

combustor are provided. Despite the simplicity of the trans-

verse fuel injection, the generated flow structures are rather

complicated. The hydrogen expands rapidly, blocking the

supersonic crossflow and causing a three-dimensional bow

shock ahead of the injector, which in turn, due to the adverse

pressure gradient, causes separation of the upstream wall

boundary layer, the formation of a subsonic region where

hydrogen and air may mix and consequently the flame may

hold.

The computational domain is discretized by means of 52M

cells. The grid is more refined close and within the flow

injectors, and stretched in the second half of the combustor.

The yþ ¼ u*y/v is w2.5. In Ref. [45] generation of the mainly

streamwise streak structures was shown to arise in the range

of yþ ¼ 5 to 40 w 50: this suggested that streaks formation at

the wall and their evolution within the turbulent boundary

layer and the outer flow is properly predicted. In fact, yþ < 5 is

small enough to predict 3D shock structures, the shock




boundary layer interaction and the large-scale turbulent

structures.

The hybridmethod adopted in the evaluation of convective

fluxes makes possible to predict the 3D shock generation in

the vicinity of the H2 injectors and the resolved vortex struc-

tures. Some pictures showing the main features of the inter-

action of the supersonic airstream with the crossflow

hydrogen injection are provided in Fig. 2 that reports an

instantaneous Mach number flowfield at X/d ¼ 14.15 (a),

Z/d ¼ 20.5 (b), and at the wall-parallel plane Y/d ¼ 0.5 (c).

The formation of shock waves at the upper wall near the

combustor entrance, the generation of a train of shock waves

reflecting from the bottomwall and impinging the flame front,

the formation of the 3D barrel shock and its Mach disk are

clearly evidenced in Fig. 3a and b. The barrel shock acts as

a blunt body obstruction to the incoming supersonic flow thus

forming a detached bow shock. Fig. 3 shows that the bow

shock is located about 0.1 cm ahead of the transverse

hydrogen jets: here the temperature increases reaching about

2300 K. The bow shock reaches its maximum intensity along

the plane of symmetry upstream of the barrel shock, where it

is a normal shock; away from this location it curves down-

stream in both the lateral and vertical directions, forming an

enveloping surface around the barrel shock. Downstream of

the normal cross-section of the bow shock, the generated

subsonic flow is accelerated again to supersonic speeds, once

it is mixed with the supersonic fluid that has passed the

oblique region of the bow shock. A large expansion fan is

generated at the injector edges and the boundaries of the jet

deflect inwards. In fact, once hydrogen is injected within the

airflow, it expands rapidly and cools down to T ¼ 150 K before

recompressing in the barrel shock. Compression waves define

the jet boundaries (Fig. 3a), and form the barrel shock. Finally

the Mach disk compresses the injected flow. The pressure

increase due to the barrel shock (see Fig. 3c) is responsible for

the boundary layer thickening and separation (taking place

w2.0 cm upstream of the injectors) and consequent formation

of l shocks. The l shocks, that typically appear in shock-

laminar boundary layer interaction, were predicted to be

very unstable in this simulation, so they are not always

present. The subsonic flow generated by the Mach disk, forms

Fig. 6 e Time averaged mass fraction of the major species

at different Z planes (b).

a slip surface with the supersonic fluid flowing around and

past the barrel shock (see Fig. 2a). The location where the

downwind side of the barrel shock intersects the Mach disk is

called triple point. From this point a shock generates on the

upstream side of the barrel shock due to the interaction of the

crossflow with the subsonic outflow from the Mach disk (see

isolines of pressure in Fig. 3a).

Two spanwise vortices adjacent to the upper wall and

before the hydrogen injection can be identified (see Fig. 3b).

The vortex tangential velocities are fairly high, w900 m/s,

even though the flow still stays subsonic (see Fig. 2a) except

Fig. 7 e Comparison of numerical and experimental

pressure distribution along the upper wall at X [ 3.5 cm

(a). Comparison of numerical and experimental time

evolution at a point on the upper wall (Y [ 0.98 cm and

Z [ 27.2 cm).



Fig. 8 e Instantaneous flowfields of vorticity magnitude at X/d [ 14.15 (a) and at the wall-parallel plane Y/d [ 1 (b). Iso-

surfaces of streamwise vorticity at L106 and 106 Hz, from Z/d [ 12.5, to Z/d [ 30 (c). Flowfields of vorticity magnitude at

constant X planes are in (d), with a range scale smaller than in (a) and (b) to cut out peaks in the H2 injection region.


very close to the H2 injection where it reaches aboutMw 1.15.

The first clockwise vortex is small (w0.15 cm) and has a high

vorticity (w107 Hz); the second rotates counter-clockwise and

is responsible for the hydrogen convection up to w1.5 cm

upstream of the fuel injection and of the bow shock itself, as it

will be clearly shown later. This second vortex is squeezed on

the upper wall with a characteristic dimension of 1 cm and

a spanwise vorticity magnitude w106 Hz. The vorticity



Fig. 9 e Slices of density gradient (a,b); slices of pressure gradient (c, d).


magnitude of these two structures can be deduced from

vorticity pictures in the next section and presents a similar

trend as shown in Won et al. [46]. It is observed that the first

recirculating region in the X-middle-jet plane is the origin of

the counter-rotating vortex pair sketched in Fig. 4a and shown

in Fig. 4b.

Fig. 3 also shows the high mixing intensity region down-

stream of the fuel injection: here, supersonic and subsonic

tangential speeds alternate, enhancing air/fuel mixing. As the

sonic hydrogen jet interacts with the supersonic air crossflow,

various coherent structures, that contribute to the enhance-

ment of fueleair mixing, develops. A schematic of the main

coherent structures is shown in Fig. 4a. The streamwise

counter-rotating vortex pair that contributes to engulf the air

freestream, and the horseshoe vortex that wraps around the

hydrogen jet and flows downstream along the wall, are clearly

identified in Fig. 4b and c. It is observed that also other

counter-rotating structures, like wake vortices, appear [48,49],

but they are not shown in Fig. 4.

Fig. 5 reports sideviews atX¼ 2.81 cmof instantaneous and

averaged fields of speciesmass fraction. Average is performed

over a time equivalent to 6 combustor chamber residence

times. The large-scale vortex structures visible in Fig. 5a that

develop along the hydrogen/air shear-layer contribute to

increase the interfacial fuel/air area, and hence mixing.

Note that the jet-to-freestream momentum ratio,

J ¼ ðrH2v2H2

=rAirv2AirÞ, is 0.512. Moving from the fuel injection

hole location up to 2 jet diameters downstream, the H2 jet

penetration is observed to vary from w1.0 d up to w1.6 d for

the central fuel inlets, and from w1.3 d up to w1.7 d for the

two lateral ones. This difference may be due to the effect of

the bow shock interaction with the lateral walls. This effect is

evidenced in Fig. 5d, where time averaged species mass frac-

tions at the plane Z¼ 4 cmare shown. In the end, to provide an

overall indicator of the average hydrogen jet penetration, it is

observed that this reaches nearly 20% of the combustor height

already at 6 diameters downstream from the injector, where it

is still possible to clearly identify the jet core. This value can be




compared with thew30% penetration predicted in Ref. [20] for

the same combustor, that however is working with a much

larger jet-to-freestream momentum ratio of 1.1 (this also

explains the differences in our results and those in Ref. [20]).

Power-law fit for the penetration height has been proposed

by various authors [47], but unfortunately, in these experi-

ments underexpanded hydrogen jet was injected into high-

temperature free air crossflow without the presence of the

upper wall, and consequently no comparisonwith the present

results can be done. The presence of the upper wall reduces

the jet penetration with respect to a free air crossflow. Fig. 5

shows the presence of OH radicals very close to the fuel

injectors, confirming that mixing and combustion take place

in a very short time: OH radicals, whose gradient is often used

to locate the flame front, are produced primarily behind the

steep bow shock, where high pressure and temperature

prevail, as well as in the recirculation zone upstream of the jet

exit, where high residence times exist. In fact, at these air

temperature (w2000 K) and pressure (w2.5 atm), once air and

hydrogen are mixed, radical kinetics is fast, of order of 10�6 s.

These results underline the importance of using hydrogen as

vu

vt¼ �ðu ,VÞu|fflfflfflfflfflfflffl{zfflfflfflfflfflfflffl}

CONV

�uV,u|fflfflfflfflfflffl{zfflfflfflfflfflffl}CP

þu $V u|fflfflfflffl{zfflfflfflffl}VS

þVr� Vpr2|fflfflfflfflfflffl{zfflfflfflfflfflffl}B

þ 1Re

nV2u|fflfflfflfflfflffl{zfflfflfflfflfflffl}

DIFF

þ 1Re

�� 1r2

Vr� ðV$s¼Þ|fflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflffl}

CV

þ1rVm� �V2

uþVðV$uÞ |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}VV

þ2rV�ðE

¼VmÞ|fflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflffl}

DV

�(16)

fuel for this kind of applications. In fact, the combustor length

scales as the flow residence time required to ensure complete

combustion. Thus, using hydrogen as fuel allows shorter

combustion chambers, thanks to its fast kinetics and mixing

(see next section). Further, because of fast kinetics, a reduced

flame model, such as a flamelet/progress variable approach,

could be adopted to economically couple chemistry and

turbulence: this approach reduces the number of transported

chemistry species in a CFD code.

While the subsonic recirculation region is dominated

mainly by spanwise vortices, the flowfield mixing is driven by

streamwise structures that convect hydrogen from the jet

core outwards. These structures become larger and larger

moving in the Z direction. This is the effect of the large pres-

sure and density gradients pumping vorticity into the flow-

field via the baroclinic term. Furthermore, due to these

streamwise structures, hydrogen is also convected towards

the adjacent H2 streams (see Fig. 5c): here, fuel and airmix and

the flame anchors, as shown by the presence of H2O.

Fig. 6 shows the average species mass fractions of H2, OH

and H2O at different Z in the combustion chamber. The

combustion efficiency, hc ¼ 1� ðRArj~yjYH2dAÞ=ðrj~yjYH2 Þinlet at

the outlet of the combustion chamber is found to be about

87.65%.

Fig. 7a compares numerical and experimental pressure

distribution along the upper wall (Y ¼ 0.98 cm) of the

combustion chamber at X ¼ 3.5 cm and 1.32 ms: the trend is

well predicted in the first part of the combustor, where the

grid is much more refined. Better agreement near the exit

region needs a finer grid to capture shock reflection. Fig. 7b

compares numerical and experimental pressure time

evolution at a point on the upper wall (Y ¼ 0.98 cm and

Z ¼ 27.2 cm). Actually, these numerical results show a better

agreement with experimental results from the High Enthalpy

Shock Tunnel Gottingen (HEG), where the pressure jumps are

less sharp with respect to the HyShot-T4 Supersonic

Combustion Experiments (Queensland). Unfortunately, only

conditions at a non 0� angle-of-attack, thus no comparisons

with these data are feasible.

3.1. Vorticity analysis

The results shown in the previous section has shown a very

intense mixing due to the strong interaction between the

airflow and the hydrogen jets. The heat released by the

hydrogen fast combustion contributes to divide and twist the

airflow into streaks, hairpin, horseshoe and counter-rotating

vortices, further enhancing mixing (see Fig. 4).

Analyzing the vorticity variable and understanding its

dynamics may help to explain mixing mechanisms in super-

sonic flows. This is an important step to identify possible

strategies for its enhancement. Vorticity evolution is ruled by

the compressible vorticity transport equation:

Equation (16) indicates that shock waves and combustion, the

viscous effects at the boundary of the injection hole and at the

fuel air interface, may produce and subsequently increase

vorticity. The baroclinic term, that can be related to the

gradient of entropy and temperature via the Gibbs equation, is

generally negligible in subsonic non-reacting flows, but is

critical and plays a key role in the mixing enhancement in

supersonic flows.

Fig. 8 shows that jujw0 at the H2 orifice exit, but becomes

very large (w106 Hz) immediately after it penetrates the

airflow core, where, accordingly, mixing times should be

w10�6 s. Fig. 8 also shows that vorticity magnitude is of order

of 107 Hz in the region upstream the fuel injection. Here, the

larger contribution to vorticity is given by the spanwise and

crosswise vorticity components. Going downstream, due to

the interaction between ux and the transverse velocity gradi-

ents, vortex stretching tilts vorticity in the streamwise direc-

tion forming horseshoe vortices (see Fig. 4c).

The density gradient distribution (w250 kg/m4) reported in

Fig. 9a and b, marks different phenomena: the boundary layer

separationregionupstreamofthehydrogeninjection; theshocks

formed at the combustor entrance, reflected on the separated

boundary layer and impinging on the bow shock (see the first Z-

slice in Fig. 9a); the slip surface emerging from theMachdisk and

merging with the shear vortices; the high density gradients

present on the flame front (see the X-slice in Fig. 9b). Fig. 9c and

d shows instead the pressure gradient distribution (w4�107 kg/

m2 s2) associated to the same flowfield: these gradients are

stronger near the fuel injection region, where all the shock

structures described in the previous section are present, and

weaken in the second half of the combustion chamber.



Fig. 10 e Baroclinic term magnitude: slices on the 4 middle

plane inlet orifices (a), slices at different Z planes from Z/

d [ 20 to Z/d [ 130 (b), baroclinic term magnitude

distribution at Y [ 0.98 cm and X [ 2.81 cm (c).


Due to the coupling of large density and pressure gradients,

the baroclinic term (B) (see Fig. 10) is of order of 1010 s2,

pumping vorticity within the airstream. This trend can be

better visualized by looking at the baroclinic term distribution

along Z at X ¼ 2.775 cm (the centre of the second H2 injector)

and Y ¼ 0.97 cm (0.01 cm from the fuel injection in the

transverse direction) in Fig. 10c. In particular, this figure

shows that a first baroclinic term peak (point 1) is at the

combustor entrance, where the first oblique shock wave is

located. The second baroclinic term peak is where the

boundary layer separates (point 2). Just downstream of this

second point, the baroclinic termdecreases since this region is

almost everywhere subsonic and characterized by negligible

density and temperature gradients. The highest peak of the

baroclinic term, of order of 1012 s�2, is located at point 7, where

the hydrogen jet rapidly expands and strong shock structures

are present. Here, the coupled effect of high density and

pressure gradients is enhanced by the low hydrogen density

(r w 0.03 kg/m3). It is not trivial to stress that considering

methane (r w 0.24 kg/m3) and kerosene (r w 2.25 kg/m3)

instead of hydrogen, and assuming in this region the same

conditions in terms of pressure, temperature, and pressure

and density gradients, the baroclinic source term would be

eight and eighty times smaller than that of hydrogen.

Comparing Fig. 10b with Fig. 5a, it can be qualitatively

deduced that the baroclinic source term is also high at the

edges of the shear eddies located downstream of injection

(between 4 cm and w8 cm) and growing in the streamwise

direction. At these edges, density gradients are high due to the

presence of a flame front. As vorticity due to the baroclinic

term convects air into these vortices and hydrogen outside of

them, the size of these eddies quickly increases. This mech-

anism weakens moving towards the end of the combustor,

because of the decreasing gradients.

Physically speaking, the baroclinic term, indicates the rate

at which the vorticity is generated and pumped into the flow.

In practice, this means that if there were not any dissipative

phenomena and if the baroclinic spin acceleration was

constant, the spin speed, i.e., the vorticity, at point 7 (as an

example) would increase by 109 Hz eachms. This is in essence

the baroclinic mechanism enhancing mixing in supersonic

combustion. It is per se a strategic conclusion for applications

because it underlines the importance of the combustor

geometry and injector configuration. In the present scramjet,

in fact, the pressure and density gradients are due to shocks

system triggered by the crossflow H2 injection. However,

nevertheless the strong source of vorticity, this injector

configuration may results in high total pressure losses and

lower thrust available. Other injector configurations with the

same capability of vorticity generation but with presumably

lower total pressure losses must to be investigated and will be

the subject of future work.

Distributions of the other terms in the compressible

vorticity transport equation are reported in Fig. 11. The

compressibility term (CP) is higher in the first part of the

combustor at the interface of hydrogen and air, where the

hydrogencore expansion is blockedby the airflow. Fig. 8 shows

vorticity peaks in correspondence of shocks and Mach disk.

There, V$u=0, so the term �uV $u is a source: compressibility

increasesvorticityandenhancesmixing.Thevortex stretching



Fig. 11 e Magnitude of the compressibility (a), vortex

stretching (b) and diffusive terms (c).


(VS) is high in the subsonic recirculation region, where it

transports vorticity created upstream by the baroclinic and

diffusive terms. In this region, the coupling between trans-

versal velocity gradients and the streamwise and the spanwise

vorticity is responsible for thevortices tilting in the streamwise

direction (i.e., forming the horseshoe vortices). The vorticity

diffusion term (DIFF) initially (i.e., close to the inlet) transfers

vorticity into the flow (it is a source) from the walls, and then

diffuses it. This term remains significant even close to the end

of the combustor. Terms related to viscosity gradients (CV, VV,

DV), not reported here, have maximum values at walls and

close to H2 injection; they are of the order of 109, hence one-

order of magnitude smaller than compressibility, vortex

stretching, baroclinic and diffusive terms.

These results confirmed what already theoretically pre-

dicted by means of nondimensional analysis in Ref. [50]: in

supersonic flows the compressibility, vortex stretching and

baroclinic terms are all of the same order of magnitude, thus

contributing in equal way but in different regions to air/fuel

mixing and combustion. Further, it is important to underline

that although vorticity is almost nil at the combustor and H2

hole inlets, it quickly becomes very large, i.e., in a distance

comparable with the hydrogen injection diameter.

4. Conclusions

In this paper the impact of using hydrogen as fuel for super-

sonic combustion has been analyzed by means of a 3D LES of

the Hyshot II scramjet combustor. A highly refined grid,

a detailed kinetic scheme and a hybrid technique capable of

resolving shocks and contact discontinuities without dissi-

pating turbulent structures in smooth regions of the flow have

been shown necessary and have been implemented.

The strong interaction among the essentially uniform

airflow entering the combustor, the heat released and the fast

hydrogen jets produces 3-D large structures and large vorticity

rates, therefore enhancing turbulent mixing. Hydrogen mix-

ing is predicted to be very fast. Counter-rotating vortices

within the H2 core flow improve turbulent diffusion of H2,

while eddies between the initially separated fuel jet streams

entrain air and are responsible for the fast air/H2 mixing.

Recirculation zones upstream and downstream of the fuel

injection orifices are observed as expected. The very low

ignition delay time of hydrogen/air mixtures favours very

efficient and rapid combustion. In fact, the flame anchors

upstream of the H2 injection, within the recirculation zone

between the bow shock and the fuel orifices, as clearly evi-

denced by the OH radicals distribution. The overall result is

that H2/air combustion is predicted very fast with a combus-

tion efficiency of 87.65%, thus confirming hydrogen as the best

candidate for SCRJ engines.

Large production of vorticity is driven by the baroclinic

term, that is enhanced by the H2 low density: the baroclinic

term w109 s�2 indicates the spin acceleration increasing by

109 Hz for each ms. This explains the high mixing in super-

sonic combustion. In fact, the combination of hydrogen

features and crossflow injection configuration enables high

mixingwithin a short combustor, that in practice can bemuch

shorter than 1 m.




Acknowledgements

These authors acknowledge the “HyShot International

Consortium” led by Professor Allan Paull of the University of

Queensland, Australia, and the Seoul National University

(Korea) group, led by Prof. Jeung, for providing the detailed

data of the HyShot experiment. These authors are also

grateful to Dr. Franca Rita Picchia, Nunzio Arcidiacono and

Filippo Donato from the ENEA Sustainable Combustion

Laboratory. Furthermore, thanks to all people working at the

CRESCO supercomputing center of ENEA Portici.

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