Research Article Numerical Simulation of Reactive Flows …downloads.hindawi.com/journals/ijae/2015/252404.pdfResearch Article Numerical Simulation of Reactive Flows in Overexpanded

Research ArticleNumerical Simulation of Reactive Flows in OverexpandedSupersonic Nozzle with Film Cooling

Mohamed Sellam and Amer Chpoun

Laboratoire de Mecanique et drsquoEnergetique drsquoEvry (LMEE) 40 rue du Pelvoux 91020 Evry Cedex France

Correspondence should be addressed to Mohamed Sellam sellamufrstuniv-evryfr

Received 9 October 2014 Revised 4 March 2015 Accepted 4 March 2015

Academic Editor Joseph Majdalani

Copyright copy 2015 M Sellam and A Chpoun This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

Reignition phenomena occurring in a supersonic nozzle flow may present a crucial safety issue for rocket propulsion systemsThese phenomena concern mainly rocket engines which use H

2gas (GH

2) in the film cooling device particularly when the nozzle

operates under over expanded flow conditions at sea level or at low altitudes Consequently the induced wall thermal loads canlead to the nozzle geometry alteration which in turn leads to the appearance of strong side loads that may be detrimental to therocket engine structural integrity It is therefore necessary to understand both aerodynamic and chemical mechanisms that areat the origin of these processes This paper is a numerical contribution which reports results from CFD analysis carried out forsupersonic reactive flows in a planar nozzle cooled with GH

2film Like the experimental observations CFD simulations showed

their ability to highlight these phenomena for the same nozzle flow conditions Induced thermal load are also analyzed in termsof cooling efficiency and the results already give an idea on their magnitude It was also shown that slightly increasing the filminjection pressure can avoid the reignition phenomena by moving the separation shock towards the nozzle exit section

1 Introduction

One of the major challenges that the aerospace industrycontinues to face is the continued increase in launcherspayload For example the latest version of the Vulcain-IIengine of the European Ariane 5 ECA launcher is able to putinto geostationary orbit a payload of about 10 tons The goalis however to reach 12 tons in the near future There are twochallenges here the increase in payload and the performanceconsolidation in terms of reliability

These challenges promote development of nozzles withhigher performances which are substantially achieved byincreasing the nozzle expansion area ratio or by developingnew innovative nozzle concepts The rocket engine nozzleswith high expansion area ratio are generally optimized foroperating at high altitudes At sea level and at low altitudesthe nozzle operates in overexpanded flow conditions thatis the ambient pressure is higher than the nozzle exitpressure The resulting adaptation shock may lead to flow

separation unsteadiness and shock interaction The ensuingside loads may be detrimental for both nozzle and otherengine components In addition these nozzles are designed toexpand and accelerate combustion gases at high temperatureTo avoid thermal loads designers adopt several nozzlecoolingmethodsThemost effective one uses the film coolingtechnique For example for Vulcain-II rocket engine thecooling system is designed in two parts a dump cooling forthe first expansion part of the nozzle and GH

2film cooling

for the second part [1 2]The present study is a contribution to the works initiated

by the CNES during the last ten years in the field of innovativenozzle researchesThemain goal is to develop new supersonicnozzle concepts for cryogenic rocket engines One issue thatattracted the interest of scientists is that related to the riskof reignition that can occur in the main flow resulting fromcombustion of GH

2used as film cooling This phenomenon

may happenwhen theGH2film ismixedwith the air engulfed

into the separated region along the mixing shear layer at high

Hindawi Publishing CorporationInternational Journal of Aerospace EngineeringVolume 2015 Article ID 252404 15 pageshttpdxdoiorg1011552015252404

2 International Journal of Aerospace Engineering

Cylindricalcombustion

chamber

Outlet caisson

C-D planarnozzle

2 injectorGH

(a) From [22]

Wall with pressuretransducers

Gas combustionInjector

Separation shock

Thermal loads due to reignition

Nozzle inlet

Recirculation zone

h = 002818 m

H2 injection

l = 00551mL = 0122m

= 0002myth

(b)

Figure 1 Mascotte test bench assembly (a) and sketch of longitudinal section of the planar nozzle (b)

P0 = 259bar of = 185 P0 = 365bar of = 187

Figure 2 PLIF images of OH radicals from [3]

temperature In this occurrence the film cooling efficiencyis altered and the induced thermal loads may be critical forthese nozzles

To understand these phenomena a campaign of experi-mental measurements was conducted at the cryogenic LH

2-

LO2ONERAMascotte test bench facility [3] The results yet

obtained for low oxidizerfuel ratios (119900119891) on the basis ofPLIF and Kulite pressure measurements already constitute avery useful database for understanding the involved physico-chemical phenomena The first series of measurements wereperformed under 119900119891 ratios of up to 3 and combustionchamber pressure up to 40 bars The first results obtainedduring this measurements campaign highlighted a reignitionphenomenon occurring in the nozzle main flow inside theseparation area

Given the complexity of these phenomena numericalsimulations performed by different computing codes cangive a better interpretation of the experimental results Thepresent numerical work is a further contribution in thisregard and consists in simulating the turbulent reactiveflows in the same operating conditions as those performedexperimentally

This work was carried out within the framework andwith the support of the French research group ATAC(Aerodynamique des Tuyeres et Arrieres Corps (Nozzles andAfterbodies Aerodynamics))

2 Objectives

The aim of this paper is to perform 2D RANS turbulentreacting flows simulations for three test cases carried outexperimentally in the ONERAMascotte test bench For thispurpose two chemical kinetic schemes and two turbulencemodels were tested to investigate their relevance in thereignition process inside the nozzle

Basically the test bench consists of a subscale planarnozzle connected to a cylindrical combustion chamber fedwith a cryogenic mixture LOx-LH2

(Figure 1(a)) This hard-ware version has been developed especially to investigate theflow separation in overexpanded regimes The combustionchamber operates under controlled total pressure and oxi-dizerfuel ratios (119900119891) The main geometrical characteristicsof the nozzle are given in Figure 1(b) Pure hydrogen gas(GH

2) serving as film cooling is injected tangentially into

the upper wall of the nozzle through a slightly supersonicinjector Five Kulite pressure transducers are taped along thiswall A schematic longitudinal cross section of the nozzle isshown in Figure 1(b)

The first results [3] obtained by PLIF visualizationsperformed in this test bench show an increase in concen-trations of OH radical near the upper wall of the nozzlersquosdivergent in the separation zoneThis suggests a reactivationof the combustion inside this area (Figure 2) During these

International Journal of Aerospace Engineering 3

experiments it was also revealed that there is unsteadinessin the radical OH emission inside the separation zone Theauthors related this phenomenon to the pressure fluctuationsobserved in the combustion chamber An example of PLIFimages obtained by this technique is depicted in Figure 2[3] However no detailed explanations have been given so farabout the occurrence of this phenomenon

Parallel to these experiments steady RANS calculationshave been carried out at ONERADEFA using the CEDRECode In these calculations the reduced chemical kineticmodel of Eklund et al [4] was used for chemical ratesHowever no process of reignition in the flowhas been pointedout from the numerical results [3]

From these experimental and numerical conclusionsfurther calculations using new chemical kinetics based onthe well-known Evans and Schexnayder model [5] were rec-ommended This last model was slightly modified by addingtwo additional reactions without excessively penalizing thecomputation time Furthermore two RANS turbulencemod-els have also been tested in these calculations The mainobjective of this studywas to investigate relevance of chemicalkinetics and turbulence models in the context of reignitionphenomenon

3 Numerical Code and Equation Formulation

31 Numerical Code The calculations presented in thispaper were performed using the FASTRAN code This codewas specifically designed for compressible flow studies athigh Mach numbers and based on solving the multispeciesReynolds-Averaged Navier-Stokes (RANS) equations witha finite volume formulation The code offers two upwinddifferencing schemes with a variety of high order slopelimiters to calculate the convective terms in the transportequations Both explicit and implicit iterative and noniter-ative time integration schemes are available for steady-stateand time accurate flow simulationsThe convective fluxes arecalculated by means of either flux difference splitting scheme(Roe) or flux vector splitting scheme (van Leer) The codealso offers a choice of several turbulence models (119896-120576 119896-120596119896-120596-SST-Menter Spalart Allmaras and Baldwin Lomax)Thefollowing sections recall the main fluid physical modellingand the flow field numerical formulations methodology usedin this code for solving reactive Navier-Stokes equations

32 Thermodynamics Gas Properties The thermal equationof state for a mixing or reacting gas is given by Daltonrsquos Lawof partial pressures such that

119901 = sum119904

120588119904

119872119908119904

119877119906119879 (1)

where 119901 is the static pressure 120588119904is the species or mixture

density 119877119906is the universal gas constant 119879 is the static

temperature and119872119908119904

is the molecular weight of the species119904

The caloric equation of state relates the total energyto other gas dynamic variables and gas properties Forcalorically perfect gas

119864119905= 120588119888V119879 +

1

2120588119906

119895119906119895 (2)

where 119864119905is the total energy per unit volume and 120588 119888V 119879 and

119906119895are the gas density the heat capacity of the gas mixture

at constant volume the static temperature and the massaveraged velocity respectively

The form of the caloric equation of state for a mixingor reacting gas depends on the database used for describingthe molecular properties of the species Two databases areavailable the first is based on molecular (or spectroscopic)data for chemical species and the second is based on fifth-order polynomial curve fits for each chemical species [6]Using molecular properties (2) can be written as

119864119905= sum

119904

120588119904(119888Vtr119904119879 + Δℎ

0

119891119879119903119904) + 119864V +

1

2120588119906

119895119906119895 (3)

where 120588119904is the species density 119862Vtr119904 is the translational-

rotational heat capacity for species 119904 at constant volumeΔℎ0

119891119879119903119904is the heat of formation at reference temperature 119879

119903

and pressure for species 119904 and 119864V is the molecular vibrationalenergy per volume

Using of polynomial curve fits for properties gives twoforms of caloric equation of state

For thermal equilibrium

119864119905= sum

119904

120588119904(ℎ

119904minus119877119906119879

119872119908119904

) +1

2120588119906

119895119906119895 (4)

For thermal nonequilibrium

119864119905= sum

119904

120588119904[119888Vtr119904119879 + Δℎ

0

119891119879119903119904minus 119879

119903(119888Vtr119904 minus

119877119906

119872119908119904

)]

+ 119864int +1

2120588119906

119895119906119895

(5)

where ℎ119904is the sensible enthalpy per unit mass for species 119904

defined as

ℎ119904= int

119879

119879119903

119888119901119904119889119879 + Δℎ

0

119891119879119903119904 (6)

where 119888119901119904is calculated from fifth-order polynomial curve fits

for each chemical species from Gordon database [6]The viscosity of each fluid species 119904 in the case of reactive

flows is calculated by the relationship of Bird et al [7]

120583119904= 266693sdot10

minus6radic119872119908119904

119879

120590Ω120583

(7)

where 120590 is the characteristic molecular diameter and Ω120583is

the viscosity collision integral The characteristic moleculardiameter is based on Lennard-Jones potentials [8] For the


mixture the viscosity is calculated by the semiempiricalrelationship of Wilke [9]

120583 = sum119904

119883119904120583119904

Φ119904

(8)

where119883119904is the mole fraction of specie 119904 and Φ

119904is given by

Φ119904= sum

119903

119883119903[1 + radic

120583119904

120583119903

(119872

119908119903

119872119908119904

)

14

]

2

[radic8(1 +119872

119908119904

119872119908119903

)]

minus1

(9)

For the diffusivity vector 119869119904 the mass diffusivity can be

represented by either Fickrsquos law [10] or a binary diffusionmodel [11] Consider

119869119904= minus120588119863

119904nabla119884

119904 (10)

where119863119904is the diffusion coefficient and119884

119904is the speciesmass

fraction119863119904is given by

119863119904=120583

120588Sc (11)

where Sc is the Schmidt number

33 Chemical Production The reactive flow calculation isobtained by solving the flow conservation equations in whichone integrates a source term120596

119904expressing themixture chem-

ical composition variation resulting from chemical reactionsIn the approach used for reacting flows the general finite

rate reaction is written as119899119904

sum119904=1

]1015840119904119903119872

119904lArrrArr

119899119904

sum119904=1

]10158401015840119904119903119872

119904 (12)

where ]1015840119904119903and ]10158401015840

119904119903are the stoichiometric coefficients of the

reaction and 119872119904represents an arbitrary molecule in the

reaction According to Kuo [11] the source term for species119904 is given by

120596119904= 119872

119908119904(]10158401015840

119904119903minus ]1015840

119904119903) [

119899119904

sum119904=1

120573119904119903119862119904]

sdot 119870119891119903

119899119904

prod119904=1

[119862119904]1205721015840

119904119903 minus 119870119887119903

119899119904

prod119904=1

[119862119904]12057210158401015840

119904119903

(13)

where 120573119904119903is the coefficient of efficiency of the third body for

the reaction 119903 119862119904is the species concentration and 119870

119891119903and

119870119887119903

are forward and backward reaction rates of a reaction119903 respectively The concentration powers 1205721015840

119904119903and 12057210158401015840

119904119903are

identical to ]1015840119904119903and ]10158401015840

119904119903 respectively for most applications

particularly for chemical kinetic reaction governed by Arrhe-nius rates of reaction

119870119891119903= 120572

119891119903119879120573119891119903 sdot 119890

(minus119864119886119903(119877sdot119879))

(14)

where 120572119891119903 120573

119891119903 and 119864

119886119903119877must be specified for each reaction

under investigation

34 Flow Field Numerical Method Basically the conserva-tion equations with appropriate closure models are expressedin vector form as

120597119876

120597119905+ nabla sdot

997888119865

119862minus (nabla sdot

997888119865

119863) = 119878 (15)

In this expression 119865119862and 119865

119863represent the convective and

diffusive fluxes respectively such as

119876 =

[[[[[[[[[[[[[[[[[[[[[[[[[

[

119864int

1205881

1205882

120588119899119904

120588119906

120588V

120588119908

119864119905

]]]]]]]]]]]]]]]]]]]]]]]]]

]

119865119862=

[[[[[[[[[[[[[[[[[[[[[[[[[

[

119864int119906

1205881119906

1205882119906

120588119899119904119906

1205881199062 + 119901

120588119906V

120588119906119908

(119864119905+ 119901) 119906

]]]]]]]]]]]]]]]]]]]]]]]]]

]

119878 =

[[[[[[[[[[[[[[[[[[[[[[[[[

[

int

1

2

119899119904

0

0

0

0

]]]]]]]]]]]]]]]]]]]]]]]]]

]

119865119863=

[[[[[[[[[[[[[[[[[[[[[[[

[

119899119904

sum

119904=1

119890V119904120588119904119880119904 + 119896int120597119879int120597119909

minus12058811198801

minus12058821198802

minus120588119899119904119880119904

120591119909119909 minus2

3120588119896

120591119909119910

120591119909119911

[119906120591119909119909 + V120591119909119910 + 119908120591119909119911 + (119896 + 119896119905)120597119879

120597119909+ 119896int

120597119879int120597119909

+sumℎ119904120588119904119880119904]

]]]]]]]]]]]]]]]]]]]]]]]

]

(16)In this system of equations 119906 V and 119908 are the velocitycomponents (119908 = 0 for 2D calculations) 120588 is the mixturedensity and 120591

119894119895is the shear stress tensor 120588

119904and 119880

119904are

respectively the species density and species velocity One cannote that for calorically perfect gas only one ldquospeciesrdquo istracked such that 119899119904 = 1 120588

119904= 120588 and 119880

119904= 0 Note that

for thermal equilibrium calculation all terms relating thecontribution of vibrational internal energy (119864int 119879int 119890V119904 )are no longer required

4 Chemical Kinetic Models

To investigate the pertinence of the chemical reactions asso-ciated with the reacting mixture issued from the combustionchamber it was expedient to test the most suitable kineticschemes for reactive H

2-O

2flow Two kinetic schemes were

selected for this study the modified Evans-Schexnaydermodel and Eklundrsquos kinetic model commonly used byONERA and CNES


Table 1 Modified Evans-Schexnayder reaction model 119896119891

incm3molesdots119872 is the third body with an efficiency = 1 for all speciesand 120579

119894= 119864

119886119877

Number Reaction 120572119894

120573119894

120579119894(K)

1 H2 + MhArrH+ H +M 55 times 1018 minus10 519872 O2 + MhArr O + O +M 72 times 1018 minus10 593403 H2O + MhArr OH + H +M 52 times 1021 minus15 593864 OH +MhArr O + H +M 85 times 1018 minus10 508305 H2O +OhArr OH + OH 58 times 1013 00 90596 H2O + HhArr OH + H2 84 times 1013 00 101167 O2 + HhArr OH + O 66 times 1014 00 84558 H2 + OhArr OH + H 55 times 1013 00 55869 H + O2 + MhArrHO2 + M 23 times 1016 00 minus40310 H + HO2 hArr OH + OH 24 times 1014 00 950

41 Modified Evans-Schexnayder This model is initiallybased on 7 species [O

2 H

2 OH H

2O N

2 and O] and 8

chemical reactionsrsquo scheme [12] In this system N2operates

as the third body anddoes not dissociateThismechanismhasbeenwidely used for simulation in supersonic andhypersonicflows particularly in the case of combustion initiation aroundobstacles or in scramjets [13ndash15] This model was proved tobe less expensive in terms of computation time howeverit presents weakness in modeling the self-ignition delay(induction time) and in estimating the reaction heat releaseThis is mainly due to the absence of hydroperoxyl radical(HO

2) in this scheme Indeed studies have shown that fast

three body recombination reactions involving the radicalHO

2 have been identified as major contributor in the heat

release process during the combustion of hydrogen with air[16]

To overcome this deficit two reactions taken from themodel of Rogers and Chinitz [14] involving this radicalhave been added to the original Evans model adding nosubstantial computation time

H +O2+MlArrrArr HO

2+M (17)

H +HO2lArrrArr OH +OH (18)

Another insufficiency attributed to this model is its autoigni-tion delay which is relatively long especially for reactionsat low temperature (asymp1000K) This problem is related to theabsence of hydrogen peroxide (H

2O

2) in the model

Adding more reactions involving this species to correctthis deficiency substantially complicates the model An alter-native solution would be to increase the production rate ofReaction 7 of the original model

O2+HlArrrArr OH +O (19)

Indeed this reaction has been identified as important in thecase of inflammation at low temperatures [14] Initially theforward rate equation for this reaction is expressed as [5]

119896119891= 22 sdot 10

14 exp(minus8455119879) (20)

This valuewas obtainedwith an accuracy of 50 for a temper-ature range of 300 to 2000K By multiplying the coefficient120572119891119903

by 3 the rate of hydroperoxyl radical production OHis increased which leads to reduction in the ignition delay[12] The corresponding ignition delay becomes compara-ble to those obtained by more complex chemical kineticmodels with more reactions Finally the modified Evans-Schexnayder kinetic model with ten chemical reactions isgiven in Table 1

Figure 3 depicts the results obtained for validation of thiskinetic model in the case of H

2-O

2combustion The results

are presented in terms of pressure and temperature riseH

2consumption and OH and H

2O formation from one-

dimensional combustion simulation In Figures 3(a) and 3(b)the initial and themodified Evans-Schexnaydermodel resultsare compared to those from more complex kinetic schemesof Rogers and Chinitz [17] Drummond [18] and Bitker andScullin [19] respectively The results clearly highlight therelevance of the added specific reactions on the ignition timedelay [12]

42 Eklund Model This reaction simplified scheme pro-posed by Eklund et al [4] and implemented on both CEDREand CPS codes has been widely used by ONERA and CNES[3 20] for nozzle reactive flow studies This scheme consistsof 7 reversible reactions and 6 chemical species [O

2 H

2 OH

H2O O and H] As can be seen in Table 2 this scheme does

not involve any third body reaction which can present anadvantage in terms of computing time

5 Results and Discussions

51 Initial Conditions and Implementation of CalculationsThe calculations were performed over a computationaldomain which includes the nozzle the injector and the out-side experimental environmentThe calculation was initiatedat the nozzle inlet using the same initial data as the exper-imental test conditions described below No-slip conditionsalong the nozzlewalls were assumed For the outlet condition1 bar fixed pressure is applied at the downstream exit sectionAdiabatic no-slip conditions are imposed for the rest of thesurrounding block boundaries

Combustion temperature and species mass fractions forthe cryogenic LH

2-LO

2combustion products at desired

operating pressure chamber and 119900119891 ratio are obtained fromseparate calculations using the CEA thermochemical code[21]

In order to perform 2D CFD simulations of the nozzlersquosflow field finite volume grids have been constructed usingalgebraic grid generator software Multiblock structuredgrids have been used in this calculation The computationaldomain includes the convergent-divergent parts of the noz-zle the injector the zone downstream and the area located onboth sides of the nozzle The dimensions of the downstreamblock are more than 70ℎ in both 119909 and 119910 directions ℎ =

0028m being the nozzle height at its exit section A part ofthe meshing used in the computational domain representing


Table 2 Reduced Eklund reaction model [4] 119896119891in cm3molesdots


120573119891119894

120579119891119894(K) 120572

119887119894120573119887119894

120579119887119894(K)

1 H2 + O2 hArr 2OH 17 times 107 0 24240 27810 0363 146202 H + O2 hArr O + OH 142 times 108 0 8258 417 times 105 03905 minus2053 OH + H2 hArrH2O + H 316 times 101 18 1526 8953 1572 93464 O + H2 hArr OH + H 207 times 105 00 6924 1153 times 108 minus002726 57695 OH + OHhArrH2O + O 55 times 1008 00 1511 2797 times 1010 minus22004 104906 H + OHhArrH2O 1105 times 1012 minus20 00 2365 times 106 1313 509107 H + HhArrH2 3265 times 1007 minus10 00 308 times 106 0664 47201

the nozzle and part of the outer domain is illustrated inFigure 4(a)

The right part of Figure 4(b) depicts the mesh systemused for the injection slot and the nearby region It alsodepicts the mesh refinement near the wall To achieve theCFD calculation up to 40000 cells were required The gridrefinement near the wall in the 119910 direction such as the firstcell-height leads to 119910+ = 1 where 119910+ is the dimensionlessdistance defined as

119910+=119910

]radic120591119908

120588119908

(21)

with 120591119908 120588

119908 and ] being the shear stress at the wall the

density and the kinematic viscosity respectively An averageof 25 cells in the normal direction of the nozzle wall wasused to resolve the boundary layer thickness Furthermorea preliminary study of the mesh refinement sensitivity wasbeforehandperformed before achieving the final calculations

The fluid is considered to be an ideal gas mixture inthermal equilibrium The mixture heat capacity at constantpressure 119888

119901(119879) is calculated as a function of temperature from

the calorific capacity of each species expressed in polynomialform The Schmidt number Sc and the turbulent Prandtlnumber are set equal to 09 for all calculations

Boundary conditions for turbulence model are alsoneeded For the 119896-120576 turbulence model the turbulent kineticenergy 119896 and the turbulent dissipation rate 120576 required at theinlets for both nozzle and injector are calculated on the basisof an estimated turbulence intensity of 5 for this nozzle [3]

Moreover the Spalart Allmaras turbulence modelrequires the kinematic turbulence viscosity ]

119905of the mixture

For Reynolds numbers Re gt 105 which is the case here avalue of the turbulent viscosity ratio namely the ratio ofturbulent viscosity to laminar viscosity (120573 = ]

119905]) up to 100

is a reasonable estimateIn this study the fluxes are evaluated at each time step

using the Roe scheme associated with the second-orderspatial accuracy MINMOD flux limiter The time integrationis performed by a fully implicit scheme with a local time stepbased on CFL number ramped from 01 to 05 within thefirst 1000 iteration cycles Convergence to 10minus6 residuals wasusually attained after 20000 to 25000 iterations

Finally the code is based on the finite rate mechanismin calculating the chemical composition Each chemicalreaction obeys the law of mass action hence the backward

rate coefficient is calculated on the basis of the equilibriumconstant for each reversible reaction

The results obtained by the numerical simulations arepresented in terms of flow Mach number field temperatureand OHmass fraction fields In addition to the PLIF picturesfive experimental wall pressure values are available Thesepressures are measured along the cooled upper nozzle walland will be compared to the calculated values in the sameplots Each test case is simulated using two chemical kineticschemes namely ldquothe modified Evans-Schexnaiyder modelrdquoand ldquothe Eklund modelrdquo Two turbulence models are alsoconsidered in this calculation the standard two-equation 119896-120576and the one-equation Spalart-Allmaras model

The operating conditions of the tested cases and the initialdata for the numerical simulations inputs are summarized inTable 3

52 Aerodynamic Field To understand the flow topology weplotted the aerodynamic flow fields in terms ofMach numberof the different tested cases As depicted in Figure 5 for eachtest case both turbulence models used in the computationpredict a similar flow pattern Indeed in such nozzle regimes(overexpanded conditions) a separation shock is createdinside the nozzle extension to adapt the flow to the outsidepressure This configuration is known as the Free SeparationShock (FSS) As sketched in Figure 5(a) in all configurationsthe separation shock impacts the opposite wall and leads theboundary layer to separate similarly as in the so-called ShockWave Boundary Layer Interaction (SWBLI) The other pointthe flow topology reveals is that relating to the shock positionAs expected this position depends on both nozzle pressureratio NPR for a given turbulence model and turbulencemodel for a given NPR as illustrated in the comparisonsgiven in Figure 5 This point will be emphasized with moredetails in wall pressure discussion below

Moreover it should be noted that an increase in theGH

2injection pressure used in the film cooling as in

the calculated Case 4 pushes back the separation shockdownstream the injection slot towards the nozzle exit sectionThis result is depicted in Figure 6 in terms of calculatedpressure profiles for Case 1 (NPR = 259 119875

0119895= 3 bars) and for

Case 4 (NPR = 259 1198750119895

= 43 bars) As shown the relativedisplacement of shock determined with respect to the length119897 of the nozzle part concerned with the fim cooling (Δ119909119897) isabout 363 A similar trend has been reported in previous


Temperature (K)4000

3000

2000

1000

002 04 06 08 10

Huber et al

x (m)

400

300

200

100

002 04 06 08 10

Pressure (kPa)

x (m)

Rogers and Chinitz 1983Drummond 1988Bittker and Scullin 1972Evans and Schexnayder 1980

020

010

00002 04 06 08 10

H2O mass fraction

x (m)


003

002

001

00002 04 06 08 10

H2 mass fraction

x (m)


003

002

001

00002 04 06 08 10

OH mass fraction

x (m)

(a) Results from the initial model

Temperature (K)4000

3000

2000

1000

002 04 06 08 10

x (m)

400

300

200

100

002 04 06 08 10

Pressure (kPa)

x (m)

020

010

00002 04 06 08 10

H2O mass fraction

x (m)

Evans and Schexnayder model

Rogers and Chinitz 1983Drummond 1988Bittker and Scullin 1972

003

002

001

00002 04 06 08 10

OH mass fraction

x (m)



003

002

001

00002 04 06 08 10

H2 mass fraction

x (m)



(b) Results from the modified model

Figure 3 Results of one-dimensional combustion tube simulation obtained with some reaction models compared to initial and modifiedEvans-Schexnayder reaction model [12]


Caisson Outlet

Nozzle inletP0 T0 Yi

WallWall

Wall

Injector inlet

(a)

(b)

P0j T0j YH2=1

1 2 3 4 5 6 7 8 9

0

001

002

003

004

005

006

007 Y

ZX

005 01 015 02 025 03

0

1

2

3

4

Figure 4 Grids system used for CFD calculation (a) nozzle with part of the surrounding area (b) nozzle with a zoom of the region near theinjection slot

Table 3 Operating test cases conditions and initial inputs for CFD calculation

Test cases 1 2 3 4lowast

Measured quantitiesLO2 mass flow (gs) 449 461 672 xLH2 mass flow (gs) 242 142 359 xof 186 325 187 6

Conditions at the H2cooling injector

1198750119895cooling (H2) (bar) 31 32 43 43

1198790119869cooling (H2) (K) 29135 29425 29565 294

Conditions at the combustion chamber1198750(combustion chamber) (bar) 259 222 365 259

1198790(calculated) (K) 1693 2577 1945 3372

Calculated species mass fractions119884H2O 073229 085903 073366 087603119884OH 0 000190 0 006548119884H2

026771 013840 026634 003777119884O 0 000001 0 000580119884H 0 000065 0 000325119884O2

0 000001 0 001168lowastThis case is performed only numerically


0

001

002

003

004

005

006

007

014 016 018 02 022

00 05 1 15 2 25 3 3

406

Mach

024 026 028 03 032

(a) Case 1-119896-120576-Evans (NPR = 259)

0

001

002

003

004

005

006

007

014 016 018 02 022

00 05 1 15 2 25 3 3

453Mach

024 026 028 03 032

(b) Case 1-Spal-Evans (NPR = 259)

0

001

002

003

004

005

006

007

014 016 018 02 022

00 05 1 15 2 25 3 3

149Mach

024 026 028 03 032

(c) Case 2-119896-120576-Evans (NPR = 222)

0

001

002

003

004

005

006

007

014 016 018 02 022

00 05 1 15 2 25 3 3

19

Mach

024 026 028 03 032

(d) Case 2-Spal-Evans (NPR = 222)

0

001

002

003

004

005

006

007

014 016 018 02 022

00 05 1 15 2 25 353 3

654

Mach

024 026 028 03 032

(e) Case 3-119896-120576-Evans (NPR = 365)

0

001

002

003

004

005

006

007

014 016 018 02 022

00 05 1 15 2 25 353 3

639

Mach

024 026 028 03 032

(f) Case 3-Spal-Evans (NPR = 365)

Figure 5 Calculated Mach number fields for Cases 1 2 and 3

0

001

002

003

004

005

006

007

014 016 018 02 022

00 05 1 15 2 25 3 3

406

Mach

024 026 028 03 032

= 259 P0j = 31barsNPR

(a)

0

001

002

003

004

005

006

007

014 016 018 02 022

00 05 1 15 2 25 3 3

155Mach

024 026 028 03 032

NPR = 259 P0j = 43bars

(b)

Figure 6 Comparison between Case 4 and Case 1 119896-120576 and Evans

works [23] where similar film injection is used to control theflow separation in overexpanded supersonic nozzles

53 Wall Pressure The calculated pressure profiles are com-pared to the experimental pressure measured by means ofKulite transducers Figure 7 depicts the pressure distributionalong the upper wall of the nozzlersquos divergent downstream ofthe injection slot

The results in Figures 7(a) and 7(b) show that the tur-bulence models used in this work were able to predict withgood accuracy the pressure rise in the separation zone forTest Case 1 (NPR = 259) and Test Case 2 (NPR = 222) Thenumerical results also show that the reignition phenomenon

significantly affects the flow field in the separation zone Dueto the combustion process the separation area becomes largerthan the corresponding frozen cases and the separation shockmoves upstreamThis result highlights the chemical reactionsinfluence on the separation shock displacement and thereforeon the pressure rise within the recirculation zone This resultcan be connected to the boundary layer which becomesthicker in reactive flow and easier to detach in response toan adverse pressure gradient This finding is quite consistentwith previous works such as in [24] Note that Test case3 is not represented here in terms of comparison betweenthe calculated and measured pressure profiles Indeed forthis particular test case large pressure fluctuations in the


018 019 02 021 022 02320000

30000

40000

50000

60000

70000

80000

90000

100000

Exp

Pw

all (

Nm

2)

Case 1-Spal-Evans

Case 1-Spal-Frozen

X (m)

Case 1-k-120576-EvansCase 1-k-120576-Frozen

(a) Calculated and measured wall pressure (Case 1)

Case 2-Spal-Evans Case 2-Spal-FrozenExp

X (m)

Case 2-k-120576-Evans

Case 2-k-120576-Eklund

Case 2-k-120576-Frozen

018 019 02 021 022 02320000

30000

40000

50000

60000

70000

80000

90000

100000

Pw

all (

Nm

2)

(b) Calculated and measured wall pressure (Case 2)

Case 4-Spal-EvansCase 1-Spal-Evans

X (m)018 019 02 021 022 023

20000

30000

40000

50000

60000

70000

80000

90000

100000

Pw

all (

Nm

2)

(c) Comparison between calculated Cases 1 and 4

Figure 7 Calculated and measured wall pressure in the zone downstream the injection slot

combustion chamber were recorded during the course ofexperiments This led to great separation shock instabilitiesand large discrepancy in measurements

Additional Test Case 4 was carried out only by numericalmeans with an oxidizerfuel ratio (119900119891 = 6) close to that ofreal rocket engines functioning with LO

2-LH

2 The nozzle

pressure ratio NPR is fixed the same way as for Test Case1 that is NPR = 259 while the total pressure of the H

2

film cooling is set to 1198750119895= 43 bars As can be seen in

Figure 7(c) augmenting the film cooling total pressure leads

the separation shock to move downstream as well as thereignition attachment point consequentlyThis possibility canbe used as will be mentioned below as means to avoid thereignition of the mixture inside the nozzle

54 Chemical Production To highlight the reignition phe-nomenon in the separation zone we plotted the flow OHmass fraction The results obtained show that OH radicalconcentrations are at levels high enough to readily suggest


0001

0002

0003

0004

0005

0006

0007

01

02

03

04

05

06

07

08

09

1

OH

H2

0

001

002

003

004

005

006

007

001

002

003

004

005

006

007

014 016 018 02 022 024 026 028 03 032

(a) Case 10001

00015

00005

0 0002

00025

0003

00035

0004

0102030405060708091

OH

H2

0

001

002

003

004

005

006

007

001

002

003

004

005

006

007

014 016 018 02 022 024 026 028 03 032

(b) Case 4

Figure 8 Calculated OH radicals and H2concentrations Evans and 119896-120576 calculations

Separation areaOutside air

Attached flame

Hot gas main flow

Mixing shearlayer

Injected GH2

Figure 9 Flow configuration as deduced from CFD calculations

a reignition of the H2-Air mixture in the separated region

The examples illustrated in Figures 8(a) and 8(b) suggestthat the entrained fresh oxygen from the outside into theseparation zone leads to the inflammation GH

2used in the

film cooling across the mixing shear layer A like-diffusionflame appears and extends downstream along the shear layerA schematic of the flow configuration with an attachedflame to the nozzle upper wall in the separation area isdepicted in Figure 9 It is worth noting that these results wereobserved for both turbulence models with modified Evans-Schexnayder chemical kinetics model but not with Eklundmodel This can be explained by the temperature levels in thenozzle main flow across the shear layer which are not highenough to reactivate the chemical reactions with the abovementioned reaction model On the other hand when thenozzle operates at pressure ratios close to the adaptation as inCase 3 (NPR = 365) no reignition process has been observedin the flow inside the nozzle Indeed as mentioned above theseparation zone size is too small that it does not allow thefull completion of the combustion process within this area Inthis case the combustion takes place in the outer caisson faraway from the nozzle exit sectionThis situation is depicted inFigure 10 for both OH concentrations and temperature plots

55 Thermal Loads The film cooling efficiency is evaluatedby a widely used parameter 120578 describing the difference

between the film cooled wall temperature at each point andthe combustion chamber temperature relative to the differ-ence between the coolant temperature and the combustionchamber temperature The cooling efficiency is expressed bythe nondimensional efficiency 120578 defined as

120578 =119879119908minus 119879

119888

119879119891minus 119879

119888

(22)

where 119879119908is the calculated wall temperature119879

119888the calculated

combustion chamber temperature and 119879119891the injected film

temperatureThe cooling efficiency along the wall depends as before

on whether the nozzle flow is fully expanded or overex-panded Figures 11(a) and 11(b) represent an example ofwall temperature calculated in the Case 1 (NPR = 259) andCase 2 (NPR = 222) respectively where the nozzle operatesin overexpanded conditions The combustion of injectedGH

2leads to an increase in wall temperature in the region

where the flame is attached The wall temperature plots arecharacterized by marked peaks up to 1600K compared tofrozen flow calculations These results represent a furtherconfirmation of the hypotheses raised previously about thereignition phenomenon As can be seen these peaks areshifted according to the observations made above about theseparation zone In this case the cooling efficiency falls tovalues close to 005 and 04 respectively for Case 1 and Case


0001

0002

0003

0004

0005

0006

0007

0008

0009 0009425OH

4944Eminus022

(a)

2000

1800

1600

1400

1200

100080

060

040

020

0 2113

1539

T (K)

(b)

Figure 10 Calculated OH concentration and flow temperature Case 3 Evans and 119896-120576 calculation The combustion takes place outside thenozzle

018 019 02 021 022 023200

400

600

800

1000

1200

1400

1600

1800

X (m)

Tw

(K)

Case 1-Spal-EvansCase 1-Spal-Frozen


(a)

200

400

600

800

1000

1200

1400

1600

1800

Tw

(K)

Case 2-Spal-Evans Case 2-Spal-Frozen

018 019 02 021 022 023X (m)




(b)

260

280

300

320

340

360

380

400

420

440

Tw

(K)

018 019 02 021 022 023X (m)

Case 3-Spal-Evans

Case 3-k-120576-EvansCase 3-k-120576-Evans

(c)Figure 11 Wall temperature profiles with reignition Cases 1 (a) and 2 (b) and without reignition for Case 3 (c)


0

02

04

06

08

1

018 019 02 021 022 023

X (m)

Coo

ling

film

effici

ency



(a)

03

04

05

06

07

08

09

1

018 019 02 021 022 023

X (m)

Coo

ling

film

effici

ency

Case 2-Spal-Evans Case 2-k-120576-FrozenCase 2-k-120576-Evans Case 2-k-120576-Eklund

(b)

092

094

096

098

1

018 019 02 021 022 023

X (m)

Coo

ling

film

effici

ency

Case 3-Spal-EvansCase 3-k-120576-Evans

(c)

Figure 12 Cooling film efficiency as function of distance from the injection slot for (a) Case 1 (b) Case 2 and (c) Case 3

2 (Figures 12(a) and 12(b)) where the temperature of theattached flame is close to the adiabatic temperature of thecombustion chamber particularly forCase 1MeanwhileCase3 shows a typical behavior of film cooling applications asit was observed in several works [2] In this case the tem-perature of the film cooling grows gradually by mixing withthe hot main flow gas (Figure 11(c)) and the correspondingefficiency (120578 gt 08) is within the range of the expected values(Figure 12(c))

6 Conclusions

This numerical study was conducted with the goal of repro-ducing some experimental tests carried out previously Themain objective was to check to which extent the chemicalkinetics and turbulence models may be relevant to highlightthe reignition phenomenon in the case of a subscale super-sonic nozzle hot flow cooled by H

2film cooling device The

main findings of this study can be summarized as follows


Even though the real separated flow is naturally unsteadythe steady RANS approach using 119896-120576 and Spalart-Allmarasmodels combined with a modified kinetic model was foundto be able to reproduce the accurate averaged flow field andthe reignition phenomenon observed experimentally

Globally the calculated wall pressures are in good agree-ment with the experimental data for the whole tested casesand the effect of chemical reactions on these quantities hasbeen pointed out

The computed steady reacting regions are slightly dif-ferent from the instantaneous PLIF measurements whichillustrate the complexity of this phenomenon Furthermoreit is demonstrated that the steady attached flame occurs alongthe mixing shear layer and the combustion regime is mostlydiffusion

When reignition occurs the temperature at the nozzlewall is such that the film cooling becomes locally inoperativeand the induced thermal loads is so high that the nozzlersquosaerodynamic properties can be altered up to being detrimen-tal for the nozzle structural integrity

As expected the choice of a turbulence model does notglobally impact the phenomena that depend on the chemicalkinetics as the reignition process however it significantlyaffects the phenomena related to the boundary layer This ishow Spalart-Allmaras model gives a better prediction of theshock position and the pressure rise in the separation zonecompared to the experimental results

Abbreviations

119862 Concentrationℎ Enthalpy119870 Rates of a reaction119872 Mach number119872

119904 Molar mass

NPR Nozzle Pressure Ratio119875 Total pressure119901 Static pressurePr Prandtl number119877119906 Universal gas constant

Re Reynolds numberSc Schmidt number119879 Temperature119906 Flow velocity119881 VolumeV Velocity in 119910 direction119908 Velocity in 119911 direction119883 Mole fraction119884 Masse fraction119909 Axial flow direction119910 Vertical (side) direction

Greek Symbols

120572 Concentration power120574 Ratio of specific heats120583 Molecular dynamic viscosity] Kinematic viscosity120588 Density of fluid

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

This work was part of the ATAC activities and the authorswould like to thank the French Space Agency (CNES) fortheir support

References

[1] L Winterfeldt B Laumert R Tano et al ldquoRedesign ofthe vulcain 2 nozzle extensionrdquo in Proceedings of the 41stIAAASMESAEASEE Joint Propulsion Conference amp ExhibitAIAA-2005-4536 2005

[2] D I Suslov R Arnolds and O J Haiden ldquoExperimentalinvestigation of cooling film efficiency in the nozzle extensionof LOXH2 subscale combustion chamberrdquo in Proceedings of the4th European Conference for Aerospace Sciences (EUCASS rsquo11)St Petersburg Russia July 2011

[3] G Ordonneau P Hervat F Grisch L Vingert and P ReijasseldquoPLIF investigation of reactive flows in the separation region ofan over-expanded two-dimensional nozzlerdquo AIAA Paper 2006-5209 2006

[4] D R Eklund J P Drummond and H A Hassan ldquoCalculationof supersonic turbulent reacting coaxial jetsrdquoAIAA journal vol28 no 9 pp 1633ndash1641 1990

[5] J S Evans and C J Schexnayder Jr ldquoInfluence of chemicalkinetics and unmixedness on burning in supersonic hydrogenflamesrdquo AIAA Journal vol 18 no 2 pp 188ndash193 1980

[6] S F Gordon and B J McBride ldquoNASA Glenn coefficients forcalculating thermodynamic properties of individual speciesrdquoTechnical Publication NASATP-2002-211556 NASA Glenn2002

[7] R B Bird W E Stewart and E N Lightfoot TransportPhenomena Wiley New York NY USA 1960

[8] R A Svehla ldquoEstimated viscosities and thermal conductivitiesof gases at high temperaturesrdquo NASA Technical Report R-1321962

[9] C RWilke ldquoA viscosity equation for gas mixturesrdquoThe Journalof Chemical Physics vol 18 no 4 pp 517ndash519 1950

[10] J D Anderson Modern Compressible Flow With HistoricalPerspective McGraw-Hill New York NY USA 2nd edition1990

[11] K K Kuo Principle of Combustion John Wiley amp Sons NewYork NY USA 1986

[12] C S Craddock Computational optimization of scramjets andshock tunnel nozzles [PhD thesis] Department of MechanicalEngineering University of Queensland Brisbane Australia1999

[13] S Yungster S Eberhardt and A P Bruckner ldquoNumericalsimulation of hypervelocity projectiles in detonable gasesrdquoAIAA journal vol 29 no 2 pp 187ndash199 1991

[14] C J Jachimowski ldquoAn analytical study of the hydrogen-airreaction mechanism with application to scramjet combustionrdquoNASA Technical Paper 2791 1988

[15] A P Bruckner C Knowlen and A Hertzberg ldquoApplicationsof the ram accelerator to hypervelocity aerothermodynamic


testingrdquo in Proceedings of the 28th Joint Propulsion Conferenceand Exhibit AIAA-92-3949 Nashville Tenn USA July 1992

[16] DMHarradine J L Lyman R C Oldenborg G L Schott andH H Watanabe ldquoHydrogenair combustion calculationsmdashthechemical basis of efficiency in hypersonic flowsrdquo AIAA Journalvol 28 no 10 pp 1740ndash1744 1990

[17] R C Rogers and W Chinitz ldquoUsing a global hydrogen-aircombustion model in turbulent reacting flow calculationsrdquoAIAA Journal vol 21 no 4 pp 586ndash592 1983

[18] J P Drummond ldquoA two-dimensional numerical simulation of asupersonic chemically reacting mixing layerrdquo NASA TM-40551988

[19] D A Bittker and V J Scullin ldquoGeneral chemical kineticscomputer program for static and flow reactions with applica-tion to combustion and shock-tube kineticsrdquo NASP TechnicalMemorandum TND-6586 1972

[20] P Durand B Vieille H Lamban et al ldquoCPS a three-dimensionnal CFD numerical code dedicated to space propul-sive flowsrdquo inProceedings of the 36th Joint Propulsion Conferenceamp Exhibit AIAA-2000-36976 July 2000

[21] S F Gordon and B J McBride ldquoComputer program forcalculation of complex chemical equilibrium compositions andapplicationsrdquo NASA RP-1311 NASA Glenn Research Center1996

[22] G Ordonneau P Hervat L Vingert S Pettito and B PouffaryldquoFirst results of heat transfer measurements in a new water-cooled combustor on theMascotte facilityrdquo in Proceedings of the4th European Conference for Aerospace Sciences (EUCASS rsquo11)2011

[23] P Reijasse and L Boccaletto ldquoNozzle flow separation withfilm coolingrdquo in Proceedings of the 38th AIAA Fluid DynamicsConference and Exhibit AIAA 2008-4150 Seattle Wash USAJune 2008

[24] P Gnemmi P Gruhn M Leplat C Nottin and S WallinldquoComputation validation on lateral jet interactions at super-sonic speedsrdquo International Journal of Engineering SystemsModelling and Simulation vol 5 no 1ndash3 pp 68ndash83 2013

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Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



Cylindricalcombustion

chamber

Outlet caisson

C-D planarnozzle

2 injectorGH

(a) From [22]

Wall with pressuretransducers

Gas combustionInjector

Separation shock

Thermal loads due to reignition

Nozzle inlet

Recirculation zone

h = 002818 m

H2 injection

l = 00551mL = 0122m

= 0002myth

(b)

Figure 1 Mascotte test bench assembly (a) and sketch of longitudinal section of the planar nozzle (b)

P0 = 259bar of = 185 P0 = 365bar of = 187

Figure 2 PLIF images of OH radicals from [3]

temperature In this occurrence the film cooling efficiencyis altered and the induced thermal loads may be critical forthese nozzles

To understand these phenomena a campaign of experi-mental measurements was conducted at the cryogenic LH

2-

LO2ONERAMascotte test bench facility [3] The results yet

obtained for low oxidizerfuel ratios (119900119891) on the basis ofPLIF and Kulite pressure measurements already constitute avery useful database for understanding the involved physico-chemical phenomena The first series of measurements wereperformed under 119900119891 ratios of up to 3 and combustionchamber pressure up to 40 bars The first results obtainedduring this measurements campaign highlighted a reignitionphenomenon occurring in the nozzle main flow inside theseparation area

Given the complexity of these phenomena numericalsimulations performed by different computing codes cangive a better interpretation of the experimental results Thepresent numerical work is a further contribution in thisregard and consists in simulating the turbulent reactiveflows in the same operating conditions as those performedexperimentally

This work was carried out within the framework andwith the support of the French research group ATAC(Aerodynamique des Tuyeres et Arrieres Corps (Nozzles andAfterbodies Aerodynamics))

2 Objectives

The aim of this paper is to perform 2D RANS turbulentreacting flows simulations for three test cases carried outexperimentally in the ONERAMascotte test bench For thispurpose two chemical kinetic schemes and two turbulencemodels were tested to investigate their relevance in thereignition process inside the nozzle

Basically the test bench consists of a subscale planarnozzle connected to a cylindrical combustion chamber fedwith a cryogenic mixture LOx-LH2

(Figure 1(a)) This hard-ware version has been developed especially to investigate theflow separation in overexpanded regimes The combustionchamber operates under controlled total pressure and oxi-dizerfuel ratios (119900119891) The main geometrical characteristicsof the nozzle are given in Figure 1(b) Pure hydrogen gas(GH

2) serving as film cooling is injected tangentially into

the upper wall of the nozzle through a slightly supersonicinjector Five Kulite pressure transducers are taped along thiswall A schematic longitudinal cross section of the nozzle isshown in Figure 1(b)

The first results [3] obtained by PLIF visualizationsperformed in this test bench show an increase in concen-trations of OH radical near the upper wall of the nozzlersquosdivergent in the separation zoneThis suggests a reactivationof the combustion inside this area (Figure 2) During these








119901 = sum119904

120588119904

119872119908119904

119877119906119879 (1)






119864119905= 120588119888V119879 +

1

2120588119906

119895119906119895 (2)





119864119905= sum

119904

120588119904(119888Vtr119904119879 + Δℎ

0

119891119879119903119904) + 119864V +

1

2120588119906

119895119906119895 (3)




119903




119864119905= sum

119904

120588119904(ℎ

119904minus119877119906119879

119872119908119904

) +1

2120588119906

119895119906119895 (4)


119864119905= sum

119904

120588119904[119888Vtr119904119879 + Δℎ

0

119891119879119903119904minus 119879

119903(119888Vtr119904 minus

119877119906

119872119908119904

)]

+ 119864int +1

2120588119906

119895119906119895

(5)


defined as

ℎ119904= int

119879

119879119903

119888119901119904119889119879 + Δℎ

0

119891119879119903119904 (6)




120583119904= 266693sdot10

minus6radic119872119908119904

119879

120590Ω120583

(7)





120583 = sum119904

119883119904120583119904

Φ119904

(8)


119904is given by

Φ119904= sum

119903

119883119903[1 + radic

120583119904

120583119903

(119872

119908119903

119872119908119904

)

14

]

2

[radic8(1 +119872

119908119904

119872119908119903

)]

minus1

(9)



119869119904= minus120588119863

119904nabla119884

119904 (10)




119863119904=120583

120588Sc (11)






sum119904=1

]1015840119904119903119872

119904lArrrArr

119899119904

sum119904=1

]10158401015840119904119903119872

119904 (12)

where ]1015840119904119903and ]10158401015840




120596119904= 119872

119908119904(]10158401015840

119904119903minus ]1015840

119904119903) [

119899119904

sum119904=1

120573119904119903119862119904]

sdot 119870119891119903

119899119904

prod119904=1

[119862119904]1205721015840

119904119903 minus 119870119887119903

119899119904

prod119904=1

[119862119904]12057210158401015840

119904119903

(13)



119891119903and

119870119887119903


119904119903and 12057210158401015840

119904119903are

identical to ]1015840119904119903and ]10158401015840



119870119891119903= 120572

119891119903119879120573119891119903 sdot 119890

(minus119864119886119903(119877sdot119879))

(14)

where 120572119891119903 120573

119891119903 and 119864


under investigation


120597119876

120597119905+ nabla sdot

997888119865


997888119865

119863) = 119878 (15)




119876 =

[[[[[[[[[[[[[[[[[[[[[[[[[

[

119864int

1205881

1205882

120588119899119904

120588119906

120588V

120588119908

119864119905

]]]]]]]]]]]]]]]]]]]]]]]]]

]

119865119862=

[[[[[[[[[[[[[[[[[[[[[[[[[

[

119864int119906

1205881119906

1205882119906

120588119899119904119906

1205881199062 + 119901

120588119906V

120588119906119908

(119864119905+ 119901) 119906

]]]]]]]]]]]]]]]]]]]]]]]]]

]

119878 =

[[[[[[[[[[[[[[[[[[[[[[[[[

[

int

1

2

119899119904

0

0

0

0

]]]]]]]]]]]]]]]]]]]]]]]]]

]

119865119863=

[[[[[[[[[[[[[[[[[[[[[[[

[

119899119904

sum

119904=1

119890V119904120588119904119880119904 + 119896int120597119879int120597119909

minus12058811198801

minus12058821198802

minus120588119899119904119880119904

120591119909119909 minus2

3120588119896

120591119909119910

120591119909119911

[119906120591119909119909 + V120591119909119910 + 119908120591119909119911 + (119896 + 119896119905)120597119879

120597119909+ 119896int

120597119879int120597119909

+sumℎ119904120588119904119880119904]

]]]]]]]]]]]]]]]]]]]]]]]

]



119904and 119880

119904are


119904= 120588 and 119880

119904= 0 Note that




2-O






119894= 119864

119886119877


120573119894

120579119894(K)



2 H

2 OH H

2O N

2 and O] and 8








H +O2+MlArrrArr HO

2+M (17)



2O

2) in the model




119896119891= 22 sdot 10

14 exp(minus8455119879) (20)




2-O







2 H

2 OH






2-LO








120573119891119894

120579119891119894(K) 120572

119887119894120573119887119894

120579119887119894(K)




119910+=119910

]radic120591119908

120588119908

(21)

with 120591119908 120588










119905]) up to 100












Case 4 (NPR = 259 1198750119895



Temperature (K)4000

3000

2000

1000

002 04 06 08 10

Huber et al

x (m)

400

300

200

100

002 04 06 08 10

Pressure (kPa)

x (m)


020

010

00002 04 06 08 10

H2O mass fraction

x (m)


003

002

001

00002 04 06 08 10

H2 mass fraction

x (m)


003

002

001

00002 04 06 08 10

OH mass fraction

x (m)


Temperature (K)4000

3000

2000

1000

002 04 06 08 10

x (m)

400

300

200

100

002 04 06 08 10

Pressure (kPa)

x (m)

020

010

00002 04 06 08 10

H2O mass fraction

x (m)



003

002

001

00002 04 06 08 10

OH mass fraction

x (m)



003

002

001

00002 04 06 08 10

H2 mass fraction

x (m)






Caisson Outlet


WallWall

Wall

Injector inlet

(a)

(b)

P0j T0j YH2=1

1 2 3 4 5 6 7 8 9

0

001

002

003

004

005

006

007 Y

ZX

005 01 015 02 025 03

0

1

2

3

4






1198750119895cooling (H2) (bar) 31 32 43 43

1198790119869cooling (H2) (K) 29135 29425 29565 294


1198790(calculated) (K) 1693 2577 1945 3372


026771 013840 026634 003777119884O 0 000001 0 000580119884H 0 000065 0 000325119884O2



0

001

002

003

004

005

006

007

014 016 018 02 022

00 05 1 15 2 25 3 3

406

Mach

024 026 028 03 032

(a) Case 1-119896-120576-Evans (NPR = 259)

0

001

002

003

004

005

006

007

014 016 018 02 022

00 05 1 15 2 25 3 3

453Mach

024 026 028 03 032


0

001

002

003

004

005

006

007

014 016 018 02 022

00 05 1 15 2 25 3 3

149Mach

024 026 028 03 032

(c) Case 2-119896-120576-Evans (NPR = 222)

0

001

002

003

004

005

006

007

014 016 018 02 022

00 05 1 15 2 25 3 3

19

Mach

024 026 028 03 032


0

001

002

003

004

005

006

007

014 016 018 02 022

00 05 1 15 2 25 353 3

654

Mach

024 026 028 03 032

(e) Case 3-119896-120576-Evans (NPR = 365)

0

001

002

003

004

005

006

007

014 016 018 02 022

00 05 1 15 2 25 353 3

639

Mach

024 026 028 03 032



0

001

002

003

004

005

006

007

014 016 018 02 022

00 05 1 15 2 25 3 3

406

Mach

024 026 028 03 032


(a)

0

001

002

003

004

005

006

007

014 016 018 02 022

00 05 1 15 2 25 3 3

155Mach

024 026 028 03 032


(b)







018 019 02 021 022 02320000

30000

40000

50000

60000

70000

80000

90000

100000

Exp

Pw

all (

Nm

2)

Case 1-Spal-Evans

Case 1-Spal-Frozen

X (m)




X (m)




018 019 02 021 022 02320000

30000

40000

50000

60000

70000

80000

90000

100000

Pw

all (

Nm

2)



X (m)018 019 02 021 022 023

20000

30000

40000

50000

60000

70000

80000

90000

100000

Pw

all (

Nm

2)





2-LH

2 The nozzle


2






0001

0002

0003

0004

0005

0006

0007

01

02

03

04

05

06

07

08

09

1

OH

H2

0

001

002

003

004

005

006

007

001

002

003

004

005

006

007

014 016 018 02 022 024 026 028 03 032

(a) Case 10001

00015

00005

0 0002

00025

0003

00035

0004

0102030405060708091

OH

H2

0

001

002

003

004

005

006

007

001

002

003

004

005

006

007

014 016 018 02 022 024 026 028 03 032

(b) Case 4



Attached flame

Hot gas main flow

Mixing shearlayer

Injected GH2




2used in the




120578 =119879119908minus 119879

119888

119879119891minus 119879

119888

(22)









0001

0002

0003

0004

0005

0006

0007

0008

0009 0009425OH

4944Eminus022

(a)

2000

1800

1600

1400

1200

100080

060

040

020

0 2113

1539

T (K)

(b)


018 019 02 021 022 023200

400

600

800

1000

1200

1400

1600

1800

X (m)

Tw

(K)



(a)

200

400

600

800

1000

1200

1400

1600

1800

Tw

(K)


018 019 02 021 022 023X (m)




(b)

260

280

300

320

340

360

380

400

420

440

Tw

(K)

018 019 02 021 022 023X (m)

Case 3-Spal-Evans




0

02

04

06

08

1

018 019 02 021 022 023

X (m)

Coo

ling

film

effici

ency



(a)

03

04

05

06

07

08

09

1

018 019 02 021 022 023

X (m)

Coo

ling

film

effici

ency


(b)

092

094

096

098

1

018 019 02 021 022 023

X (m)

Coo

ling

film

effici

ency


(c)



6 Conclusions










Abbreviations


119904 Molar mass



Greek Symbols




Acknowledgment


References





























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation
















119901 = sum119904

120588119904

119872119908119904

119877119906119879 (1)






119864119905= 120588119888V119879 +

1

2120588119906

119895119906119895 (2)





119864119905= sum

119904

120588119904(119888Vtr119904119879 + Δℎ

0

119891119879119903119904) + 119864V +

1

2120588119906

119895119906119895 (3)




119903




119864119905= sum

119904

120588119904(ℎ

119904minus119877119906119879

119872119908119904

) +1

2120588119906

119895119906119895 (4)


119864119905= sum

119904

120588119904[119888Vtr119904119879 + Δℎ

0

119891119879119903119904minus 119879

119903(119888Vtr119904 minus

119877119906

119872119908119904

)]

+ 119864int +1

2120588119906

119895119906119895

(5)


defined as

ℎ119904= int

119879

119879119903

119888119901119904119889119879 + Δℎ

0

119891119879119903119904 (6)




120583119904= 266693sdot10

minus6radic119872119908119904

119879

120590Ω120583

(7)





120583 = sum119904

119883119904120583119904

Φ119904

(8)


119904is given by

Φ119904= sum

119903

119883119903[1 + radic

120583119904

120583119903

(119872

119908119903

119872119908119904

)

14

]

2

[radic8(1 +119872

119908119904

119872119908119903

)]

minus1

(9)



119869119904= minus120588119863

119904nabla119884

119904 (10)




119863119904=120583

120588Sc (11)






sum119904=1

]1015840119904119903119872

119904lArrrArr

119899119904

sum119904=1

]10158401015840119904119903119872

119904 (12)

where ]1015840119904119903and ]10158401015840




120596119904= 119872

119908119904(]10158401015840

119904119903minus ]1015840

119904119903) [

119899119904

sum119904=1

120573119904119903119862119904]

sdot 119870119891119903

119899119904

prod119904=1

[119862119904]1205721015840

119904119903 minus 119870119887119903

119899119904

prod119904=1

[119862119904]12057210158401015840

119904119903

(13)



119891119903and

119870119887119903


119904119903and 12057210158401015840

119904119903are

identical to ]1015840119904119903and ]10158401015840



119870119891119903= 120572

119891119903119879120573119891119903 sdot 119890

(minus119864119886119903(119877sdot119879))

(14)

where 120572119891119903 120573

119891119903 and 119864


under investigation


120597119876

120597119905+ nabla sdot

997888119865


997888119865

119863) = 119878 (15)




119876 =

[[[[[[[[[[[[[[[[[[[[[[[[[

[

119864int

1205881

1205882

120588119899119904

120588119906

120588V

120588119908

119864119905

]]]]]]]]]]]]]]]]]]]]]]]]]

]

119865119862=

[[[[[[[[[[[[[[[[[[[[[[[[[

[

119864int119906

1205881119906

1205882119906

120588119899119904119906

1205881199062 + 119901

120588119906V

120588119906119908

(119864119905+ 119901) 119906

]]]]]]]]]]]]]]]]]]]]]]]]]

]

119878 =

[[[[[[[[[[[[[[[[[[[[[[[[[

[

int

1

2

119899119904

0

0

0

0

]]]]]]]]]]]]]]]]]]]]]]]]]

]

119865119863=

[[[[[[[[[[[[[[[[[[[[[[[

[

119899119904

sum

119904=1

119890V119904120588119904119880119904 + 119896int120597119879int120597119909

minus12058811198801

minus12058821198802

minus120588119899119904119880119904

120591119909119909 minus2

3120588119896

120591119909119910

120591119909119911

[119906120591119909119909 + V120591119909119910 + 119908120591119909119911 + (119896 + 119896119905)120597119879

120597119909+ 119896int

120597119879int120597119909

+sumℎ119904120588119904119880119904]

]]]]]]]]]]]]]]]]]]]]]]]

]



119904and 119880

119904are


119904= 120588 and 119880

119904= 0 Note that




2-O






119894= 119864

119886119877


120573119894

120579119894(K)



2 H

2 OH H

2O N

2 and O] and 8








H +O2+MlArrrArr HO

2+M (17)



2O

2) in the model




119896119891= 22 sdot 10

14 exp(minus8455119879) (20)




2-O







2 H

2 OH






2-LO








120573119891119894

120579119891119894(K) 120572

119887119894120573119887119894

120579119887119894(K)




119910+=119910

]radic120591119908

120588119908

(21)

with 120591119908 120588










119905]) up to 100












Case 4 (NPR = 259 1198750119895



Temperature (K)4000

3000

2000

1000

002 04 06 08 10

Huber et al

x (m)

400

300

200

100

002 04 06 08 10

Pressure (kPa)

x (m)


020

010

00002 04 06 08 10

H2O mass fraction

x (m)


003

002

001

00002 04 06 08 10

H2 mass fraction

x (m)


003

002

001

00002 04 06 08 10

OH mass fraction

x (m)


Temperature (K)4000

3000

2000

1000

002 04 06 08 10

x (m)

400

300

200

100

002 04 06 08 10

Pressure (kPa)

x (m)

020

010

00002 04 06 08 10

H2O mass fraction

x (m)



003

002

001

00002 04 06 08 10

OH mass fraction

x (m)



003

002

001

00002 04 06 08 10

H2 mass fraction

x (m)






Caisson Outlet


WallWall

Wall

Injector inlet

(a)

(b)

P0j T0j YH2=1

1 2 3 4 5 6 7 8 9

0

001

002

003

004

005

006

007 Y

ZX

005 01 015 02 025 03

0

1

2

3

4






1198750119895cooling (H2) (bar) 31 32 43 43

1198790119869cooling (H2) (K) 29135 29425 29565 294


1198790(calculated) (K) 1693 2577 1945 3372


026771 013840 026634 003777119884O 0 000001 0 000580119884H 0 000065 0 000325119884O2



0

001

002

003

004

005

006

007

014 016 018 02 022

00 05 1 15 2 25 3 3

406

Mach

024 026 028 03 032

(a) Case 1-119896-120576-Evans (NPR = 259)

0

001

002

003

004

005

006

007

014 016 018 02 022

00 05 1 15 2 25 3 3

453Mach

024 026 028 03 032


0

001

002

003

004

005

006

007

014 016 018 02 022

00 05 1 15 2 25 3 3

149Mach

024 026 028 03 032

(c) Case 2-119896-120576-Evans (NPR = 222)

0

001

002

003

004

005

006

007

014 016 018 02 022

00 05 1 15 2 25 3 3

19

Mach

024 026 028 03 032


0

001

002

003

004

005

006

007

014 016 018 02 022

00 05 1 15 2 25 353 3

654

Mach

024 026 028 03 032

(e) Case 3-119896-120576-Evans (NPR = 365)

0

001

002

003

004

005

006

007

014 016 018 02 022

00 05 1 15 2 25 353 3

639

Mach

024 026 028 03 032



0

001

002

003

004

005

006

007

014 016 018 02 022

00 05 1 15 2 25 3 3

406

Mach

024 026 028 03 032


(a)

0

001

002

003

004

005

006

007

014 016 018 02 022

00 05 1 15 2 25 3 3

155Mach

024 026 028 03 032


(b)







018 019 02 021 022 02320000

30000

40000

50000

60000

70000

80000

90000

100000

Exp

Pw

all (

Nm

2)

Case 1-Spal-Evans

Case 1-Spal-Frozen

X (m)




X (m)




018 019 02 021 022 02320000

30000

40000

50000

60000

70000

80000

90000

100000

Pw

all (

Nm

2)



X (m)018 019 02 021 022 023

20000

30000

40000

50000

60000

70000

80000

90000

100000

Pw

all (

Nm

2)





2-LH

2 The nozzle


2






0001

0002

0003

0004

0005

0006

0007

01

02

03

04

05

06

07

08

09

1

OH

H2

0

001

002

003

004

005

006

007

001

002

003

004

005

006

007

014 016 018 02 022 024 026 028 03 032

(a) Case 10001

00015

00005

0 0002

00025

0003

00035

0004

0102030405060708091

OH

H2

0

001

002

003

004

005

006

007

001

002

003

004

005

006

007

014 016 018 02 022 024 026 028 03 032

(b) Case 4



Attached flame

Hot gas main flow

Mixing shearlayer

Injected GH2




2used in the




120578 =119879119908minus 119879

119888

119879119891minus 119879

119888

(22)









0001

0002

0003

0004

0005

0006

0007

0008

0009 0009425OH

4944Eminus022

(a)

2000

1800

1600

1400

1200

100080

060

040

020

0 2113

1539

T (K)

(b)


018 019 02 021 022 023200

400

600

800

1000

1200

1400

1600

1800

X (m)

Tw

(K)



(a)

200

400

600

800

1000

1200

1400

1600

1800

Tw

(K)


018 019 02 021 022 023X (m)




(b)

260

280

300

320

340

360

380

400

420

440

Tw

(K)

018 019 02 021 022 023X (m)

Case 3-Spal-Evans




0

02

04

06

08

1

018 019 02 021 022 023

X (m)

Coo

ling

film

effici

ency



(a)

03

04

05

06

07

08

09

1

018 019 02 021 022 023

X (m)

Coo

ling

film

effici

ency


(b)

092

094

096

098

1

018 019 02 021 022 023

X (m)

Coo

ling

film

effici

ency


(c)



6 Conclusions










Abbreviations


119904 Molar mass



Greek Symbols




Acknowledgment


References





























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











120583 = sum119904

119883119904120583119904

Φ119904

(8)


119904is given by

Φ119904= sum

119903

119883119903[1 + radic

120583119904

120583119903

(119872

119908119903

119872119908119904

)

14

]

2

[radic8(1 +119872

119908119904

119872119908119903

)]

minus1

(9)



119869119904= minus120588119863

119904nabla119884

119904 (10)




119863119904=120583

120588Sc (11)






sum119904=1

]1015840119904119903119872

119904lArrrArr

119899119904

sum119904=1

]10158401015840119904119903119872

119904 (12)

where ]1015840119904119903and ]10158401015840




120596119904= 119872

119908119904(]10158401015840

119904119903minus ]1015840

119904119903) [

119899119904

sum119904=1

120573119904119903119862119904]

sdot 119870119891119903

119899119904

prod119904=1

[119862119904]1205721015840

119904119903 minus 119870119887119903

119899119904

prod119904=1

[119862119904]12057210158401015840

119904119903

(13)



119891119903and

119870119887119903


119904119903and 12057210158401015840

119904119903are

identical to ]1015840119904119903and ]10158401015840



119870119891119903= 120572

119891119903119879120573119891119903 sdot 119890

(minus119864119886119903(119877sdot119879))

(14)

where 120572119891119903 120573

119891119903 and 119864


under investigation


120597119876

120597119905+ nabla sdot

997888119865


997888119865

119863) = 119878 (15)




119876 =

[[[[[[[[[[[[[[[[[[[[[[[[[

[

119864int

1205881

1205882

120588119899119904

120588119906

120588V

120588119908

119864119905

]]]]]]]]]]]]]]]]]]]]]]]]]

]

119865119862=

[[[[[[[[[[[[[[[[[[[[[[[[[

[

119864int119906

1205881119906

1205882119906

120588119899119904119906

1205881199062 + 119901

120588119906V

120588119906119908

(119864119905+ 119901) 119906

]]]]]]]]]]]]]]]]]]]]]]]]]

]

119878 =

[[[[[[[[[[[[[[[[[[[[[[[[[

[

int

1

2

119899119904

0

0

0

0

]]]]]]]]]]]]]]]]]]]]]]]]]

]

119865119863=

[[[[[[[[[[[[[[[[[[[[[[[

[

119899119904

sum

119904=1

119890V119904120588119904119880119904 + 119896int120597119879int120597119909

minus12058811198801

minus12058821198802

minus120588119899119904119880119904

120591119909119909 minus2

3120588119896

120591119909119910

120591119909119911

[119906120591119909119909 + V120591119909119910 + 119908120591119909119911 + (119896 + 119896119905)120597119879

120597119909+ 119896int

120597119879int120597119909

+sumℎ119904120588119904119880119904]

]]]]]]]]]]]]]]]]]]]]]]]

]



119904and 119880

119904are


119904= 120588 and 119880

119904= 0 Note that




2-O






119894= 119864

119886119877


120573119894

120579119894(K)



2 H

2 OH H

2O N

2 and O] and 8








H +O2+MlArrrArr HO

2+M (17)



2O

2) in the model




119896119891= 22 sdot 10

14 exp(minus8455119879) (20)




2-O







2 H

2 OH






2-LO








120573119891119894

120579119891119894(K) 120572

119887119894120573119887119894

120579119887119894(K)




119910+=119910

]radic120591119908

120588119908

(21)

with 120591119908 120588










119905]) up to 100












Case 4 (NPR = 259 1198750119895



Temperature (K)4000

3000

2000

1000

002 04 06 08 10

Huber et al

x (m)

400

300

200

100

002 04 06 08 10

Pressure (kPa)

x (m)


020

010

00002 04 06 08 10

H2O mass fraction

x (m)


003

002

001

00002 04 06 08 10

H2 mass fraction

x (m)


003

002

001

00002 04 06 08 10

OH mass fraction

x (m)


Temperature (K)4000

3000

2000

1000

002 04 06 08 10

x (m)

400

300

200

100

002 04 06 08 10

Pressure (kPa)

x (m)

020

010

00002 04 06 08 10

H2O mass fraction

x (m)



003

002

001

00002 04 06 08 10

OH mass fraction

x (m)



003

002

001

00002 04 06 08 10

H2 mass fraction

x (m)






Caisson Outlet


WallWall

Wall

Injector inlet

(a)

(b)

P0j T0j YH2=1

1 2 3 4 5 6 7 8 9

0

001

002

003

004

005

006

007 Y

ZX

005 01 015 02 025 03

0

1

2

3

4






1198750119895cooling (H2) (bar) 31 32 43 43

1198790119869cooling (H2) (K) 29135 29425 29565 294


1198790(calculated) (K) 1693 2577 1945 3372


026771 013840 026634 003777119884O 0 000001 0 000580119884H 0 000065 0 000325119884O2



0

001

002

003

004

005

006

007

014 016 018 02 022

00 05 1 15 2 25 3 3

406

Mach

024 026 028 03 032

(a) Case 1-119896-120576-Evans (NPR = 259)

0

001

002

003

004

005

006

007

014 016 018 02 022

00 05 1 15 2 25 3 3

453Mach

024 026 028 03 032


0

001

002

003

004

005

006

007

014 016 018 02 022

00 05 1 15 2 25 3 3

149Mach

024 026 028 03 032

(c) Case 2-119896-120576-Evans (NPR = 222)

0

001

002

003

004

005

006

007

014 016 018 02 022

00 05 1 15 2 25 3 3

19

Mach

024 026 028 03 032


0

001

002

003

004

005

006

007

014 016 018 02 022

00 05 1 15 2 25 353 3

654

Mach

024 026 028 03 032

(e) Case 3-119896-120576-Evans (NPR = 365)

0

001

002

003

004

005

006

007

014 016 018 02 022

00 05 1 15 2 25 353 3

639

Mach

024 026 028 03 032



0

001

002

003

004

005

006

007

014 016 018 02 022

00 05 1 15 2 25 3 3

406

Mach

024 026 028 03 032


(a)

0

001

002

003

004

005

006

007

014 016 018 02 022

00 05 1 15 2 25 3 3

155Mach

024 026 028 03 032


(b)







018 019 02 021 022 02320000

30000

40000

50000

60000

70000

80000

90000

100000

Exp

Pw

all (

Nm

2)

Case 1-Spal-Evans

Case 1-Spal-Frozen

X (m)




X (m)




018 019 02 021 022 02320000

30000

40000

50000

60000

70000

80000

90000

100000

Pw

all (

Nm

2)



X (m)018 019 02 021 022 023

20000

30000

40000

50000

60000

70000

80000

90000

100000

Pw

all (

Nm

2)





2-LH

2 The nozzle


2






0001

0002

0003

0004

0005

0006

0007

01

02

03

04

05

06

07

08

09

1

OH

H2

0

001

002

003

004

005

006

007

001

002

003

004

005

006

007

014 016 018 02 022 024 026 028 03 032

(a) Case 10001

00015

00005

0 0002

00025

0003

00035

0004

0102030405060708091

OH

H2

0

001

002

003

004

005

006

007

001

002

003

004

005

006

007

014 016 018 02 022 024 026 028 03 032

(b) Case 4



Attached flame

Hot gas main flow

Mixing shearlayer

Injected GH2




2used in the




120578 =119879119908minus 119879

119888

119879119891minus 119879

119888

(22)









0001

0002

0003

0004

0005

0006

0007

0008

0009 0009425OH

4944Eminus022

(a)

2000

1800

1600

1400

1200

100080

060

040

020

0 2113

1539

T (K)

(b)


018 019 02 021 022 023200

400

600

800

1000

1200

1400

1600

1800

X (m)

Tw

(K)



(a)

200

400

600

800

1000

1200

1400

1600

1800

Tw

(K)


018 019 02 021 022 023X (m)




(b)

260

280

300

320

340

360

380

400

420

440

Tw

(K)

018 019 02 021 022 023X (m)

Case 3-Spal-Evans




0

02

04

06

08

1

018 019 02 021 022 023

X (m)

Coo

ling

film

effici

ency



(a)

03

04

05

06

07

08

09

1

018 019 02 021 022 023

X (m)

Coo

ling

film

effici

ency


(b)

092

094

096

098

1

018 019 02 021 022 023

X (m)

Coo

ling

film

effici

ency


(c)



6 Conclusions










Abbreviations


119904 Molar mass



Greek Symbols




Acknowledgment


References





























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












119894= 119864

119886119877


120573119894

120579119894(K)



2 H

2 OH H

2O N

2 and O] and 8








H +O2+MlArrrArr HO

2+M (17)



2O

2) in the model




119896119891= 22 sdot 10

14 exp(minus8455119879) (20)




2-O







2 H

2 OH






2-LO








120573119891119894

120579119891119894(K) 120572

119887119894120573119887119894

120579119887119894(K)




119910+=119910

]radic120591119908

120588119908

(21)

with 120591119908 120588










119905]) up to 100












Case 4 (NPR = 259 1198750119895



Temperature (K)4000

3000

2000

1000

002 04 06 08 10

Huber et al

x (m)

400

300

200

100

002 04 06 08 10

Pressure (kPa)

x (m)


020

010

00002 04 06 08 10

H2O mass fraction

x (m)


003

002

001

00002 04 06 08 10

H2 mass fraction

x (m)


003

002

001

00002 04 06 08 10

OH mass fraction

x (m)


Temperature (K)4000

3000

2000

1000

002 04 06 08 10

x (m)

400

300

200

100

002 04 06 08 10

Pressure (kPa)

x (m)

020

010

00002 04 06 08 10

H2O mass fraction

x (m)



003

002

001

00002 04 06 08 10

OH mass fraction

x (m)



003

002

001

00002 04 06 08 10

H2 mass fraction

x (m)






Caisson Outlet


WallWall

Wall

Injector inlet

(a)

(b)

P0j T0j YH2=1

1 2 3 4 5 6 7 8 9

0

001

002

003

004

005

006

007 Y

ZX

005 01 015 02 025 03

0

1

2

3

4






1198750119895cooling (H2) (bar) 31 32 43 43

1198790119869cooling (H2) (K) 29135 29425 29565 294


1198790(calculated) (K) 1693 2577 1945 3372


026771 013840 026634 003777119884O 0 000001 0 000580119884H 0 000065 0 000325119884O2



0

001

002

003

004

005

006

007

014 016 018 02 022

00 05 1 15 2 25 3 3

406

Mach

024 026 028 03 032

(a) Case 1-119896-120576-Evans (NPR = 259)

0

001

002

003

004

005

006

007

014 016 018 02 022

00 05 1 15 2 25 3 3

453Mach

024 026 028 03 032


0

001

002

003

004

005

006

007

014 016 018 02 022

00 05 1 15 2 25 3 3

149Mach

024 026 028 03 032

(c) Case 2-119896-120576-Evans (NPR = 222)

0

001

002

003

004

005

006

007

014 016 018 02 022

00 05 1 15 2 25 3 3

19

Mach

024 026 028 03 032


0

001

002

003

004

005

006

007

014 016 018 02 022

00 05 1 15 2 25 353 3

654

Mach

024 026 028 03 032

(e) Case 3-119896-120576-Evans (NPR = 365)

0

001

002

003

004

005

006

007

014 016 018 02 022

00 05 1 15 2 25 353 3

639

Mach

024 026 028 03 032



0

001

002

003

004

005

006

007

014 016 018 02 022

00 05 1 15 2 25 3 3

406

Mach

024 026 028 03 032


(a)

0

001

002

003

004

005

006

007

014 016 018 02 022

00 05 1 15 2 25 3 3

155Mach

024 026 028 03 032


(b)







018 019 02 021 022 02320000

30000

40000

50000

60000

70000

80000

90000

100000

Exp

Pw

all (

Nm

2)

Case 1-Spal-Evans

Case 1-Spal-Frozen

X (m)




X (m)




018 019 02 021 022 02320000

30000

40000

50000

60000

70000

80000

90000

100000

Pw

all (

Nm

2)



X (m)018 019 02 021 022 023

20000

30000

40000

50000

60000

70000

80000

90000

100000

Pw

all (

Nm

2)





2-LH

2 The nozzle


2






0001

0002

0003

0004

0005

0006

0007

01

02

03

04

05

06

07

08

09

1

OH

H2

0

001

002

003

004

005

006

007

001

002

003

004

005

006

007

014 016 018 02 022 024 026 028 03 032

(a) Case 10001

00015

00005

0 0002

00025

0003

00035

0004

0102030405060708091

OH

H2

0

001

002

003

004

005

006

007

001

002

003

004

005

006

007

014 016 018 02 022 024 026 028 03 032

(b) Case 4



Attached flame

Hot gas main flow

Mixing shearlayer

Injected GH2




2used in the




120578 =119879119908minus 119879

119888

119879119891minus 119879

119888

(22)









0001

0002

0003

0004

0005

0006

0007

0008

0009 0009425OH

4944Eminus022

(a)

2000

1800

1600

1400

1200

100080

060

040

020

0 2113

1539

T (K)

(b)


018 019 02 021 022 023200

400

600

800

1000

1200

1400

1600

1800

X (m)

Tw

(K)



(a)

200

400

600

800

1000

1200

1400

1600

1800

Tw

(K)


018 019 02 021 022 023X (m)




(b)

260

280

300

320

340

360

380

400

420

440

Tw

(K)

018 019 02 021 022 023X (m)

Case 3-Spal-Evans




0

02

04

06

08

1

018 019 02 021 022 023

X (m)

Coo

ling

film

effici

ency



(a)

03

04

05

06

07

08

09

1

018 019 02 021 022 023

X (m)

Coo

ling

film

effici

ency


(b)

092

094

096

098

1

018 019 02 021 022 023

X (m)

Coo

ling

film

effici

ency


(c)



6 Conclusions










Abbreviations


119904 Molar mass



Greek Symbols




Acknowledgment


References





























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












120573119891119894

120579119891119894(K) 120572

119887119894120573119887119894

120579119887119894(K)




119910+=119910

]radic120591119908

120588119908

(21)

with 120591119908 120588










119905]) up to 100












Case 4 (NPR = 259 1198750119895



Temperature (K)4000

3000

2000

1000

002 04 06 08 10

Huber et al

x (m)

400

300

200

100

002 04 06 08 10

Pressure (kPa)

x (m)


020

010

00002 04 06 08 10

H2O mass fraction

x (m)


003

002

001

00002 04 06 08 10

H2 mass fraction

x (m)


003

002

001

00002 04 06 08 10

OH mass fraction

x (m)


Temperature (K)4000

3000

2000

1000

002 04 06 08 10

x (m)

400

300

200

100

002 04 06 08 10

Pressure (kPa)

x (m)

020

010

00002 04 06 08 10

H2O mass fraction

x (m)



003

002

001

00002 04 06 08 10

OH mass fraction

x (m)



003

002

001

00002 04 06 08 10

H2 mass fraction

x (m)






Caisson Outlet


WallWall

Wall

Injector inlet

(a)

(b)

P0j T0j YH2=1

1 2 3 4 5 6 7 8 9

0

001

002

003

004

005

006

007 Y

ZX

005 01 015 02 025 03

0

1

2

3

4






1198750119895cooling (H2) (bar) 31 32 43 43

1198790119869cooling (H2) (K) 29135 29425 29565 294


1198790(calculated) (K) 1693 2577 1945 3372


026771 013840 026634 003777119884O 0 000001 0 000580119884H 0 000065 0 000325119884O2



0

001

002

003

004

005

006

007

014 016 018 02 022

00 05 1 15 2 25 3 3

406

Mach

024 026 028 03 032

(a) Case 1-119896-120576-Evans (NPR = 259)

0

001

002

003

004

005

006

007

014 016 018 02 022

00 05 1 15 2 25 3 3

453Mach

024 026 028 03 032


0

001

002

003

004

005

006

007

014 016 018 02 022

00 05 1 15 2 25 3 3

149Mach

024 026 028 03 032

(c) Case 2-119896-120576-Evans (NPR = 222)

0

001

002

003

004

005

006

007

014 016 018 02 022

00 05 1 15 2 25 3 3

19

Mach

024 026 028 03 032


0

001

002

003

004

005

006

007

014 016 018 02 022

00 05 1 15 2 25 353 3

654

Mach

024 026 028 03 032

(e) Case 3-119896-120576-Evans (NPR = 365)

0

001

002

003

004

005

006

007

014 016 018 02 022

00 05 1 15 2 25 353 3

639

Mach

024 026 028 03 032



0

001

002

003

004

005

006

007

014 016 018 02 022

00 05 1 15 2 25 3 3

406

Mach

024 026 028 03 032


(a)

0

001

002

003

004

005

006

007

014 016 018 02 022

00 05 1 15 2 25 3 3

155Mach

024 026 028 03 032


(b)







018 019 02 021 022 02320000

30000

40000

50000

60000

70000

80000

90000

100000

Exp

Pw

all (

Nm

2)

Case 1-Spal-Evans

Case 1-Spal-Frozen

X (m)




X (m)




018 019 02 021 022 02320000

30000

40000

50000

60000

70000

80000

90000

100000

Pw

all (

Nm

2)



X (m)018 019 02 021 022 023

20000

30000

40000

50000

60000

70000

80000

90000

100000

Pw

all (

Nm

2)





2-LH

2 The nozzle


2






0001

0002

0003

0004

0005

0006

0007

01

02

03

04

05

06

07

08

09

1

OH

H2

0

001

002

003

004

005

006

007

001

002

003

004

005

006

007

014 016 018 02 022 024 026 028 03 032

(a) Case 10001

00015

00005

0 0002

00025

0003

00035

0004

0102030405060708091

OH

H2

0

001

002

003

004

005

006

007

001

002

003

004

005

006

007

014 016 018 02 022 024 026 028 03 032

(b) Case 4



Attached flame

Hot gas main flow

Mixing shearlayer

Injected GH2




2used in the




120578 =119879119908minus 119879

119888

119879119891minus 119879

119888

(22)









0001

0002

0003

0004

0005

0006

0007

0008

0009 0009425OH

4944Eminus022

(a)

2000

1800

1600

1400

1200

100080

060

040

020

0 2113

1539

T (K)

(b)


018 019 02 021 022 023200

400

600

800

1000

1200

1400

1600

1800

X (m)

Tw

(K)



(a)

200

400

600

800

1000

1200

1400

1600

1800

Tw

(K)


018 019 02 021 022 023X (m)




(b)

260

280

300

320

340

360

380

400

420

440

Tw

(K)

018 019 02 021 022 023X (m)

Case 3-Spal-Evans




0

02

04

06

08

1

018 019 02 021 022 023

X (m)

Coo

ling

film

effici

ency



(a)

03

04

05

06

07

08

09

1

018 019 02 021 022 023

X (m)

Coo

ling

film

effici

ency


(b)

092

094

096

098

1

018 019 02 021 022 023

X (m)

Coo

ling

film

effici

ency


(c)



6 Conclusions










Abbreviations


119904 Molar mass



Greek Symbols




Acknowledgment


References





























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Temperature (K)4000

3000

2000

1000

002 04 06 08 10

Huber et al

x (m)

400

300

200

100

002 04 06 08 10

Pressure (kPa)

x (m)


020

010

00002 04 06 08 10

H2O mass fraction

x (m)


003

002

001

00002 04 06 08 10

H2 mass fraction

x (m)


003

002

001

00002 04 06 08 10

OH mass fraction

x (m)


Temperature (K)4000

3000

2000

1000

002 04 06 08 10

x (m)

400

300

200

100

002 04 06 08 10

Pressure (kPa)

x (m)

020

010

00002 04 06 08 10

H2O mass fraction

x (m)



003

002

001

00002 04 06 08 10

OH mass fraction

x (m)



003

002

001

00002 04 06 08 10

H2 mass fraction

x (m)






Caisson Outlet


WallWall

Wall

Injector inlet

(a)

(b)

P0j T0j YH2=1

1 2 3 4 5 6 7 8 9

0

001

002

003

004

005

006

007 Y

ZX

005 01 015 02 025 03

0

1

2

3

4






1198750119895cooling (H2) (bar) 31 32 43 43

1198790119869cooling (H2) (K) 29135 29425 29565 294


1198790(calculated) (K) 1693 2577 1945 3372


026771 013840 026634 003777119884O 0 000001 0 000580119884H 0 000065 0 000325119884O2



0

001

002

003

004

005

006

007

014 016 018 02 022

00 05 1 15 2 25 3 3

406

Mach

024 026 028 03 032

(a) Case 1-119896-120576-Evans (NPR = 259)

0

001

002

003

004

005

006

007

014 016 018 02 022

00 05 1 15 2 25 3 3

453Mach

024 026 028 03 032


0

001

002

003

004

005

006

007

014 016 018 02 022

00 05 1 15 2 25 3 3

149Mach

024 026 028 03 032

(c) Case 2-119896-120576-Evans (NPR = 222)

0

001

002

003

004

005

006

007

014 016 018 02 022

00 05 1 15 2 25 3 3

19

Mach

024 026 028 03 032


0

001

002

003

004

005

006

007

014 016 018 02 022

00 05 1 15 2 25 353 3

654

Mach

024 026 028 03 032

(e) Case 3-119896-120576-Evans (NPR = 365)

0

001

002

003

004

005

006

007

014 016 018 02 022

00 05 1 15 2 25 353 3

639

Mach

024 026 028 03 032



0

001

002

003

004

005

006

007

014 016 018 02 022

00 05 1 15 2 25 3 3

406

Mach

024 026 028 03 032


(a)

0

001

002

003

004

005

006

007

014 016 018 02 022

00 05 1 15 2 25 3 3

155Mach

024 026 028 03 032


(b)







018 019 02 021 022 02320000

30000

40000

50000

60000

70000

80000

90000

100000

Exp

Pw

all (

Nm

2)

Case 1-Spal-Evans

Case 1-Spal-Frozen

X (m)




X (m)




018 019 02 021 022 02320000

30000

40000

50000

60000

70000

80000

90000

100000

Pw

all (

Nm

2)



X (m)018 019 02 021 022 023

20000

30000

40000

50000

60000

70000

80000

90000

100000

Pw

all (

Nm

2)





2-LH

2 The nozzle


2






0001

0002

0003

0004

0005

0006

0007

01

02

03

04

05

06

07

08

09

1

OH

H2

0

001

002

003

004

005

006

007

001

002

003

004

005

006

007

014 016 018 02 022 024 026 028 03 032

(a) Case 10001

00015

00005

0 0002

00025

0003

00035

0004

0102030405060708091

OH

H2

0

001

002

003

004

005

006

007

001

002

003

004

005

006

007

014 016 018 02 022 024 026 028 03 032

(b) Case 4



Attached flame

Hot gas main flow

Mixing shearlayer

Injected GH2




2used in the




120578 =119879119908minus 119879

119888

119879119891minus 119879

119888

(22)









0001

0002

0003

0004

0005

0006

0007

0008

0009 0009425OH

4944Eminus022

(a)

2000

1800

1600

1400

1200

100080

060

040

020

0 2113

1539

T (K)

(b)


018 019 02 021 022 023200

400

600

800

1000

1200

1400

1600

1800

X (m)

Tw

(K)



(a)

200

400

600

800

1000

1200

1400

1600

1800

Tw

(K)


018 019 02 021 022 023X (m)




(b)

260

280

300

320

340

360

380

400

420

440

Tw

(K)

018 019 02 021 022 023X (m)

Case 3-Spal-Evans




0

02

04

06

08

1

018 019 02 021 022 023

X (m)

Coo

ling

film

effici

ency



(a)

03

04

05

06

07

08

09

1

018 019 02 021 022 023

X (m)

Coo

ling

film

effici

ency


(b)

092

094

096

098

1

018 019 02 021 022 023

X (m)

Coo

ling

film

effici

ency


(c)



6 Conclusions










Abbreviations


119904 Molar mass



Greek Symbols




Acknowledgment


References





























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Caisson Outlet


WallWall

Wall

Injector inlet

(a)

(b)

P0j T0j YH2=1

1 2 3 4 5 6 7 8 9

0

001

002

003

004

005

006

007 Y

ZX

005 01 015 02 025 03

0

1

2

3

4






1198750119895cooling (H2) (bar) 31 32 43 43

1198790119869cooling (H2) (K) 29135 29425 29565 294


1198790(calculated) (K) 1693 2577 1945 3372


026771 013840 026634 003777119884O 0 000001 0 000580119884H 0 000065 0 000325119884O2



0

001

002

003

004

005

006

007

014 016 018 02 022

00 05 1 15 2 25 3 3

406

Mach

024 026 028 03 032

(a) Case 1-119896-120576-Evans (NPR = 259)

0

001

002

003

004

005

006

007

014 016 018 02 022

00 05 1 15 2 25 3 3

453Mach

024 026 028 03 032


0

001

002

003

004

005

006

007

014 016 018 02 022

00 05 1 15 2 25 3 3

149Mach

024 026 028 03 032

(c) Case 2-119896-120576-Evans (NPR = 222)

0

001

002

003

004

005

006

007

014 016 018 02 022

00 05 1 15 2 25 3 3

19

Mach

024 026 028 03 032


0

001

002

003

004

005

006

007

014 016 018 02 022

00 05 1 15 2 25 353 3

654

Mach

024 026 028 03 032

(e) Case 3-119896-120576-Evans (NPR = 365)

0

001

002

003

004

005

006

007

014 016 018 02 022

00 05 1 15 2 25 353 3

639

Mach

024 026 028 03 032



0

001

002

003

004

005

006

007

014 016 018 02 022

00 05 1 15 2 25 3 3

406

Mach

024 026 028 03 032


(a)

0

001

002

003

004

005

006

007

014 016 018 02 022

00 05 1 15 2 25 3 3

155Mach

024 026 028 03 032


(b)







018 019 02 021 022 02320000

30000

40000

50000

60000

70000

80000

90000

100000

Exp

Pw

all (

Nm

2)

Case 1-Spal-Evans

Case 1-Spal-Frozen

X (m)




X (m)




018 019 02 021 022 02320000

30000

40000

50000

60000

70000

80000

90000

100000

Pw

all (

Nm

2)



X (m)018 019 02 021 022 023

20000

30000

40000

50000

60000

70000

80000

90000

100000

Pw

all (

Nm

2)





2-LH

2 The nozzle


2






0001

0002

0003

0004

0005

0006

0007

01

02

03

04

05

06

07

08

09

1

OH

H2

0

001

002

003

004

005

006

007

001

002

003

004

005

006

007

014 016 018 02 022 024 026 028 03 032

(a) Case 10001

00015

00005

0 0002

00025

0003

00035

0004

0102030405060708091

OH

H2

0

001

002

003

004

005

006

007

001

002

003

004

005

006

007

014 016 018 02 022 024 026 028 03 032

(b) Case 4



Attached flame

Hot gas main flow

Mixing shearlayer

Injected GH2




2used in the




120578 =119879119908minus 119879

119888

119879119891minus 119879

119888

(22)









0001

0002

0003

0004

0005

0006

0007

0008

0009 0009425OH

4944Eminus022

(a)

2000

1800

1600

1400

1200

100080

060

040

020

0 2113

1539

T (K)

(b)


018 019 02 021 022 023200

400

600

800

1000

1200

1400

1600

1800

X (m)

Tw

(K)



(a)

200

400

600

800

1000

1200

1400

1600

1800

Tw

(K)


018 019 02 021 022 023X (m)




(b)

260

280

300

320

340

360

380

400

420

440

Tw

(K)

018 019 02 021 022 023X (m)

Case 3-Spal-Evans




0

02

04

06

08

1

018 019 02 021 022 023

X (m)

Coo

ling

film

effici

ency



(a)

03

04

05

06

07

08

09

1

018 019 02 021 022 023

X (m)

Coo

ling

film

effici

ency


(b)

092

094

096

098

1

018 019 02 021 022 023

X (m)

Coo

ling

film

effici

ency


(c)



6 Conclusions










Abbreviations


119904 Molar mass



Greek Symbols




Acknowledgment


References





























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0

001

002

003

004

005

006

007

014 016 018 02 022

00 05 1 15 2 25 3 3

406

Mach

024 026 028 03 032

(a) Case 1-119896-120576-Evans (NPR = 259)

0

001

002

003

004

005

006

007

014 016 018 02 022

00 05 1 15 2 25 3 3

453Mach

024 026 028 03 032


0

001

002

003

004

005

006

007

014 016 018 02 022

00 05 1 15 2 25 3 3

149Mach

024 026 028 03 032

(c) Case 2-119896-120576-Evans (NPR = 222)

0

001

002

003

004

005

006

007

014 016 018 02 022

00 05 1 15 2 25 3 3

19

Mach

024 026 028 03 032


0

001

002

003

004

005

006

007

014 016 018 02 022

00 05 1 15 2 25 353 3

654

Mach

024 026 028 03 032

(e) Case 3-119896-120576-Evans (NPR = 365)

0

001

002

003

004

005

006

007

014 016 018 02 022

00 05 1 15 2 25 353 3

639

Mach

024 026 028 03 032



0

001

002

003

004

005

006

007

014 016 018 02 022

00 05 1 15 2 25 3 3

406

Mach

024 026 028 03 032


(a)

0

001

002

003

004

005

006

007

014 016 018 02 022

00 05 1 15 2 25 3 3

155Mach

024 026 028 03 032


(b)







018 019 02 021 022 02320000

30000

40000

50000

60000

70000

80000

90000

100000

Exp

Pw

all (

Nm

2)

Case 1-Spal-Evans

Case 1-Spal-Frozen

X (m)




X (m)




018 019 02 021 022 02320000

30000

40000

50000

60000

70000

80000

90000

100000

Pw

all (

Nm

2)



X (m)018 019 02 021 022 023

20000

30000

40000

50000

60000

70000

80000

90000

100000

Pw

all (

Nm

2)





2-LH

2 The nozzle


2






0001

0002

0003

0004

0005

0006

0007

01

02

03

04

05

06

07

08

09

1

OH

H2

0

001

002

003

004

005

006

007

001

002

003

004

005

006

007

014 016 018 02 022 024 026 028 03 032

(a) Case 10001

00015

00005

0 0002

00025

0003

00035

0004

0102030405060708091

OH

H2

0

001

002

003

004

005

006

007

001

002

003

004

005

006

007

014 016 018 02 022 024 026 028 03 032

(b) Case 4



Attached flame

Hot gas main flow

Mixing shearlayer

Injected GH2




2used in the




120578 =119879119908minus 119879

119888

119879119891minus 119879

119888

(22)









0001

0002

0003

0004

0005

0006

0007

0008

0009 0009425OH

4944Eminus022

(a)

2000

1800

1600

1400

1200

100080

060

040

020

0 2113

1539

T (K)

(b)


018 019 02 021 022 023200

400

600

800

1000

1200

1400

1600

1800

X (m)

Tw

(K)



(a)

200

400

600

800

1000

1200

1400

1600

1800

Tw

(K)


018 019 02 021 022 023X (m)




(b)

260

280

300

320

340

360

380

400

420

440

Tw

(K)

018 019 02 021 022 023X (m)

Case 3-Spal-Evans




0

02

04

06

08

1

018 019 02 021 022 023

X (m)

Coo

ling

film

effici

ency



(a)

03

04

05

06

07

08

09

1

018 019 02 021 022 023

X (m)

Coo

ling

film

effici

ency


(b)

092

094

096

098

1

018 019 02 021 022 023

X (m)

Coo

ling

film

effici

ency


(c)



6 Conclusions










Abbreviations


119904 Molar mass



Greek Symbols




Acknowledgment


References





























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










018 019 02 021 022 02320000

30000

40000

50000

60000

70000

80000

90000

100000

Exp

Pw

all (

Nm

2)

Case 1-Spal-Evans

Case 1-Spal-Frozen

X (m)




X (m)




018 019 02 021 022 02320000

30000

40000

50000

60000

70000

80000

90000

100000

Pw

all (

Nm

2)



X (m)018 019 02 021 022 023

20000

30000

40000

50000

60000

70000

80000

90000

100000

Pw

all (

Nm

2)





2-LH

2 The nozzle


2






0001

0002

0003

0004

0005

0006

0007

01

02

03

04

05

06

07

08

09

1

OH

H2

0

001

002

003

004

005

006

007

001

002

003

004

005

006

007

014 016 018 02 022 024 026 028 03 032

(a) Case 10001

00015

00005

0 0002

00025

0003

00035

0004

0102030405060708091

OH

H2

0

001

002

003

004

005

006

007

001

002

003

004

005

006

007

014 016 018 02 022 024 026 028 03 032

(b) Case 4



Attached flame

Hot gas main flow

Mixing shearlayer

Injected GH2




2used in the




120578 =119879119908minus 119879

119888

119879119891minus 119879

119888

(22)









0001

0002

0003

0004

0005

0006

0007

0008

0009 0009425OH

4944Eminus022

(a)

2000

1800

1600

1400

1200

100080

060

040

020

0 2113

1539

T (K)

(b)


018 019 02 021 022 023200

400

600

800

1000

1200

1400

1600

1800

X (m)

Tw

(K)



(a)

200

400

600

800

1000

1200

1400

1600

1800

Tw

(K)


018 019 02 021 022 023X (m)




(b)

260

280

300

320

340

360

380

400

420

440

Tw

(K)

018 019 02 021 022 023X (m)

Case 3-Spal-Evans




0

02

04

06

08

1

018 019 02 021 022 023

X (m)

Coo

ling

film

effici

ency



(a)

03

04

05

06

07

08

09

1

018 019 02 021 022 023

X (m)

Coo

ling

film

effici

ency


(b)

092

094

096

098

1

018 019 02 021 022 023

X (m)

Coo

ling

film

effici

ency


(c)



6 Conclusions










Abbreviations


119904 Molar mass



Greek Symbols




Acknowledgment


References





























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0001

0002

0003

0004

0005

0006

0007

01

02

03

04

05

06

07

08

09

1

OH

H2

0

001

002

003

004

005

006

007

001

002

003

004

005

006

007

014 016 018 02 022 024 026 028 03 032

(a) Case 10001

00015

00005

0 0002

00025

0003

00035

0004

0102030405060708091

OH

H2

0

001

002

003

004

005

006

007

001

002

003

004

005

006

007

014 016 018 02 022 024 026 028 03 032

(b) Case 4



Attached flame

Hot gas main flow

Mixing shearlayer

Injected GH2




2used in the




120578 =119879119908minus 119879

119888

119879119891minus 119879

119888

(22)









0001

0002

0003

0004

0005

0006

0007

0008

0009 0009425OH

4944Eminus022

(a)

2000

1800

1600

1400

1200

100080

060

040

020

0 2113

1539

T (K)

(b)


018 019 02 021 022 023200

400

600

800

1000

1200

1400

1600

1800

X (m)

Tw

(K)



(a)

200

400

600

800

1000

1200

1400

1600

1800

Tw

(K)


018 019 02 021 022 023X (m)




(b)

260

280

300

320

340

360

380

400

420

440

Tw

(K)

018 019 02 021 022 023X (m)

Case 3-Spal-Evans




0

02

04

06

08

1

018 019 02 021 022 023

X (m)

Coo

ling

film

effici

ency



(a)

03

04

05

06

07

08

09

1

018 019 02 021 022 023

X (m)

Coo

ling

film

effici

ency


(b)

092

094

096

098

1

018 019 02 021 022 023

X (m)

Coo

ling

film

effici

ency


(c)



6 Conclusions










Abbreviations


119904 Molar mass



Greek Symbols




Acknowledgment


References





























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0001

0002

0003

0004

0005

0006

0007

0008

0009 0009425OH

4944Eminus022

(a)

2000

1800

1600

1400

1200

100080

060

040

020

0 2113

1539

T (K)

(b)


018 019 02 021 022 023200

400

600

800

1000

1200

1400

1600

1800

X (m)

Tw

(K)



(a)

200

400

600

800

1000

1200

1400

1600

1800

Tw

(K)


018 019 02 021 022 023X (m)




(b)

260

280

300

320

340

360

380

400

420

440

Tw

(K)

018 019 02 021 022 023X (m)

Case 3-Spal-Evans




0

02

04

06

08

1

018 019 02 021 022 023

X (m)

Coo

ling

film

effici

ency



(a)

03

04

05

06

07

08

09

1

018 019 02 021 022 023

X (m)

Coo

ling

film

effici

ency


(b)

092

094

096

098

1

018 019 02 021 022 023

X (m)

Coo

ling

film

effici

ency


(c)



6 Conclusions










Abbreviations


119904 Molar mass



Greek Symbols




Acknowledgment


References





























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0

02

04

06

08

1

018 019 02 021 022 023

X (m)

Coo

ling

film

effici

ency



(a)

03

04

05

06

07

08

09

1

018 019 02 021 022 023

X (m)

Coo

ling

film

effici

ency


(b)

092

094

096

098

1

018 019 02 021 022 023

X (m)

Coo

ling

film

effici

ency


(c)



6 Conclusions










Abbreviations


119904 Molar mass



Greek Symbols




Acknowledgment


References





























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation















Abbreviations


119904 Molar mass



Greek Symbols




Acknowledgment


References





























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation






















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









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