Part 27

Combustion/Supersonic Flow

1

Wide-range Single Engine Operated from Subsonic to Hypersonic Conditions: Designed by Computational Fluid Dynamics

Ken Naitoh1, Kazushi Nakamura1, Takehiro Emoto1, and Takafumi Shimada1

1 Faculty of Science and Engineering, Waseda University, 3-4-1 Ookubo, Shinjuku, Tokyo 169-8555 Japan k-naito@waseda.jp

A new type of single engine capable of operating over a wide range of Mach numbers from subsonic to hypersonic regimes is proposed for airplanes. Traditional piston engines, turbojet engines, and scram engines work only under a narrower range of operating conditions. The new engine has no compressors or turbines such as those used in conventional turbojet engines. A notable feature is its system of super multijets that collide to compress gas for the transonic regime. A numerical model simulating compressible turbulence with chemical reactions based on the CIP and BI-SCALES methods is employed to design the engine. The maximum power of this engine will be sufficient for actual use. For the higher Mach numbers in supersonic and hypersonic conditions, this engine can take the mode of a ram or scramjet engine.

1. Introduction

Traditional engines such as piston engines, turbojet engines, ram engines, and scram jet engines operate only in a narrow range of Mach numbers. Piston engines work well in the subsonic regime and turbojet engines are also suitable around the transonic regime, whereas ram and scram jet engines can be employed only for supersonic or hypersonic conditions. Although combinations of traditional engines can theoretically propel aircraft beyond the Earth’s atmosphere, such aircraft would be too heavy and complex to use. Rocket systems, on the other hand, require too much fuel and have safety issues. The key question is whether or not the compressors and turbines of turbojets systems can be eliminated. [1] 2. Outline of the new single engine For low Mach number conditions, a new pulsed compression concept is achieved by

jetflows that collide at a single point after the airflow enters from super multiple side passages I2 and nozzles for super multijets C2. (See the combustion area in Fig.1.) After combustion occurs around the collision point of the jetflows, the side passages generating these super multijet flows are alternately closed by means of a rotating flat plate C4. The outflow from each side passage pulsates because small holes provided in the rotating flat

2 Ken Naitoh et al

plate alternately direct flow to the side passages. Because the rotating plate is flat, less energy is needed for rotating it.

Fig. 1 Wide-range single engine operating from subsonic to hypersonic regimes. [2] The super multiple side passages are completely closed for higher Mach numbers. Under the condition, the main intake passage I1 located in front of the super multijet nozzles, takes in air more. That results in a ram or scramjet engine for supersonic and hypersonic conditions. (See the combustion area in Fig.1.) As the jet nozzles are covered by the smooth shape of the wings I3, the area of the main intake passage I1 gradually changes along the engine axis, which prevents separation flows. (Fig.2.) (Accordingly, the main intake passage can also have the effect of Laval nozzle.) We examined the potential of this engine by using numerical simulations. Three-

dimensional compressible Navier-Stokes equations were solved with a simplified two-step chemical reaction model. The cubic interpolated pseudo-particle (CIP) method [3] applied for the governing equation of the multi-level formulation [4, 5, 6] was employed, which is suitable for calculating both compressible and incompressible problems. The peak pressure at the combustion center was found to be over 2.5 MPa, while that

just before ignition was over 1.0 MPa. (Fig. 3.) The maximum power of this engine will be sufficient for actual use. (Table 1) Figure 4 shows the computed temperature distribution in the combustion chamber

surrounded by seventeen nozzle jets during one cycle in a subsonic regime. Figure 5 presents the instantaneous stream lines of the exhausted flow. 3. Advantages of this engine (a) There are no mechanical components around the center axis of the engine, because

of the combustion point produced by the super multiple jets coming from the side passages. Then, the axisymmetric engine design means the higher temperature region of burned gas is far from the solid walls of the engine. This geometry markedly reduces the heat loss at the walls, to substantially improve efficiency and power.

Wide-range single engine 3

(b) In turbojet engines, the burned gas temperature is limited by reliability of the turbine blades. However, the proposed engine permits higher temperatures, i.e., higher compression ratios before combustion. This also leads to better efficiency and higher power.

Fig. 2 Super multijet nozzles generating compression and the wings covering the jets. Fig. 3 Time history of pressure at the center of combustion area. Table 1 Power performance of the new engine

4 Ken Naitoh et al

Fig. 4 Time evolution of the temperature distribution during one cycle of detonation.

Fig.5 Instantaneous streamlines in the combustion area. 4. Engine start The engine system shown in Fig. 1 cannot work at very low Mach numbers less than 0.1

or under starting conditions. To overcome this issue, we propose an ultimate engine system that can also be used at engine start. (Fig. 6) This ultimate system is the extended version fitted with a special piston system having an exhaust duct and a rotating plate for closing the duct (twister system). The engine system is practicable, because both the engine with super multijets and the piston engine are of the pulsating type, which should allow a smooth transition between the two. A combination of turbojet and piston engines would be difficult to achieve. 5. Noise level The vapor fuel distribution inside the combustion chamber can be changed by varying

the fuel injectors and their injection timings. Figure 7 shows the influence of fuel distribution patterns on pressure time histories. Optimization of the fuel distributions will lower the peak pressure after combustion, thereby reducing the noise level, while the high power is kept.

Wide-range single engine 5

6. Conclusion The proposed engine capable of operating from startup to hypersonic conditions promises to bring a new transport mode. The automobile mode with the piston engine can be used from startup to takeoff from highway, while the pulsating mode of colliding super multijets works around the transonic regime and the steady flow mode of ram and scram jets can be employed for hypersonic conditions. First, we want to develop a small passenger vehicle system for ground and air, at a price of equal to that of luxury automobiles with a 5-liter engine. The present research on the new engine may represent the first quantum leap in

engineering fields achieved by using only computational fluid dynamics. We will shortly enter an age of “computer-aided prototyping (CAP)” for achieving several quantum leaps. Fig. 6 Wide-range single engine operating from startup to hypersonic conditions. [2] Fig. 7 Pressure time histories for different vapor fuel distributions. (A higher pressure peak for a center charge and two lower ones for a surrounding charge of fuels)

6 Ken Naitoh et al

References 1. Shimada T, Naitoh K, Nakamura K, and Emoto T. (2009). Computation of aero-craft

engine based on supermulti jet, Proceedings of 23rd Conference on CFD, Sendai. 2. Naitoh K, submitted as Japanese Patent. 3. Takewaki H, Nishiguchi A, and Yabe T (1985). The Cubic-Interpolated Pseudo-

Particle (CIP) Method for Sorving Hyperbolic-Type Equations”, J. Comput. Phys. Vol. 61, p.261.

4. Naitoh K and Kuwahara K (1992). Large eddy simulation and direct simulation of compressible turbulence and combusting flows in engines based on the BI-SCALES method, Fluid Dynamics Research 10, pp.299-325.

5. Naitoh K, Nakagawa Y, and Shimiya H. (2008) Stochastic determinism approach for simulating the transition points in internal flows with various inlet disturbances. Proc. of ICCFD5, Computational Fluid Dynamics 2008, Springer-Verlag.

6. Naitoh K. and Shimiya H. (2010) Stochastic determinism capturing the transition point from laminar flow to turbulence. Accepted for publishing in Japan Journal of Industrial and Applied Mathematics, [Also in Proc. of 6th Int. Symposium on Turbulence and Shear Flow Phenomena (TSFP6), 2009].

Numerical Simulations of the Performance of Scramjet Engine Model with Pylon Set Located in the Inlet Blankson1, I.M., Gonor2, A.L., and Khaikine3, V.A. Abstract. This work is devoted to numerical simulations of the flow in the scramjet engine model with hydrogen/air mixture combustion. The sub-scale model consists of the inlet with pylons, fuel injectors located on pylons, mixing region, combustion chamber, and nozzle. The goal of this work is to obtain efficient and stable combustion in the combustion chamber and thrust using this design, and to compare it with other existing scramjet engine models. A pylon set is proposed for installation in the rectangular inlet to decrease drag of the inlet and to create several air/fuel mixing layers to increase mixing efficiency. A movable cylindrical rod was placed in the combustor to initiate shock-induced combustion. Numerical simulations were conducted using the NASA CFD code VULCAN and performance of this scramjet engine model was computed. These simulations showed that efficient combustion and resulting thrust addition in the case of this design significantly exceeds the drag introduced by the obstacle in the combustor. As a result, in the relatively short combustor, we obtained the combustion efficiency, ηc = 0.85, and a relatively high value of the engine model specific impulse, Isp = 1275 sec. 1. Geometry of the proposed scramjet engine model Based on the results on the He/Air mixing efficiency in the inlet with pylons [1], we have investigated flow and combustion of the air/fuel mixture in the model scramjet engine. Such engine is built of a relatively short inlet with pylons, combustor, and nozzle (Fig. 1).

The inlet and combustion chamber are two-dimensional, while the nozzle has three-dimensional configuration with flat surfaces and rectangular cross section. The sizes of the scramjet engine were chosen so that the experimental testing of this model in hypersonic wind tunnels were

1 Blankson, I.M., Senior Technologist, Isaiah.M.Blankson@nasa.gov NASA Glenn Research Center, Cleveland, OH 44135, USA 2 Gonor, A.L., Research Professor (deceased), AGonor@rogers.com Hampton University, Hampton, VA 23668, USA 3 Khaikine, V.A., Research Scientist, Vitali.Khaikine@hamptonu.edu Hampton University, Hampton, VA 23668, USA

possible. It is to be noted, that this scramjet model is significantly smaller than the CIAM/NASA scramjet model [2], well-known X-43 model [3-5], and the Japan scramjet model [6-8]. In the suggested configuration a short inlet transforms to the combustor at the distance l / H = 5. Here l is the distance between the pylon trailing edge and combustor, H – channel height. Total length of the engine model, including nozzle, is 0.95 meters.

Fig. 1: General view of the scramjet engine Fig. 2: Telescope Inlet-Nozzle model with H2 model. combustion – combustor zoom. 2. CFD analysis of the scramjet model performance Numerical simulations of the flow with combustion in the channel and engine nozzle were conducted using the NASA CFD code VULCAN. The analysis of the temperature distribution showed that the temperature of the air/fuel mixture in the channel is not high enough for the intensive and stable combustion to occur. Due to this, it was suggested to place a cylindrical obstacle (cylindrical rod) at the entrance of the combustion chamber. This cylindrical rod will favor the increase in the temperature in the area of combustion triggering (Fig. 1).

The Mach number distribution near the obstacle and in the combustion chamber is shown in Fig. 2. In the immediate region after the obstacle, in its trace, according to Fig. 2 and according to the Mach number distribution in a cross section (Fig. 3), there exists a subsonic region, which allows the possibility for the subsonic reactive flow. The configuration of the head shock wave in front of the cylindrical rod proves that, first, the flow field in the channel is non-uniform, and, second, a shock-induced combustion occurs near the head shock wave, which (under the certain conditions) can transform into detonation combustion. The latter also agrees with the temperature field distribution shown in Fig. 4 where the bow shock wave is accompanied by the narrow zone of high

temperature and with the high values of the mass fraction H2O shown in Fig. 5. The temperature peak, according to Fig. 6, occurs in the obstacle trace, and the stream in the channel intensively combusts.

The water, hydroxyl, and hydrogen mass fraction distributions in the cross sections of combustor are shown in Figs. 7-9. Plots of OHc

2 and OHc

relate to the cross section, located immediately after the cylindrical rod in

Fig. 3: Mach number distribution in a cross Fig. 4: Temperature flow field in the plane immediately behind the cylindrical rod. combustor.

Fig. 5: H2O mass fraction distribution in the Fig. 6: Static temperature distribution combustor. immediately behind cylindrical rod. the combustor. The values of mass fractions, shown in these plots, confirm that intensive combustion takes place in the whole volume of the channel, except small regions near the top and bottom walls. Such distributions of the reaction products occur in all cross sections of the channel up to the nozzle entrance. The distribution of the hydrogen mass fraction at the nozzle entrance cross section (Fig. 9), where the combustion begins to die out, shows that there exists a small excess of hydrogen (approximately

15%) which remains unburned. Obviously, this is due to the non-uniform distribution of the flow parameters in channel cross sections. However, in general, the combustion in the channel is stable and is accompanied by the significant heat generation.

Fig. 7: H2O mass fraction distribution in a Fig. 8: OH mass fraction distribution in a cross plane immediately behind the cross plane immediately behind the cylindrical obstacle. cylindrical obstacle.

Fig. 9: H2 mass fraction distribution at the Fig. 10: Dependence of combustion nozzle entrance cross section. efficiency, ηc, vs. the distance from the combustor entrance.

The combustion efficiency, ηc, was defined [6] as the ratio between the H2 consumption rate and the H2 supply rate. It can be presented as:

∫ ∫−=H H

lowHxHc dyucdyuc0 0

inf22/1 ρρη (1)

where H is the combustor height, 2Hc - mass fraction of the H2 in the

current combustor cross plane, x = constant, placed between inflow and

outflow cross sections. Taking into account that denominator in (1) for our model of the engine equals 1.656*10-2 kg/s and 0 < ηc < ηcmax, one has ηcmax = 0.85 (or 85%), which is a high value for the combustion efficiency. For example, ηcmax = 0.55 for the advanced scramjet engine design developed in [6-8]. The plot of ηc(x) along the combustion chamber axis is depicted in Fig. 10.

The relatively high pressure in the combustor also confirms high value of the combustion efficiency. This pressure reaches the values of approximately 1.5*105 Pa, which exceeds pressure at the combustor entrance by 4.4 times, and which leads to the nozzle pressure ratio that equals to 55.6. The length of combustion chamber was determined under the condition of the maximum pressure at the nozzle entrance. It turned out that using this assumption, combustor length equals only 6.8% of the total engine length. Such short combustor became possible due to the intensive combustion that takes place in its channel. It is to be noted, that these results on the intensification of combustion became possible only because of the movable cylindrical obstacle which was introduced and added into the engine design. The optimum location of this cylindrical rod was determined using numerical simulations results. These numerical simulations showed that the thrust addition in this case significantly exceeds the drag introduced by the obstacle.

The calculation of the force characteristics of different engine components and of the total engine design gives the following results:

Drag:

Pylons (3) – 0.81 kg; Forebody and channel with combustor (including side walls) – 8.78 kg; Cylindrical obstacle – 4.3 kg;

Thrust: Nozzle – 34.91 kg;

Net engine model thrust – 21.02 kg.

One should note that previous numerical simulations and experimental tests at Mach number 4 [9] showed that pylons, located at the inlet entrance (without fuel injection), produced additional thrust. However, in the current design with fuel injectors located on pylons, a small additional drag occurs, which one can relate to the fact that additional shock waves are produced by the fuel jets. Nevertheless, there is a possibility to improve pylons thrust by replacing existing inlet forebody with a two-stage wedge or with a wedge that transforms partial into a curvilinear surface. Such shape leads to isentropic compression and turns the flow by

a bigger angle compared to the current shape with a single wedge. As a result the drag and total pressure losses, caused by the main shock wave, will decrease, and pylons are placed at a bigger angle to the flow, which increase their thrust.

Now let us estimate the efficiency of the engine model using the usual criterion -ratio of the total engine thrust to fuel flow weight per unit time. This value may be represented as:

∫==H

lowHsp dyucgDQQTI

0inf)(,

2ρ (2)

where T – is the net engine thrust, D and H – width and height of the channel, respectively,

2Hc - mass fraction of the injectant, g = 9.81 m/s2. The index “inflow” refers to the entry plane of the combustor. It turned out that for the given engine model, according to (2), Isp = 1275 sec. The same characteristic, determined by using (2) for engines mentioned above [6-8], equals Isp = 850 sec, for the equal values of equivalent ratio, Ø = 1, corresponding to the maximum thrust.

The relatively high value of Isp obtained for the scramjet model with movable rod is rather unexpected since the cylindrical rod induces additional shock and losses of total pressure. To clarify this situation we used 1-D approach presented in [10]. The difference of total pressure in different points of 1-D flow containing shocks, heat inflow, q, through the outer boundary or from chemical reactions, and uncompensated heat inflow, q`, caused by the irreversible (viscous) processes may be represented as follows,

∫ ∫ −−−=−1

0

1

0

0'0

00

000 )1(x

x

x

xshxxf pdxq

TT

dxqTT

pp δρρ (3)

where subscript 0 relates to stagnation values of the parameters, dxdqqx /= and dxdqqx /`` = . The heat inflows q and q` are given per

unit mass and unit length, respectively, δp0sh is the difference between total pressure values in front of the shock and behind it. According to Eq. (3), movable rod placed in the combustor increases δp0sh and losses of the total pressure in the flow. On the other hand, the first item on the right hand side of (3) may be in this case smaller, compared with the one for combustor with diffusion combustion. The fact is that intensive detonation type combustion occurs at short distances, ∆x, from shock, that is qx ≠ 0 only at x ∈ (x0, x0+∆x) with T ~ T0. In the case of slow diffusion combustion the values of qx ≠ 0 occur within long interval along the flow whereas combustion transpires at T < T0. As a result, the overall losses of the total pressure in the scramjet design with rod can turn out to be smaller than in

the case of the scramjet based on the diffusion combustion, since the reduction of first and second items in (3) may offset the increase of the third item. 3. Conclusions New model of scramjet engine with pylons located in the inlet and movable rod located in the combustor was designed. Numerical simulations of this scramjet engine model were conducted and it was shown that in spite of the non-uniform flow field and non-uniform air/fuel mixture, suggested design allows to obtain intensive combustion which takes place in the whole volume of the combustor channel, and to generate thrust. Comparison of this model with other scramjet engine models available in literature showed that even with no optimization of major parameters of the given engine model, the performance of this design according to conducted numerical simulations is promising. The specific impulse of the proposed scramjet engine model, Isp = 1275 sec. References 1. A. Akyurtlu, J. Akyurtlu, A.L. Gonor, V. Khaikine, A.D. Cutler, and I.M.

Blankson, “Numerical and Experimental Tests of a Supersonic Inlet with Pylon Set and Fuel Injection through Pylons,” AIAA Paper 2006-1032.

2. Rodriguez, C. G., Computational Fluid Dynamics Analysis of the Central Institute of Aviation Motors/NASA Scramjet, Journal of Propulsion and Power, v. 19, # 4, 2003.

3. Ferlemann, S. M., McClinton, C. R., et al, Hyper–X Mach 7 Scramjet Design, Ground Test and Fight Results, AIAA 2005 – 3322.

4. Rogers, R. S., Scramjet Development Tests Supporting the Mach 10 Flight of the X-43, AIAA 2005 – 3351.

5. Ferlemann, P. G., Comparison of Hyper-X Mach 10 Scramjet Preflight Prediction and Flight Data, AIAA 2005 – 3352.

6. Kouchi, T., Mitani, T., Masuya, G., Numerical Simulation in Scramjet Combustion with Boundary Layer Bleeding, Journal of Propulsion and Power, v. 21, # 4, 2005.

7. Mitani, T., et al., Boundary-Layer Control in Mach 4 and Mach 6 Scramjet Engines, Journal of Propulsion and Power, v. 21, # 4, 2005.

8. Tomioka, S., et al., Distributed Fuel Injection for Performance Improvement of Staged Supersonic Combustor, Journal of Propulsion and Power, v. 21, # 4, 2005.

9. Gilinsky, M.M., Khaikine, V., Akyurtlu, A., Akyurtlu, J., Blankson, I. M., et al., Numerical and Experimental Tests of a Supersonic Inlet Utilizing a Pylon Set for Mixing, Combustion and Thrust Enhancement, AIAA – 2005 – 3290.

10. Chernyi, G. G., Gas Dynamics, CRS Press, N.Y., 1994.

Scale adaptive simulations over a supersonic car

Guillermo Araya, Ben Evans, Oubay Hassan & Kenneth Morgan

Abstract In this study, the unsteady Reynolds-averaged Navier-Stokes equationsare employed together with the Menter SST-SAS turbulence model in compressibleflows. Numerical simulations over a supersonic car, the BLOODHOUND SSC [1],are shown and discussed with Mach numbers up to 1.3.

1 Introduction

Computational fluid dynamics (CFD) has experienced a notable growth in the lastfew decades. Nowadays, most engineering designs and technical projects rely oncomputational predictions before making critical design decisions; additionally,CFD may also be employed to gain important insight into the flow physics beforeperforming an expensive experiment. Recently, significant attention has been paid torelatively low-cost (compared to large eddy simulations, LES) time-dependent com-putations of complex flows for industrial applications, e.g. geometries with mov-ing parts, wing flutter, noise prediction, etc. Particularly, the unsteady Reynolds-averaged Navier–Stokes (URANS) methodology has became quite popular, due toits successes in predicting the most energetic modes or coherent structures. How-ever, URANS has frequently been accused of inaccurately representing the correctspectrum of turbulent scales, even if the numerical grid and the time step would beof sufficient resolution. In this study, the URANS equations for compressible floware solved over a supersonic car, the BLOODHOUND SSC [1]. The Menter SSTturbulence model is employed in conjunction with a recently developed SAS model(scale adaptive simulations) by Menter et al. [2]. This allows capturing more detailsof the flow or the ‘small turbulent scales’. The FLITE flow solver [3] developed atSwansea University is applied, based on a finite volume approach with stabiliza-tion and discontinuity capturing. Modelling the aerodynamics of a supersonic caris very challenging. This is due to the presence of highly separated flow regionsand shock waves; not to mention the numerical modelling of the rotating wheelsand accounting for the car–ground interaction. The aerodynamic performance ofthe BLOODHOUND SSC, as well as the most relevant aspects of the flow physicswill be analyzed by using the Menter SST-SAS model in this study.

Civil & Computational Engineering Centre, Swansea University, Swansea SA2 8PP,UK, e-mail: araya@mailaps.org ; B.J.Evans@swansea.ac.uk ; O.Hassan@swansea.ac.uk ;K.Morgan@swansea.ac.uk

1

2 Guillermo Araya, Ben Evans, Oubay Hassan & Kenneth Morgan

2 Numerical ResultsThe Swansea FLITE3D flow solver [3], which employs unstructured meshes and afinite–volume approach, is used in the assessment of the Menter SST-SAS turbu-lence model. More details about the numerical code can be found in [4]. The resultsof classical aerodynamic test cases are presented in this section, together with adiscussion concerning the application to the BLOODHOUND supersonic car.

2.1 Acoustic cavityNumerical simulation of flow over a 3-D rectangular cavity are presented. The cav-ity configuration is selected as the M219 experimental test case of Henshaw [5].The geometry dimensions of the M219 cavity are L× W × D = 5×1×1 (length,width, and depth), with a depth D of 4 inches. The freestream Mach number, M∞, is0.85 and the Reynolds number is 19.6×106, based on the cavity depth. The hybridmesh consisted of around 3.37 million tetrahedral elements, 4472 prisms and 459pyramids. The mesh has 20 viscous layers for boundary layer capturing and the firstoff wall point is located at y/D = 2.5× 10−6. The selected normalized time stepis ∆ t∗ = ∆ t/(D/U∞) = 0.05. The time variation of the total drag over the cavity,normalized by the reference surface and freestream dynamic pressure, can be ob-served in fig. 1. Additionally, figure 2 shows iso-surfaces of Ω 2 − S2, where Ω isthe vorticity and S2 is the scalar invariant of the strain rate tensor. This parameterrepresents the large scale turbulence structures of the flow and qualitatively verysimilar structures were obtained by [2] in the cavity.

t* = t / (D/U∞)

Tot

alD

rag

/(q

xS)

0 10 20 30 40 50-1

0

1

2

3

4

5

6

Fig. 1: Time variation of the total drag in the acoustic cavity.

2.2 ONERA M6 wingIn simulation of flow over the ONERA M6 wing [6], the freestream Mach numberM∞ = 0.84 and the total Reynolds number is 12×106 , based on the mean geometricchord. This case is tested at an angle of attack α = 6.0o. This case at the maximumangle of attack is very challenging for the turbulence models, due to the presence ofhighly–separated flow. A hybrid mesh is employed, consisting of around 6.3 milliontetrahedral elements, 0.25 million prisms and 11.6 thousand pyramids. The wingsurface is represented using around 1.1 million triangles. The mesh has 35 viscouslayers for boundary layer capturing and the first off wall point is located at y+ ≈0.4 in wall units, for points located in the vicinity of the leading edge, where the

Scale adaptive simulations over a supersonic car 3

Fig. 2: Iso-surfaces of Ω 2 −S2 in the acoustic cavity.

skin friction is high. In figure 3(a) the pressure coefficient distribution is depictedat y/(b/2) = 0.44 after a time-averaging of t∗ = 2, with a very good agreementwith experimental data by [6]. In addition, the iso-surfaces of instantaneous vorticity(module) in fig. 3(b) show the significant increase of vorticity due to the presenceof shocks in the ONERA M6 wing.

2.3 F15 fighterThe third example consists on the generic F15 fighter configuration. The freestreamMach number is M∞ = 0.9, the total Reynolds number is 358×106 and the angle ofattack is five degrees. The hybrid mesh is composed by around 2.2 million nodesand 10.2 million elements. In table 1, the corresponding values of the pressure coef-ficients, Cp, are exhibited for the upper and lower surfaces at three different pointsin the upper and lower surfaces (labeled as a,b and c in figure 4). The computed Cpare compared with experimental data collected in wind-tunnel and in flight [7]. Ingeneral, the comparison of present results with experimental data is fair. The mostsignificant discrepancies were found in point b of the lower surface, which may indi-cate a poor resolution of the mesh in this zone or an insufficient sample for statisticscomputation; and, further investigation must be done. Figure 5 shows iso-surfacesof the instantaneous vorticity. Clearly, the appearance of large turbulence scales canbe appreciated due to the SAS model.

2.4 Supersonic carPreliminary simulations have been undertaken of unsteady flows over the supersoniccar, BLOODHOUND SSC, at a free stream Mach number of M∞ = 1.3. The totalReynolds number is approximately 390×106 based on the stream wise length (L ∼13m) of the car. One of the latest configurations (10b) has been considered, with ahybrid mesh of approximately 14 million elements and 3.12 million nodes. In fig. 6,

4 Guillermo Araya, Ben Evans, Oubay Hassan & Kenneth Morgan

x/c

Cp

0 0.25 0.5 0.75 1

-1.75

-1.5

-1.25

-1

-0.75

-0.5

-0.25

0

0.25

0.5

0.75

1

Experiment (upper)Experiment (lower)SST-SAS

y/(b/2) = 0.44M = 0.84Re = 1x106

α = 6.0°

(a) Pressure coefficient for y/(b/2) = 0.44

(b) Iso-surfaces of instantaneous vorticity

Fig. 3: ONERA M6 wing at α = 6.0o (Menter SST-SAS).

Table 1: Pressure coefficients Cp in F15 at α = 5o

Upper surface Lower surfacePoint Present Cp Flight data Wind-tunnel data Present Cp Flight data Wind-tunnel data

a −0.33 −0.24 −0.35 −0.36 −0.62 −0.42b −0.15 −0.35 −0.2 −0.24 −0.01 −0.083c −0.11 −0.1 −0.08 −0.023 −0.015 0.0034

Scale adaptive simulations over a supersonic car 5

(a) Upper surface (b) Lower surface

Fig. 4: Iso-contours of pressure coefficient in F15 fighter.

Fig. 5: Iso-surfaces of instantaneous vorticity in the F15 fighter.

the time variation of the total drag over the car up to a non-dimensional time, t∗,of 28 can be observed. Despite the relatively short calculated physical time, someimportant conclusions can be drawn from numerical results so far. Fig. 7 depictsthe iso-contours of the streamwise velocity at t∗ = 28 at the half cross-sectionalplane of the supersonic car. The vertical iso-lines at the entrance of the intake ductsuggests the presence of a normal shock. Inside the duct, the flow experiences aslight deceleration from approximately a normalized velocity of 0.8 to 0.6 at theinlet turbofan. Two zones of highly accelerated flow and high lift are observed overthe car: at the intake duct and over the horizontal tail. In addition, both engine outlets(turbofan and hybrid rocket) represent important sources of vorticity, as seen infig. 8. Finally, in figure 9 iso-surfaces of the parameter Ω 2 − S2 are depicted. Itcan be observed the large turbulence structures flowing out downstream from thewheels. Although the selected wheel configuration might increase significantly theshape drag, this design allows the formation of oblique shocks well far from thewheel-ground interface.

6 Guillermo Araya, Ben Evans, Oubay Hassan & Kenneth Morgan

t* = t / (L/U∞)

Tot

alD

rag

/(q

xS)

5 10 15 20 251

1.2

1.4

1.6

1.8

2

Fig. 6: Time variation of the total drag in the supersonic car.

Fig. 7: Iso-contour of instantaneous streamwise velocity at the half cross-sectionalplane.

Fig. 8: Iso-contour of instantaneous vorticity at the half cross-sectional plane in thecar rear.

Scale adaptive simulations over a supersonic car 7

Fig. 9: Iso-surfaces of Ω 2 −S2 in BLOODHOUND SSC.

3 CONCLUSIONSAn evaluation of the Menter SST-SAS turbulence model in URANS of turbulentcompressible flows is performed for a number of 3D aerodynamic test cases (acous-tic cavity, ONERA M6 wing and F15 fighter) by means of the Swansea FLITE3Dflow solver. Furthermore, preliminary numerical predictions of the flow over theBLOODHOUND supersonic car [1] have also been carried out and important in-sights were acquired on the most significant aspects of flow phenomena.

References

1. http://www.bloodhoundssc.swan.ac.uk/2. Menter F.R., Egorov Y. and Rusch D.: Steady and unsteady flow modelling using the k -

√kL

model. In Turbulence, Heat and Mass Transfer 5, Proc. of The International Symposium onTurbulence, Heat and Mass Transfer Dubrovnik, Croatia, September 25-29 (2006).

3. Morgan K., Peraire J., Peiro J. and Hassan O.: The computation of 3-dimensional flows usingunstructured grids. Computer Methods in Applied Mechanics and Engineering 87, 335–352(1991).

4. Sørensen K.A., A multigrid accelerated procedure for the solution of compressible fluid flowson unstructured hybrid meshes. PhD thesis, University of Wales, Swansea (2002).

5. Henshaw, M. J., M219 cavity case. In: Verification and validation data for computationalunsteady aerodynamics, Tech. Rep. RTO-TR-26, AC/323/(AVT) TP/19, pp. 453472 (2000).

6. Schmitt V. and Charpin F., Pressure distributions of the ONERA M6 wing at transonic Machnumbers, Report AR–138, AGARD, Paris (1979).

7. Webb L., Varda D. and Whitmore S., Flight and wind-tunnel comparisons of the inlet/airframeinteraction of the F-15 Airplane. NASA, Technical paper 2374 (1984)

Rotating detonation engine injection velocity limitand nozzle effects on its propulsion performance

Jian-Ping Wang and Ye-Tao Shao

State Key Laboratory of Turbulence and Complex Systems,Department of Mechanicsand Aerospace Engineering, Peking University, Beijing, China. 100871Tel. +86-10-82529038Email: wangjp@pku.edu.cn

1 Introduction

The concept of a RDE, which is also called a continuous detonation waveengine (CDWE), was first achieved experimentally in short time by Voitsekho-viskii [1] in the early 1960s. In recent years, RDEs have been extensively studiedfrom an experimental viewpoint by Bykovskii et al. [2-4]. The serial experi-ments achieved both liquid and gas fuel detonation in combustors with differ-ent shapes and with supersonic or subsonic injection flow. From a numericalviewpoint, some two-dimensional simulations [5,6,7] and three-dimensionalsimulations [8,9] have been done for the flow field of RDEs as well as differ-ent aspects of their propulsive performance. All of the above experimental andnumerical investigations show the advantages and applicability of the RDEconcept.An RDE can work continuously under various operation conditions of subsonicand supersonic injection. However, the limitation of injection velocity beyondwhich RDEs no longer work and the accompanying changes in the DW propa-gation mode have not yet been investigated. In the present study, we investigatethese questions by computing a series of cases with injection velocities rangingfrom 50 to 2000m/s.Furthermore, a detail propulsion performance analysis for an RDE with dif-ferent type of nozzles is carried out. RDEs with four types of nozzle, namelyconstant area nozzle, Laval nozzle, diverging nozzle and converging nozzle arenumerically simulated to investigate their propulsion performance.

2 Physical model and numerical method

A one-step chemical kinetic model was used in this simulation. Three-dimensionalEuler equations in generalized coordinates are used as governing equations.The geometry of the chamber and the overview of the continuous propagationprocesses of an RDE with an injection velocity of 500 m/s are illustrated in Fig.1.The inner radius of the chamber was 40 mm, the outer radius was 53 mm, andthe tube length was 60 mm. The head wall was closed but was perforated withsmall, uniformly distributed ports or slits, which were used to inject combustiblegas into the chamber. When the head-wall pressure pw exceeded the injection

2 Jian-Ping Wang and Ye-Tao Shao

stagnation pressure, the reaction mixture could not be injected into the chamberand a rigid wall condition was set locally. Otherwise, we assumed that theinjection flow maintained a constant state of 0.103 MPa, 300 K with the injectionvelocity from 50 to 2000 m/s for the different cases.

Fig. 1. Continuous propagation processes an RDW from 0 to 850 µs. Panels (a) and (b)show the pressure contour, and panels (c) and (d) show how the contour of the reactionprogress parameter β. Point 1 indicates CJ detonation, point 2 is the DW, point 3 is theoblique shock wave, point 4 is the detonation product, point 5 is the new injected freshgas mixture, and point 6 is the deflagration interface front.

3 Results and discussions

3.1 Injection velocity limit

Figures 1(a) and 1(b) show the pressure contour at t = 0 and 100 µs, respectively.The DW is ignited by a branching, pre-detonation tube that is connected tan-gentially to the outer wall of the combustor. In numerical simulations, a sectionof classical CJ detonation is set, as shown in Fig. 1(a), then is substituted ofthe pre-detonation ignition for simplicity. After ignition, the DW propagatesazimuthally around the combustor. Because the DW’s velocity is approximately2000m/s, the injection fuel velocity is 500m/s. However, the velocity of the de-flagration wave at the interface between the detonation product and the newinjected fuel is approximately several meters per second. Only a thin layer ofnew injected fuel is burnt out, so that enough injected fuel could maintain theunreacted state to support a continuously propagating DW. Figures 1(c) and1(d) show the reaction progress parameter contour β at 150 and 850 µs, respec-tively. These figures show that, at 850 µs, the DW has propagated more than sixrounds, and it can continuously propagate for a long time. The numerical results

Velocity Limit and Nozzle Effects of RDE 3

in Fig.1 agree well qualitatively with existing experimental results [2]. The DWmaintains an acute angle of approximately 20 with respect to the fuel injectiondirection so that it moves against the injection flow direction, thereby avoidingbeing blown downstream. Because of this inclination, the azimuthal branch ve-locity is lower than the classical CJ velocity. Figure 2 shows the history of thepressure and temperature at a point on the head piece (x = 48 mm, y = 0mm, z =4mm) from 0 to 850 µs. We see that after the initial unsteadiness dies down, theDW gradually begins to propagate around the tube. The pressure peak contactsthe high temperature front following it has the typical detonation structure. Be-tween 117 and 729 µs, the DW makes four rounds, so the magnitude of the DWvelocity is 1850 m/s. This value is close to VCJ, which is approximately 1984 m/s.We expand the combustor to plane and extract out the middle layer. Figures

Time /µs

Pre

ssur

e/M

Pa

0 200 400 600 8000

1

2

3

4

Time /µs

Tem

pera

ture

/K

0 200 400 600 8000

1000

2000

3000

4000

Fig. 2. A single history of the evolution of point pressure and temperature at the headpiece(x = 45 mm, y = 0 mm, z = 10 mm) of the combustor from 0 to 850 µs.

z/m

0 1 2 3 4 5 6

0.02

0.04

0.06(a) Win=100m/s

θ<5

z/m

0 1 2 3 4 5 6

0.02

0.04

0.06(b) Win=1000m/s

θ=33

Angle coordinate \arc

z/m

0 1 2 3 4 5 6

0.02

0.04

0.06(c) Win=2000m/s

θ=90

Fig. 3. Pressure counter on middle surface of the combustor with injection velocity Winof 100, 1000, and 2000m/s.

4 Jian-Ping Wang and Ye-Tao Shao

3(a) to 3(c) show the flow field structure with an injection velocity of 100,1000,and 2000m/s, respectively. It is seen that the DW inclination angle increases withincreasing inflow velocity. When the injection velocity is 100m/s, the inclinationangle is less than 5 i.e., almost perpendicular to the head wall. When the injectionvelocity decreases to 50m/s, then the injected fuel layer becomes too narrow tomaintain the detonation strength, and detonation is attenuated to conventionalcombustion. When the injection velocity is 1000m/s, the inclination angle is 20.From Fig.3(c), we see that increasing the injection velocity from 1000 to 2000m/scauses the DW to gradually become parallel with the head wall. Because theinjection velocity is greater than VCJ, the self-sustained detonation-wave struc-tures moves with a velocity of 2000m/s-VCJ in the direction from the head wallto the open end.

3.2 Nozzle effect

Fig. 4. Cut sections of RDE configurations studied(Unit: mm).

Cut sections of different type combustor configurations are detailedly showedin Fig. 4. The front parts of these combustors have the same configurations. Atthe nozzle part, the Laval tube and the diverging nozzle have the same exit areaand the converging nozzle exit area equals 0.62 times of the combustor’s depth.These geometry parameters are designed partly according to the ratio betweenthe steady state detonation product pressure and the environment pressure. Setconstant injection stagnation pressure of 2MPa and constant stagnation temper-ature of 500K.The gross thrust F, the gross specific impulse and the fuel mass flow rate persquare meter are calculated from the following formulas:

F(t) =

head(ρw2+p−p∞)dA (1)

˙m(t) =1

Ahead

headρwdA (2)

Velocity Limit and Nozzle Effects of RDE 5

Igsp =

exit(ρw2+p−p∞)dA

Aheadgm(3)

First, Fig.5 shows the thrust history of these models from initial time to 1500µs.

Fig. 5. Thrust history of these four type nozzles RDE

After the flow field becomes steady, these models can continuously create enor-mous almost constant thrust. The Diverging nozzle RDE create about 1900Nthrust which is a very admirable value for this small combustor. The constantarea nozzle RDE outputs the smallest thrust of about 1600N.Figure 6 shows the fuel based gross specific history. For these four type of

Fig. 6. Gross specific impulse history from 0-1500µs.

nozzles, the gross specific impulse ranges from 1540s to 1750s. The Laval nozzlehas the best performance. The average mass flux is showed in Fig. 7. It can beenseen that these values just have a little difference, the average mass flow rate isabout 320kg/(m2*s) which is also a very significant value. It exhibits the mass

6 Jian-Ping Wang and Ye-Tao Shao

Fig. 7. The average mass flow rate per square meter dotm for four type nozzles

flow rate advantage of an RDE.

4 Conclusions

The typical flow field structure of RDE was numerically obtained and it agreeswell with the existence experiment. Our numerical simulation indicates thata rotating detonation can propagate continuously for a wide range of fuel-injection velocities from 100m/s to VCJ. When the injection velocity is greaterthan VCJ, the mode becomes a standing mode. When the injection velocity islower than 100m/s, detonation changes to deflagration. Different kinds of nozzleeffects on an RDE performance were compared. We found that the Laval nozzlehad the best performance of 1800 N thrust, 1750s gross specific impulse and 313kg/(m2*s) mass rate.

References

1. B.V. Voitsekhovskii, Soviet Journal of Applied Mechanics and Technical Physics. 129(6)(1959) 157-164.

2. F.A. Bykovskii, S.A. Zhdan, E.F. Vedernikov, Journal of Propulsion and Power. 22(6)(2006) 1204-1216.

3. F.A. Bykovskii, V.V. Mitrofanov, E.F. Vedernikov, Combustion, Explosion, and ShockWave. 33(3) (1997) 344-353.

4. F.A. Bykovskii, E.F. Vedernikov, Combustion, Explosion, and Shock Wave. 39(3) (2003)323-334.

5. S.A. Zhdan, F.A. Bykovskii, E.F. Vedernikov, Combustion, Explosion, and Shock Wave.43(4) (2007) 449-459.

6. M. Hishida, T. Fujiwara, P. Wolanski, Shock Waves. 19(1) (2009) 1-10.7. A. K. Hayashi, Y. Kimura, T. Yamada, AIAA 2009-633, Florida (2009)8. T. H. Yi, C. Turangan, J. Lou, AIAA 2009-634, Florida (2009)9. Y.T. Shao. M. Liu, J.P. Wang, 22st ICDERS, Minsk(2009)