THE engine startup and ignition of in-orbit rocket thrusters are

Transcription

1 JOURNAL OF PROPULSION AND POWER Vol. 34, No. 2, March April 2018 Simulations of Injection of Liquid Oxygen/Gaseous Methane Under Flashing Conditions Thomas Ramcke, Arne Lampmann, and Michael Pfitzner Bundeswehr University Munich, Neubiberg, Germany DOI: /1.B36412 The startup of in-orbit rocket engines using cryogenic propellants is characterized by near-vacuum conditions leading to rapid flash evaporation of liquid oxidizer or fuel before ignition. The evolution of a flashing oxygen spray as well as the interaction with a coaxial gaseous methane injection is studied and compared to experiments using numerical methods. A flash evaporation model for superheated cryogenic droplets using an Euler Lagrange method is implemented into a computational fluid dynamics solver. A simplified droplet flash evaporation model is used to calculate the coupling between Eulerian and Lagrangian phases with their respective source terms. Nomenclature A = area, m 2 B T = Spalding heat transfer number C d = drag coefficient c p = specific heat, J kg K d = droplet diameter, m F T = correcting function g = gravitational acceleration, m s 2 H = enthalpy, J h = specific enthalpy, J kg J = mass flow rate, kg s m = droplet mass, kg _m = evaporation rate, kg s NP = droplet particles per parcel Nu = Nusselt number Pr = Prandtl number p = pressure, Pa _Q = heat transfer rate, W R = radial distance, m Re = Reynolds number R p = superheat parameter r = droplet radius, m S = viscosity parameter, K S = source term S sh = superheat parameter T = temperature, K t = time, s u = velocity, m s V = velocity magnitude, m s x, y = Cartesian coordinates, m Y = spray width, m Y i = mass fraction α sh = heat transfer coefficient, J m 2 K s Δh v = latent heat, J kg ΔT = superheat, K Presented as Paper at the 54th AIAA Aerospace Sciences Meeting, AIAA Science and Technology Forum and Exposition 2016, San Diego, CA, 4 8 January 2016; received 2 August 2016; revision received 19 June 2017; accepted for publication 28 October 2017; published online 21 December Copyright 2017 by Thomas Ramcke. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission. All requests for copying and permission to reprint should be submitted to CCC at employ the ISSN (print) or (online) to initiate your request. See also AIAA Rights and Permissions *Institute for Thermodynamics, Werner-Heisenberg-Weg 39; thomas. ramcke@unibw.de. Doctorate Candidate, Institute for Thermodynamics, Werner-Heisenberg- Weg 39; arne.lampmann@unibw.de. Full Professor, Institute for Thermodynamics, Werner-Heisenberg-Weg 39; michael.pfitzner@unibw.de. λ = thermal conductivity, W m K μ = viscosity, kg m s ρ = density, kg m 3 τ = stress tensor, N m 2 Subscripts b = boiling cond = conductive d = droplet eff = effective flash = flash evaporation heat = heat transfer i = internal inj = injection l = liquid mass = mass mom = momentum n = normal out = outlet p = particle RMS = root mean square ref = reference res = resulting sat = saturation sh = superheat v = vapor 0 = reference, original = ambient I. Introduction THE engine startup and ignition of in-orbit rocket thrusters are critical for reliable space operations. Historically, storable hypergolic propellants like monomethylhydrazine (MMH) and dinitrogen tetroxide (NTO) were the preferred choice, exploiting the characteristic self-ignition upon contact of the liquids. The European Chemicals Agency identified hydrazine as a substance of very high concern [1] under the Registration, Evaluation, Authorisation and Restriction of Chemicals regulation [2]. Therefore, it is necessary to develop an alternative propellant combination, preferably using green propellants. One possible green propellant combination is cryogenic liquid oxygen and methane. In addition to them being classified as green propellants, this combination has further advantages. Compared to MMH/NTO, a higher specific impulse can be achieved. Low boiling and freezing points simplify the requirements for the thermal management, rendering this combination as also attractive for longterm missions. However, the combination of liquid oxygen and methane LOX CH 4 is not hypergolic, and therefore requires a forced ignition. Therefore, a well defined fuel-oxidizer mixture at 395

2 396 RAMCKE, LAMPMANN, AND PFITZNER this work is to analyze numerical simulations for fully flashing oxygen sprays interacting with injected gaseous methane using previously published experiments by Manfletti [7,11] as a validation basis. Fig. 1 Saturation curve for oxygen: From injection (point 1) quasiisothermal to superheated state (point 2), and reaching equilibrium through isobaric flash evaporation (point 3). ignition start is needed in order to guarantee safe ignition and subsequent stable combustion. Before in-orbit engine startup, the combustion chamber is typically at low temperatures and exposed to near-vacuum conditions. At startup, first the liquid oxidizer is injected into the chamber and undergoes a sudden quasi-isothermal isentropic pressure drop below the saturation pressure [3], leading to a superheated state (see Fig. 1). A subsequent isobaric phase change process toward the equilibrium condition leads to an explosive evaporation of part of the liquid known as flash evaporation or flashing. This superheated injection will continue until the evaporated liquid raises the chamber pressure above the saturation pressure evaluated at the temperature of the injected liquid. In general, a gaseous fuel injection into a low-pressure environment will lead to an expanding flow, resulting in supersonic velocities and high Mach numbers. The flow velocities will be reduced downstream through a system of shocks. Injected simultaneously, the flashing oxidizer and the underexpanded fuel will interact with each other, leading to a mixture that needs to be ignitable for combustion. Generally, superheated sprays can be categorized into three different regimes [4]: Mechanical breakup will dominate the spray atomization for low superheat, whereas in the fully flashing regime at high superheat, the injected liquid will disintegrate directly at the exit of the injector orifice. A third transition regime exists where a liquid core may be formed. The degree of superheat can be characterized in different ways [5 7] either by the temperature difference between the injection temperature and saturation temperature at chamber pressure [Eq. (1)], by taking this difference and dividing it by the difference between the saturation temperature at injection pressure and the chamber pressure [Eq. (2)], or directly by the ratio of saturation pressure evaluated at injection temperature and the chamber pressure [Eq. (3)]: ΔT T inj T sat p (1) S sh T inj T sat p T sat p inj T sat p (2) R p p satt inj p (3) In previous work, we reported on the injection and flash evaporation of liquid nitrogen [8,9]. We implemented a Lagrangian droplet model extension for superheated droplet flash evaporation into the commercial computational fluid dynamics (CFD) code ANSYS Fluent and compared it to an experiment [10]. The scope of II. Models and Numerical Approach The droplet spray calculations in the combustion chamber are performed using the Euler Lagrange method, where the Eulerian fields are solutions of partial differential equations, and the Lagrange droplet parcels (evolving according to ordinary differential equations) are calculated separately. Eulerian fields and Lagrangian particles interact with each other through source terms for momentum, heat, and mass exchange. The Reynolds-averaged Navier Stokes equations for continuity and momentum are used for the Eulerian fields in the following form, written in Cartesian tensor form: ρ t ρu x i S mass (4) i t ρu i ρu x i u j S mom p j x j μ ui u j 2 x j x i 3 δ u l ij x l x i ρu 0 x iu 0 j (5) j The energy equation for the Eulerian reference frame takes the interaction with the particles into account: h t ρ u ρ h pρ u2 2 λ eff T X h i J i τ eff u pρ u2 p 2 S heat (6) The source terms in the mass, momentum, and energy equations need to be calculated from the particles transported in the Lagrangian reference frame. The trajectory of a particle is calculated by integration of the forces acting on it, written in a Lagrangian frame of reference: du p dt u u p 18μ C d Re p 24ρ p d 2 p gρ p ρ ρ p (7) The particle Reynolds number Re p is defined here as follows: Re p ρ d p ju p u j μ (8) The ANSYS Fluent code does not provide a Lagrangian module for the superheated mass and energy transfer of the droplet; therefore, an extension has been developed using user-defined functions (UDFs), which calculate the respective mass and energy source terms in the case of superheated droplets. Modeling superheated spray injection is very complex due to flash boiling already starting upstream in the injector with bubble growth and breakup, and with the physical dynamics within the droplet itself. Upon injection, the liquid adapts instantaneously to the low pressure of the chamber. This pressure is lower than the saturation pressure evaluated at the droplet temperature, leading to a high superheat of the liquid. It responds in sudden explosionlike fashion, shattering the liquid jet into fine droplets right at the injector orifice exit. The physical processes inside these formed droplets are complex as well, characterized by strong mixing of the superheated liquid combined with possible nucleation sites inside the droplet. Resolving all these phenomena inside every droplet would not be feasible for simulations of the entire spray; therefore, in order to reduce the computational requirements, a simplified approach is used that is based on the classical D-square law (D 2 -t) law [25]. Adachi et al. [12] used an empirical heat transfer coefficient inside a superheated droplet to

3 RAMCKE, LAMPMANN, AND PFITZNER 397 represent the experimentally observed increased vaporization rate by flash evaporation. In more recent work, Kawano et al. [13] developed an analytical description using nucleation theory for multicomponent fuel injection at high pressure. In the present study, a single component injection at near-vacuum conditions is examined at the first stage of the combustor startup process. The droplet s surface mass fraction for a single component setup is always unity. This would lead to an infinite high Spalding mass transfer number in the Kawano model. Due to this limitation, the model of Kawano et al. [13] is not applicable to our setup and we follow the approach by Zuo et al. [14] and Schmehl and Steelant [15] with an adaption to liquid oxygen. The implementation of this model was previously described by Ramcke and Pfitzner for the case of liquid nitrogen [8]. The influence of the inlet conditions has been analyzed, and the heat transfer toward the continuous phase was validated. A spatially uniform but time-dependent temperature is assumed inside the droplet, thus reflecting an assumed high mixing intensity. The internal energy transport from the droplet to its surface is modeled with an internal heat transfer coefficient α sh, which includes all effects related to superheat evaporation from the droplet. Thus, the evaporating mass flow rate due to internal heat transfer becomes the following: _m flash α shat d T b Δh v (9) Adachi et al. [12] proposed an empirical correlation for this coefficient α sh in the context of pentane (C 5 H 12 ), depending on the absolute droplet superheat ΔT: 0K ΔT 5K:α sh kj m 2 K s 0.76T d T b K ΔT 25 K: α sh kj m 2 K s 0.027T d T b 2.33 (10a) (10b) 25 K ΔT: α sh kj m 2 K s 13.8T d T b 0.39 (10c) Preliminary studies showed an underestimation of the flash evaporation rate of oxygen using the Adachi correlation for the provided setup. Adachi et al. [12] derived their correlation for pentane (C 5 H 12 ) based on the absolute superheat. Because this definition of the superheat is not dimensionless, its general validity, independent of the material properties, is questionable. A superheating of a droplet by the same ΔT leads to a bigger relative increase of the superheat for oxygen than for pentane because the evaporation takes place at a lower temperature level. Thus, the superheat is normalized and made dimensionless using the normal boiling point of pentane. The new formulation will be referred to as the adapted superheat ΔT eff : ΔT T b;n;c5 H 12 ΔT eff;o 2 T b;n;o2 (11) Figure 2 shows the heat transfer coefficients for these two different formulations. The evaporation of the superheated droplet is additionally influenced by the surrounding gas because a cold or hot environment will decrease or increase the effective evaporation rate, respectively. An implicit formulation for the evaporation rate _m cond due to conductive energy transport from the gas side to the droplet surface can be derived, evaluating the energy balance, assuming a quasisteady transport in the vapor phase around the droplet, and accounting for the boundary conditions [14,15]: _m cond 2π λ ref Nu r c d ln p;ref 1 _m flash _m cond 1 1 _m flash _m cond h h b Δh v (12) The evaporation mass flow from the surface leads to a blowing effect, resulting in a thicker laminar boundary layer around the droplet. This effect intensifies with increasing droplet superheat. Therefore, a Stefan flow modification has been implemented according to Zuo et al. [14] using a Nusselt number modified by a function F T, which is based on the Spalding heat transfer number B T : with F T B T 1 B T 0.7 ln1 B T B T (13) B T c p;reft T b (14) Δh v The Nusselt number in Eq. (12) is now calculated from the following: Nu 2 Nu 0 2 (15) F T where Nu 0 is the standard Nusselt number of film theory from the Frössling correlation [16]: with Fig. 2 Original and adapted Adachi correlations. Nu Re 1 2 Pr 1 3 (16) Pr μ refc p;ref λ ref ; Re ρ u rel d p μ ref (17) Properties in Eqs. (12), (14), and (17) are evaluated at a reference temperature T ref determined by the one-third rule: T ref 1 3 T 2 3 T b (18) By combining Eqs. (9) and (12), the overall mass source _m res _m flash _m cond of mass transferred to the Eulerian gas-phase field equation, and consequently the mass sink to the Lagrangian droplet, can be obtained. The droplet temperature evolution is calculated according to Schmehl and Steelant [15] by evaluating the integral energy balance of the droplet: m d h l T d t m d th l T d _Q {z} m d th v T b {z} H d t _H (19) In addition, the stationary energy balance across the liquid vapor interface

4 398 RAMCKE, LAMPMANN, AND PFITZNER m d t h lt d h v T b _Q i _Q (20) with a splitting of the heat transfer rate into a contribution from the continuous phase _Q and an inner heat transfer rate within the droplet _Q i is considered. Solving Eq. (20) for _Q, inserting it in Eq. (19), and using dh l T c p;l dt yields, for the change in droplet temperature, T d t Q _ i (21) m d c p;l which depends solely on the internal heat transfer rate. Adachi et al. [14] modeled the internal heat transfer rate based on convective heat transfer _Q i;sh α sh AT d T b (22) whereby the empirical heat transfer coefficient α sh was used. To determine the flashing mass flow rate, they divided Eq. (22) by the latent heat at equilibrium state Δh v, leading to Eq. (9). However, the amount of enthalpy needed for evaporation derived in Eq. (20) is lower because the initial state of the droplet is superheated. This additional heat flux _Q i;add provided by the cooling of the evaporating mass to boiling state has to be considered in the internal heat transfer rate. Using the mass balance of the droplet m d t the internal heat transfer rate can be determined: _m res (23) _Q i _Q i;sh _Q i;add _m flash Δh v _m res h l T d h l T b (24) Thus, the droplet temperature evolution depending on the total and flashing mass flow rates becomes dt d dt Δh _m res T d T b _m v 1 flash (25) c p;l m d The influence of the Stefan flow correction as well as the energy provided by the gaseous phase are taken into account by including the cooling of the combined mass flow rate _m res. The energy source term in the Eulerian gas phase is calculated by considering the energy of the evaporated mass and the heat conducted between the droplet and its surrounding. In the present work, the implemented superheated droplet UDFs are coupled to the solver only when the condition of superheat [p < p sat T] applies. If this condition does not apply, the D 2 -t law, modified according to Miller et al. [17] and Sazhin [18], considering convection and diffusion effects is used. This is important to capture the transition from flash boiling evaporation to the evaporation of droplets in a hot combusting environment. The spreading of the spray is mainly determined by the expansion in the dense droplet field as a result of the flash evaporation and the inner droplet dynamics, whereas droplet turbulence interaction becomes less significant. Thus, the unsteady Reynolds-averaged Navier Stokes (URANS) equations are solved using the pressurebased coupled solver, which solves the momentum and continuity equations simultaneously. Second-order discretization is used in space and time. Turbulence is modeled using the realizable k ε model with enhanced wall treatment [19]. The specific heat of the gaseous phase of oxygen and methane is calculated using NASA polynomials [20], where values have been extended for low temperatures. The viscosity of the gaseous phase is calculated by a temperature-dependent Sutherland viscosity law [21]: Table 1 Parameters for Sutherland law viscosity calculation μ 0, kg m s T 0,K S,K O CH μ μ 0 T 0 S T S T 1.5 (26) which has been fitted to National Institute of Standards and Technology [22] data. Table 1 shows the used coefficients for oxygen and methane. The gas-phase density is calculated using the ideal gas law because a study using the Peng Robinson equation of state revealed no differences due to the low pressure. The mixture properties are determined using a mass-weighted mixing law. The temperature decrease due to flash evaporation might lead to condensation, freezing, or desublimation in the chamber. The region where condensation, freezing, or desublimation might occur is small and limited to the injection zone. Condensation in this region will occur as a methane oxygen mixture. The modeling of condensation of multicomponent mixtures is quite complex and outside the scope of this study. Thermal radiation is neglected. III. Validation Case Manfletti conducted experiments of the injection and laser ignition of mixtures of oxygen methane and oxygen hydrogen in a lowpressure combustion chamber [7,11]. Data from one setup of the oxygen methane experiments were used as a validation basis for the numerical simulations. The preflow before ignition consists of two stages where, in the first stage, superheated liquid oxygen is injected into an evacuated chamber for 100 m s. After this time period, in a second stage, a gaseous methane coflow is added for another 150 m s, resulting in an overall preflow time of 250 m s. A third stage would be the ignition of the mixture generated in the first two stages. The quasi-cylindrical chamber has a diameter of 60 mm, the throat diameter is 26.6 mm, and the chamber length between the injector and throat is 138 mm. The chamber has two windows for visual observation and one window for the laser ignition, thus resulting in a not entirely circular chamber with a reduced volume. The coaxial injector at the centerline consists of an inner oxygen injector with a diameter of d mm and an outer methane annular slit (d mm;d mm), which are both separated by a post of 0.4 mm width without a recess. Figure 3 shows images from the experiment for the LOX jet in stage 1 (left) and for the coaxial LOX GCH 4 jet in stage 2 (right). The spray region in the chamber with numerous droplets is black in the schlieren images due to the large density gradients at the droplet surfaces. Thus, the spray contour becomes visible. The density ratio between the liquid and gaseous phases is for saturated oxygen at 90 K (inlet conditions) and is increasing for a decreasing temperature. Thus, the density gradient at the droplet surfaces is significantly larger than the density gradients in the continuous flow. Due to the highly transient processes in the experiment, generating reproducible experimental data is difficult; the schlieren images are a reliable source for visualizing the spray spreading. For the simulations, the chamber has been modeled as a threedimensional (3-D) 36 deg wedge type, using periodic boundary conditions on the sides to reduce required computational time. Because only part of the entire chamber has been modeled when using the 36 deg wedge, the particles very close to the axis tend to move radially outward because there is no momentum pushing them back onto the axis. This is a known deficit of the used boundary conditions, but previous studies with nitrogen sprays [8] showed that the implications on the results were minimal; hence, the reduction in T 0

5 RAMCKE, LAMPMANN, AND PFITZNER 399 Fig. 3 Schlieren images from experiments for LOX (left) and coaxial LOX GCH 4 (right) (reprinted from work by Manfletti [7]; Copyright 2013 by C. Manfletti). Fig. 4 Final mesh after mesh studies used for simulations. required computational time as compared to a simulation of a full 3-D chamber justifies this approach. The structured hexahedral mesh consists of approximately 120,000 cells and is shown in Fig. 4. The mesh in the radial direction features 14 cells along the oxygen injection plane, 6 cells along the post, 12 cells along the methane injection plane, and 46 cells along the faceplate. The wedge has a resolution of 10 cells in the circumferential direction; in the axial direction, the mesh consists of 154 cells with refinement in the oxygen injection area and in the throat area. The mesh resolution is the result of a mesh refinement study, with a coarse grid consisting of 63,525 cells and a fine grid consisting of 180,570 cells. The number of cells in the circumferential direction is kept constant; the mesh resolution is changed, especially in the injection regions for both radial and axial directions. Figure 5 shows the resulting injection pressure, the peak values of the velocity magnitude along the centerline, and the spray width at x 35 mm for all three different grid resolutions after stage 1. The resolution of the coarse grid is not sufficient to fully resolve the flowfield, whereas the fine-grid results show only minor differences to the results from the grid used in this work. The resulting sprays are very similar for all grids, and the spray width differs only slightly in the area for 25 mm < x < 45 mm. A mass flow inlet is used as a boundary condition for the methane; the liquid oxygen is defined through the particle settings, defining the mass flow, injection temperature, velocity, and diameter distribution. In the experiments, backpressures between 20 and 75 mbar could be measured before priming. In the simulation, the outlet boundary condition is a pressure outlet, where simulations with two different values have been performed, namely, 25 and 100 mbar. Important boundary condition values are shown in Table 2. Using the initial static chamber pressure, the resulting superheat at the start of injection can be calculated. In this setup, the initial superheat of liquid oxygen is ΔT 17.3 K, orr p 10, for the 100 mbar case and ΔT 24.7 K,orR p 40, for the 25 mbar case. In accordance with flashing spray characteristics, it is assumed that the liquid jet breaks up immediately at the injector orifice exit, where the sudden pressure drop and subsequent expansion of enclosed vapor nuclei shatter the liquid jet into very fine droplets. Flashing sprays are known to produce an almost uniform or very narrow diameter distribution [23,24]; therefore, a narrow Rosin Rammler diameter distribution for the liquid oxygen is used (see Table 3). The droplet diameter distribution was determined in preliminary studies by matching the experimental spray width and contour angle [8]. The mean diameter is based on an approximation considering the bubble nucleation rate [6] and assuming twice the number of droplets as compared to vapor bubbles [24]. Because resolving every single droplet would be computationally very demanding, the concept of droplet parcels is used, where every numerical parcel represents a number of physical droplets. The ratio for every parcel is called number of particles per parcel NP. The constant NP parcel release method has been used, where every injected parcel has a constant NP of 100. Therefore, the number of injected parcels in every time step is a function of the diameter distribution and the time step, which improves the numerical stability and results in a more physical representation of the spray in the postprocessing as compared to a boundary condition injecting a constant number of parcels per time step. A solid cone injection is used as the inlet condition for the droplet parcels. Every parcel is therefore injected with a constant-velocity magnitude (jv inj j20 m s). The parcel velocity is estimated using the continuity equation and the measured mass flow regarding the effects of wall roughness, flash-boiling within the injector and Fig. 5 Mesh refinement study: peak pressure in injection area, peak velocity along the centerline, and spray width at x 35 mm after stage 1.

6 400 RAMCKE, LAMPMANN, AND PFITZNER Table 2 Important boundary conditions for simulation LOX CH 4 Case 1 Case 2 _m, g s p out, mbar T, K T sat (p ), K Table 3 Particle injection: Rosin-Rammler size distribution Parameter Value Diameter distribution d min 10 μm d max 20 μm d mean 16 μm n spread 8 Parcel injection Release Constant NP Spray Solid cone immediate atomization. A maximum injection angle of α inj;max 50 deg is defined, and each individual parcel injection angle is distributed randomly across the injection surface. The velocity magnitude and maximum injection angle are calculated, based on previous studies with cryogenic nitrogen spray [8]. IV. Results and Discussion Simulation results for three different setups are presented in this section for both the preflow and the coaxial flow. The simulations using the adapted formulation for the inner heat transfer coefficient are named case 1 with 100 mbar backpressure and case 2 with 25 mbar backpressure. A third simulation with 25 mbar backpressure using the original Adachi formulation for the inner heat transfer coefficient is named case 3. A. Stage 1: LOX Preflow Figure 6 shows snapshots of the numerical parcels of the resulting LOX spray after stage 1 for all three cases. Note that only the numerical parcels are plotted, with the droplet diameter increased 15-fold; the actual number of physical droplets is higher by a factor of NP. All parcels are projected from the 3-D wedge into a twodimensional representation, where the y axis represents the distance R to the centerline. The sprays of the superheated liquid oxygen injection have the typical characteristics of a flashing spray: most notably, with a very high spray angle. However, the typical bowl shape of a superheated injection is not formed because the droplets collide with the relatively close chamber wall before that distinct shape can be developed. After 100 m s, almost the entire chamber is filled with droplets for all cases. As shown in Fig. 3 (left), a chamber completely filled with liquid droplets could also be observed in the experiments. The total number of droplet parcels present in the entire simulation domain after 100 m s is more than one million parcels for case 1 and less than one-third of that for cases 2 and 3. For case 1, the particles accumulate on the outer side of the chamber: especially the smaller droplets. For both cases 2 and 3 with 25 mbar backpressure, the particles are distributed more homogeneously in the chamber. For all three cases, the particles cannot follow the nozzle contour in the diverging section of the nozzle, and the flow including the droplets detaches from the wall. A stratification of the different droplet sizes can be seen in this area. This is due to the limited number of different classes used in the droplet size distribution. However, the droplet behavior in the divergent part of the nozzle is of almost no significance for the droplet dynamics upstream of the nozzle throat, especially in the injection zone. Due to the projection method used in Fig. 6, the represented volume increases with the radial distance. Therefore, the apparent number of droplets would increase even for a homogeneous particle density in the chamber. Figure 7 shows a cross section of the simulated wedge, where all droplet parcels are plotted within a section cutting through the middle of the chamber (0.05 < x < 0.08). In this representation, the higher number of spray parcels for case 1 and the more homogeneous distribution of the parcels in the radial Fig. 6 Resulting spray parcels after 100 m s (end of stage 1) for cases 1, 2, and 3 (from top to bottom).

7 RAMCKE, LAMPMANN, AND PFITZNER 401 Fig. 7 Droplet parcels between axial positions 0.05 < x < 0.08 for cases 1, 2, and 3 (from left to right). direction for cases 2 and 3 become visible. The deceptive impression of a too sparse droplet distribution close to the chamber axis for all three cases in Fig. 6 is disproved. A recirculation zone exists in the corner between the faceplate and the wall, where particles accumulate. This recirculation zone is visible in Fig. 8, which shows the contour of the velocity magnitude as well as stream traces for cases 1 and 2. Case 3 is not shown in this figure because it is very similar to case 2. A stronger expansion with higher velocities is reached with lower backpressure due to the higher superheat, and thus the flash evaporation rate. The stronger radial expansion of cases 2 and 3 reduces the size of the recirculation zone between chamber wall and faceplate, and it generates an almost parallel flow to the faceplate, leading to the differing sprays in this area. Small particles with low inertia are more likely to follow the underlying flowfield and become trapped in recirculation zones. Due to the larger recirculation zone in case 1, more small particles are trapped in this region near the chamber wall, resulting in a more inhomogeneous droplet spreading. Two areas of high velocity can be identified for both cases: the injection region and the nozzle throat. In the near-injector region, the liquid oxygen is accelerated due to the high flashing intensity and subsequent expansion. The velocity decreases to its lowest values after the flash evaporation is terminated. Reaching the chamber throat region, the velocity increases again without reaching sonic speed. The pressure drop in the diverging part of the nozzle leads to an evaporation of the droplets again, and thus an acceleration for the gaseous phase. The droplets from the outer part of the chamber cannot follow the contour; therefore, an area of low velocity is created due to the strong interaction and momentum exchange between the droplets and the gaseous phase. Figure 9 shows the velocity magnitude along the centerline as well as the static pressure, averaged over a time span of 5m s. Due to the similar injection boundary conditions, the mean velocities at the injector are identical for all three cases. The static pressure difference at the faceplate for cases 1 and 2 is of the order of the near-constant pressure difference downstream in the chamber. During the first 4 mm, the pressure decreases with a similar rate, leading to a similar acceleration of the fluids. The maximum in the velocity is located where the pressure becomes constant; the constant pressure level is reached further downstream for the lower-pressure cases, increasing the acceleration length, and thus the maximum velocity. The lower evaporation rate of case 3 with the original Adachi correlation causes a faster decrease of the pressure at the faceplate, and thus lower acceleration of the continuous fluid as compared to case 2. However, the lower evaporation rate increases the length of flash evaporation along the axis and leads to a smoother decrease of the fluid velocity. Compared to case 1, the later inception of a lower stationary pressure causes a longer acceleration length, and therefore a higher-velocity maximum. A strong coupling between the gaseous phase and the spray leads to fluctuations in the velocity magnitude in the flashing region, as can be observed by the fluctuations in Fig. 10, represented by the rms values of the URANS simulation. The fluctuations in the velocity field are a characteristic feature of flashing sprays. Due to the varying droplet diameters, the evaporation process occurs at different rates. Depending on the spreading of droplet sizes within each cell, the flow is accelerated more or less. Thus, there can still be evaporation and Fig. 8 Stream traces and velocity magnitude at the end of stage 1 (top case is stage 1, and bottom case is stage 2).

8 402 RAMCKE, LAMPMANN, AND PFITZNER Fig. 9 Continuous phase velocity magnitude (left) and static pressure (right) along the centerline after stage 1 (5 m s time span). Fig. 10 Fluctuations of the continuous field velocity along the centerline after stage 1 (5 m s time span). fluctuations in the velocity of especially large droplets, even if most droplets within one cell are at saturation temperature. The values of the fluctuations are again higher at lower backpressure, as well as the absolute velocity; and the highest fluctuations are located just downstream of the velocity peak. The fluctuations for the cases with 25 mbar backpressure are very similar, although a higher fluctuation can be observed just downstream of the injection. Using the adapted inner heat transfer coefficient moves the location of the biggest fluctuations slightly downstream. The superheat is the driving force, and thus a direct indicator for flash evaporation. Figure 11 shows the superheat and temperature averaged over all droplets within each cell along the centerline. The superheat is consumed by evaporation, leading to a continuous decrease of the droplet temperature. Immediately after injection, the droplets directly start to evaporate. The increased pressure limits the evaporation rate. Thus, the superheat cannot be consumed as fast as in a case with constant pressure, leading to the maximum of the superheat slightly downstream of the injector. The higher static pressure of case 1 in the injection region reduces the amount of superheat as compared to case 2, and the earlier reach of a stationary chamber pressure causes a faster depletion of superheat. The adaption in the Adachi correlation increases the heat flow within the droplet for the same amount of superheat as compared to the original implementation. Thus, a higher flash evaporation rate at a lower effective superheat is reached for cases 1 and 2. The smaller evaporation rate of case 3 leads to a stronger increase of the superheat in the injector region and a slower decrease of the continuous phase temperature. After depletion of the superheat, the droplets reach a region of normal evaporation. Because no heat is being added to the flow, the entire chamber adapts to a temperature corresponding to the saturation temperature of the oxygen at the current chamber pressure when a steady-state condition is reached. B. Stage 2: Coaxial LOX Plus GCH 4 After 100 m s of LOX injection, stage 2 begins, where a coaxial jet of gaseous methane is added to the liquid oxygen spray. The injector geometry is designed for steady combustion at higher chamber pressures. Although this has very little effect on the liquid oxygen, because it is practically incompressible, the methane is highly underexpanded when injected into the chamber. This leads to a very strong acceleration of the methane right after injection, with very high velocities reaching more than 800 m s. The resulting Mach number in the simulations locally reached values of more than four. The supersonic jet is subsequently decelerated through a shock system. In the experiment, a distinct pattern of shock systems could be observed. Numerical simulations require a very fine mesh in order to capture the detailed shock front system. A study has been performed using a finer mesh in the region where shocks are to be expected in order to better analyze the influence of the shock system on the spray. The mesh could not be refined enough to accurately capture the actual shocks; however, the finer mesh showed no significant changes in the overall flowfield or the spray. This leads to the assumption that the current mesh is fine enough to resolve the main characteristics of spray and jet interaction. A strong interaction is taking place between the flashing oxygen spray and the methane, leading to a very different spray pattern as compared to the methaneless preflow in stage 1. The sprays of all three cases, shown in Fig. 12, are very similar. Again, snapshots are shown where the y axis shows the distance of the droplet parcels to the centerline. The expanding methane jet encapsulates the oxygen flow and forces the region of atomization of the oxygen jet and flashing of the droplets to move downstream. Subsequently, the flashing of the oxygen expands the spray and pushes the methane to the outside. Because the droplets cannot escape in the radial direction through the encapsulating methane jet, the droplet sizes are homogeneously mixed throughout the spray. The spray now reaches the wall a long distance down the chamber. The standard wall model mainly takes particle reflection at the walls into account while also allowing

9 RAMCKE, LAMPMANN, AND PFITZNER 403 Fig. 11 Temperature (left) and superheat (right) of droplets along the centerline after stage 1 (5 m s time span, averaged over all droplets within computational cell). Fig. 12 Resulting spray parcels after stage 2 for cases 1, 2, and 3 (from top to bottom). particles to stick, leading to an increased droplet flow from the divergent part of the nozzle toward the chamber axis. Further studies of the nozzle area show that the influence of this numerical effect is hardly significant for the continuous flow and the upstream droplet behavior. Contrary to the LOX-only preflow in stage 1, the increased mass flow prevents stratification of different droplet sizes and a complete detaching of the flow and droplets in the nozzle. The methane flow increases the chamber pressure, and thus reduces differences in the superheat. Therefore, the differences in the backpressures now have only a limited effect on the flowfields. Comparing the two 25 mbar cases, the adapted α sh formulation (case 2) leads to a stronger vaporization, resulting in a stronger radial expansion and a wider spray than for the original Adachi formulation (case 3). Compared to the experiment, the spray is very similar in the limited view of the experimental window. The delayed spray expansion including the resulting spray angle is well captured. However, the available images from the experiment suggest that the expansion continues a little further downstream than predicted in the simulations. This can be seen in Fig. 13, where a schlieren image Fig. 13 Schlieren image of the experiment in the background (reprinted from Manfletti [7]; Copyright 2013 by C. Manfletti) and spray from simulation printed on top.

10 404 RAMCKE, LAMPMANN, AND PFITZNER Fig. 14 Stream traces and velocity magnitude of coaxial LOX GCH 4 preflow after stage 2. from the experiment is shown in the background, with droplet parcels from simulation results plotted on top. Figure 14 shows the contour plot of the velocity magnitude and the stream traces for case 2. The recirculation zone at the chamber wall is extended as compared to stage 1 due to the high-velocity methane jet confining the oxygen expansion. Immediately after injection, the expanding methane jet is slightly deflected toward the oxygen flow. When the oxygen droplets start to flash evaporate, the methane jet is pushed outward until the superheat of the droplets is consumed. Subsequently, the evaporation (and thus the expanding force) vanishes and the methane flow is mixed into the spray, resulting in a small recirculation zone in the dense spray area. Further downstream, the flow is accelerated again due to the converging nozzle and due to the low-pressure suction from the outlet. Toward the centerline, the high number of droplets produces a large drag, resulting in a lower velocity. The velocity is shown quantitatively along the centerline in Fig. 15 for all three cases; mean values and rms fluctuations are averaged over 5m s. After injection, a two-stage acceleration phase forms along the centerline. The first acceleration stage for the first 5 mm is mainly due to expansion of the oxygen; afterward, the high-speed methane drags the oxygen along. The second acceleration stage is driven by the expansion due to flash evaporation. The recirculation zone following the flashing zone shows high relative fluctuation magnitudes due to the unsteady nature of such kinds of a flow feature. This indicates that it is a low velocity rather than a recirculation zone. The velocity magnitude for the original Adachi formulation (case 3) does not decelerate as much as for the other cases in the recirculation zone. This can be explained by the fact that the adapted formulation for α sh results in faster consumption of the superheat and a shorter expansion phase. The velocity of the methane also decreases after the initial expansion phase; therefore, a shorter flashing region results in a higher methane velocity at the mixing inception, and therefore a stronger recirculation zone. In case 3, the methane velocity creating the recirculation zone is lower; therefore, the recirculation zone is less prominent. The averaged droplet temperature and superheat are shown for all three cases at the end of stage 2 in Fig. 16. Due to the expansion of the methane after the injection, the pressure at the faceplate is above the saturation pressure and falls below p sat only 3 mm downstream of the injector. Thus, there is no flash evaporation at the faceplate and a constant droplet temperature. With decreasing pressure, more flash evaporation occurs, consuming the droplet superheat. Analogously to stage 1, the temperature decrease is slower for case 3 due the reduced inner heat transfer of the original Adachi correlation. The similar chamber pressures for cases 1 and 2 result in a similar distribution of the droplet temperatures along the center axis. During the LOX methane coflow phase, the evaporation of the oxygen is enhanced through heat transfer from warm methane to cold oxygen. Nonetheless, the superheat and the heat from the methane are not sufficient to completely evaporate the droplets. But, because of the increased axial momentum due to the methane injection, the total number of droplet parcels (and therefore the overall liquid mass in the chamber) decreases. This can be seen in the total number of parcels in the domain after 150 m s of coaxial flow, which is less than 100,000 for all cases, and therefore drastically smaller than in stage 1. The static chamber pressure is increased as compared to stage 1 due to the additional methane injection. The resulting static pressure plotted along the centerline is shown in Fig. 17 for all three cases. After an initial region of high pressure, the expansion reduces the achieved values. Subsequently, the static pressure increases and reaches a plateau in the second chamber half. All three cases show almost identical pressures; however, due to the enhanced flash evaporation resulting from the adapted inner heat transfer coefficient, cases 1 and 2 reach slightly higher values in the zone of flash evaporation. The chamber pressure reaches values of 136 mbar along the centerline and values of 141 mbar at the wall, where the pressure was measured in the experiment. Compared to the experiment, where a pressure of approximately 200 mbar after stage 2 could be achieved [7], this is quite a large deviation. Therefore, an additional case with a different setup has been simulated (case 4). In the experiment, a mass flow of oxygen between Fig. 15 Mean values (left) and fluctuations (right) along the centerline after stage 2 (5 m s time span).

11 RAMCKE, LAMPMANN, AND PFITZNER 405 Fig. 16 Temperature (left) and superheat (right) of droplets along the centerline after stage 2 (5 m s time span, averaged over all droplets within computational cell). Fig. 17 span). Static pressure at 250 m s along the centerline (5 m s time 50 and 60 g s was reported. To test the sensitivity of results regarding this uncertainty, the mass flow was increased in this additional case from 55 to 60 g s. Because the superheat had a large effect on the amount of liquid evaporating, the injection temperature had been raised from 90 to 92 K. The reduced volume of the experimental setup due to the presence of windows was captured by reducing the cylindrical chamber length by 8 mm. Due to the increased evaporation mass flow, the static wall pressure was raised to 159 mbar, which corresponded to a deviation from the experiment of approximately 20%. Also, the spray experienced only a slight increase in radial expansion. The pressure difference to the experiment could explain the possible deviations in the spray pattern because the expansion of the methane would be terminated earlier at higher pressures. Although the assumption of immediate jet breakup in the injector orifice exit plane is justified for the spray in stage 1, where high flashing is present immediately at the entrance into the chamber, in stage 2, the flashing starts further downstream, as described previously. Hence, the assumption of immediate jet breakup is strictly not valid anymore. However, the influence of the boundary condition seemingly has little influence on the resulting spray in stage 2, as the flashing region has been observed to be the main influence factor in the simulations. Thus, the assumption of solely droplet injection due to the immediate flash evaporation is sufficient for the stages 1 and 2. Because ignition and subsequent steady combustion generate higher chamber pressures, suitable atomization models like standard jet breakup will need to be applied for the third stage: ignition. Figure 18 shows the methane mass fraction in the chamber section at the end of stage 2 at 250 m s for case 2. The methane distribution in the chamber matches the stream traces (Fig. 14). The recirculation zone at the chamber wall creates a homogeneous mixture in this region. Methane slightly penetrates the inner oxygen core after injection and is pushed outward by the subsequent oxygen expansion. The end of the pure oxygen core aligns with the beginning of the inner recirculation zone. The stoichiometric mass fraction of methane (0.2) between the methane jet and the oxygen spray is in a region of very high mixture fraction gradients; therefore, the spatial region with mixtures within the flammability limit is very narrow. This may explain the difficulties of igniting the mixture seen in the experiments. In the recirculation zone, the methane mass fraction is around at 250 m s, whereas the values are slightly higher in the area of the faceplate than downstream reaching the converging nozzle part. Figure 19 shows the oxygen and methane mass fraction for the gaseous phase along the centerline for cases 1 and 2, quantifying the increasing methane mass fraction. The drastic increase of the methane mass fraction after termination of the flash evaporation at around 40 mm is clearly visible, along with a gradual increase along the centerline. The values in the chamber are very similar for the different backpressures. An increased pressure at Fig. 18 CH 4 mass fraction of coaxial LOX GCH 4 injection at 250 m s.

12 406 RAMCKE, LAMPMANN, AND PFITZNER injection parameter is reduced and the differences in the spray spreading can be ascribed to the flashing model. All in all, most characteristics of the experimental spray could be reproduced with the used methods, keeping in mind the simplification in the chamber geometry and considering only flash evaporation downstream of the injector. Acknowledgments This research project has been supported by Munich Aerospace e.v. in the program titled Propulsion Technologies for Green In-Orbit Spacecraft. The authors thank Chiara Manfletti and DLR, German Aerospace Center for providing the experimental images. Fig. 19 Oxygen and methane mass fraction at 250 m s along the centerline (gas phase, 5m stime span). the inlet of case 2, together with a slower consumption of superheat, moves the recirculation zone slightly further downstream. Thus, the mixing starts a little later at lower backpressure and reaches minimally lower values than at 100 mbar backpressure. However, the two cases show very different behaviors in the diverging part of the nozzle. The lower backpressure case results in a pressure drop below the saturation pressure of the oxygen, which enhances the evaporation, and thus increases the oxygen content in the gaseous phase. For the higher-pressure case, little change of the oxygen mass fraction occurs in the nozzle. V. Conclusions The simulation of preflow of cryogenic propellants for satellite rocket engines to ensure reliable ignition is very important in order to achieve a safe and successful mission. The initially very low pressure in the combustor leads to strong flash evaporation of injected liquids such as liquid oxygen. Added gaseous fuel injection like methane using a coaxial injector leads to a strong coupling between the highly flashing oxygen spray and the underexpanded supersonic methane jet. Numerical simulations using the Euler Lagrange approach have been conducted, where a simplified droplet flash evaporation model for superheated droplets in a low-pressure environment has been implemented into a commercial computational fluid dynamics solver. Results for the first-stage preflow operating solely with superheated LOX show a strong flash evaporation immediately after injection, generating a high-velocity spray with a large spray angle. The entire chamber is filled with oxygen droplets, which is in agreement with the experiments. Injecting gaseous methane into a low-pressure chamber almost entirely filled with liquid droplets leads to a supersonic methane jet, which interacts with the droplets and creates a dense core of oxygen spray, with delayed flash evaporation and spray expansion. The injection raises the chamber pressure from initially 100 mbar to around 160 mbar after stage 2, which is less than the measured 200 mbar in the experiments. It is shown that small changes in the inlet conditions can influence the pressure raise in the chamber but have little influence on the contour of the spray. Thus, the spray from the experiment could be reasonably well reproduced. The recirculation zone at the faceplate is captured, as well as the spray contour. The confined injection of the droplet spray, the spray spreading angle, and the spray width match the experimental data within a reasonable accuracy. The influence of the adapted Adachi correlation for stage 1 is limited to the immediate injection region, with small differences in droplet temperature and mean flow velocity. A slightly better agreement between experimental and simulated spray contours is obtained for the adapted Adachi correlation in stage 2 as compared to the original formulation. The coaxial methane injection suppresses the widening of the spray contour. Thus, the influence of the droplet References [1] SVHC Support Document EC Number , European Chemicals Agency ECHA, Member State Committee (MSC-18), Helsinki, May [2] Regulation (EC) No 1907/2006 Concerning the Registration, Evaluation, Authorisation and Restriction of Chemicals (REACH), Official Journal of the European Union, European Parliament, and the Council of the European Union, 2006, pp [3] Reinke, P., Surface Boiling of Superheated Liquid, Paul Scherrer Inst., PSI Rept , Villigen, Switzerland, [4] Witlox, H., Harper, M., Bowen, P., and Cleary, V., Flashing Liquid Jets and Two-Phase Droplet Dispersion II. Comparison and Validation of Droplet Size and Rainout Formulation, Journal of Hazardous Materials, Vol. 142, No. 3, 2007, pp doi: /j.jhazmat [5] Lecourt, R., Barricau, P., and Steelant, J., Spray Velocity and Drop Size Measurements in Vacuum Conditions, 20th Annual Conference on Liquid Atomization and Spray Systems, Vol. 20, ILASS-Americas, Chicago, IL, May [6] Lamanna, G., Kamoun, H., Weigand, B., and Steelant, J., Towards a Unified Treatment of Fully Flashing Sprays, International Journal of Multiphase Flow, Vol. 58, Jan. 2014, pp doi: /j.ijmultiphaseflow [7] Manfletti, C., Laser Ignition of an Experimental Cryogenic Reaction and Control Thruster: Pre-Ignition Conditions, Journal of Propulsion and Power, Vol. 30, No. 4, 2014, pp doi: /1.b34916 [8] Ramcke, T., and Pfitzner, M., Numerical Simulations of Atomization and Flash Evaporation of Cryogenic Nitrogen Injection, 8th International Symposium on Turbulence, Heat and Mass Transfer, Sarajevo, Bosnia, and Herzegovina, ICHMT, Ankara, 2015, pp [9] Luo, M., Ramcke, T., Pfitzner, M., and Haidn, O. J., Experimental and Numerical Investigation of Flash Atomization with Cryogenic Fluids, 9th International Conference on Multiphase Flow (ICMF 2016), AIDIC, Florence, Italy, [10] Luo, M., and Haidn, O. J., The Effect of Injector Geometry on the Flashing Spray with Cryogenic Fluid, 6th European Conference for Aeronautics and Space Sciences, EUCASS, Krakow, Poland, July [11] Manfletti, C., Laser Ignition of an Experimental Cryogenic Reaction and Control Thruster: Ignition Energies, Journal of Propulsion and Power, Vol. 30, No. 4, 2014, pp doi: /1.b35115 [12] Adachi, M., McDonell, V. G., Tanaka, D., Senda, J., and Fujimoto, H., Characterization of Fuel Vapor Concentration Inside a Flash Boiling Spray, SAE Technical Paper , Warrendale, PA, 1997, doi: / [13] Kawano, D., Ishii, H., Suzuki, H., Goto, Y., Odaka, M., and Senda, J., Numerical Study on Flash-Boiling Spray of Multicomponent Fuel, Heat Transfer Asian Research, Vol. 35, No. 5, 2006, pp doi: /(issn) x [14] Zuo, B., Gomes, A. M., and Rutland, C. J., Modelling Superheated Fuel Sprays and Vaporization, International Journal of Engine Research, Vol. 1, No. 4, 2000, pp doi: / [15] Schmehl, R., and Steelant, J., Computational Analysis of the Oxidizer Preflow in an Upper-Stage Rocket Engine, Journal of Propulsion and Power, Vol. 25, No. 3, 2009, pp doi: / [16] Aggarwal, S. K., and Peng, F., A Review of Droplet Dynamics and Vaporization Modeling for Engineering Calculations, Journal of Engineering for Gas Turbines and Power, Vol. 117, No. 3, 1995, Paper 453. doi: /