Development and Assessment of Altitude Adjustable Convergent Divergent Nozzles Using Passive Flow Control

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2 Development and Assessment of Altitude Adjustable Convergent Divergent Nozzles Using Passive Flow Control A dissertation submitted to the Graduate School of the University of Cincinnati in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the School of Aerospace Systems of the College of Engineering by Mohamed Mandour Eldeeb October, 2014 B.S. Military Technical College, Egypt 1994 M.S. Military Technical College, Egypt 2001 Committee Chair: Shaaban Abdallah, Ph.D.

3 Abstract The backward facing steps nozzle (BFSN) is a new developed ow adjustable exit area nozzle for large rocket engines. It consists of two parts, the rst is a base nozzle with small area ratio and the second part is a nozzle extension with surface consists of backward facing steps. The number of steps and their heights are carefully chosen to produce controlled ow separation at steps edges that adjust the nozzle exit area at all altitudes (pressure ratios). The BFSN performance parameters are assessed numerically in terms of thrust and side loads against the dual-bell nozzle with the same pressure ratios and cross sectional areas. Numerical method is validated by solving two- and three-dimensional turbulent ow through a planar dual-bell nozzle at dierent pressure ratios and comparing the numerical results with available experimental data and numerical results. The numerical results for the pressure distributions over the planar dual-bell nozzle walls show a good agreement with the experimental data. Cold ow inside the planar BFSN and planar DBN are simulated using three-dimensional turbulent Navier-Stoke equations solver at dierent pressure ratios. The pressure distribution over the upper and the lower nozzles walls show a symmetrical ow separation location inside the BFSN and an asymmetrical ow separation location inside the DBN at same vertical plane. The side loads are calculated by integrate the pressure over the nozzles walls at dierent pressure ratios for both nozzles. Time dependent solution for the DBN and the BFSN are obtained by solving two-dimensional turbulent ow. The side loads over the upper and lower nozzles walls are plotted against the ow time. The BFSN side loads history shows a small values of uctuated side loads compared with the DBN which shows a high values with high uctuations. Hot ow three-dimensional numerical solutions inside the axi-symmetric BFSN and DBN are obtained at dierent pressure ratios and compared to assess the BFSN performance against the DBN. Pressure distributions over the nozzles walls at dierent circumferential angels are plotted for both nozzles. The results show that the ow separation location is axi-symmetric inside iii

4 the BFSN with symmetrical pressure distributions over the nozzle circumference at dierent pressure ratios. While the DBN results show an asymmetrical ow separation locations over the nozzle circumference at all pressure ratios. For further conrmation of the axi-symmetric nature of the ow in the BFSN, two-dimensional axi-symmetric solutions are obtained at same pressure ratios and boundary conditions. The results show that the side loads in the BFSN is 0.01%-0.6% of its value in the DBN for same pressure ratio. The ow separation position from the 3-D simulations for each PR shows a good agreement with its position in the 2-D axi-symmetric simulation for same PR. The ow parameters at the nozzle exit are calculated the 3-D and the 2-D solutions and compared to each other. The maximum dierence between the 3-D and the 2-D solutions is less than 1%. All the numerical results conrmed that the ow inside the BFSN is axi-symmetric. That is a very important nding which has the following implications: 1) two dimensional solution can be used to analyze the BFSN, calculate the nozzle thrust, the ow exit velocity, etc, 2) unsteady ow solution are now possible because of the major reduction of the CPU time for 2D solutions compared to 3D solution, and 3) the axi-symmetric solution is suitable for design practices of unsteady ow. To study the eect of the number of the backward facing steps on the nozzle performance, the number of the backward facing steps varied from two to forty. Since the most of the rocket mission is taking place at high altitude, a high PR of 1500 is taken as design point for the parametric study. The thrust values for all BFSNs are calculated at the design point and compared to the thrust of the DBN at same PR. The results show that as the number of backward facing steps increase, the nozzle performance in terms of thrust becomes closer to the DBN performance. The BFSN with two and six steps are simulated for pressure ratios range from 148 to 1500 and compared with the DBN and a conventional parabolic contour bell nozzle. Expandable BFSN study is carried out on the BFSN with two steps where the nozzle operation is divided into three modes related to the operating altitude (PR). At sea-level, the BFSN operates in mode-1 with expansion area limited to the base nozzle exit area. As altitude increase, the rst transition takes place by expanding the rst step results in increasing the expansion area to the rst step exit area. Second transition takes place at higher altitude by expanding the second step results in increasing the expansion area to the total nozzle exit area. Backward facing steps concept is applied to a full scale parabolic contour nozzle by adding two iv

5 backward facing steps at the end of the parabolic nozzle increasing its expansion area results in 1.8% increasing in its performance in terms of thrust coecient at high altitudes. v

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7 Acknowledgment All thanks are due to my Lord. It was only through ALLAH's help and support that this work was accomplished. I would like to express my special appreciation and thanks to my advisor Professor Dr. Shaaban Abdallah, He has been a tremendous mentor for me. I would like to thank him for encouraging my research and for allowing me to grow as a research scientist. He oers unconditional time to me in his oce and over the phone to discuss problems that I have encounter. I would also like to thank my committee members, professor Mark Turner, professor Jong Guen Lee, professor Milind Jog for serving as my committee members and for giving me advices about my work. My deepest appreciation to Dr. Mark Turner for his guidance and help. I am also very thankful to the people at School of Aerospace Systems. Special thanks to Mr. Rob Ogden for their assistance. A special thanks to my family. Words cannot express how grateful I am to my father for all of the sacrices that they made on my behalf, my motherin-law, and brothers. Their prayer for me was what sustained me thus far. I would also like to thank all of my friends who supported me in writing, and incented me to strive towards my goal. At the end I would like express appreciation to my beloved wife Asmaa Gabr who spent sleepless nights with and was always my support in the moments when there was no one to answer my queries. vii

8 Contents 1 Introduction Flow separation in rocket nozzles Side loads Flow separation control Trip rings Vented nozzle Active uid injection Nozzles with temporary insert A new nozzle concept Dual-bell nozzle Dissertation Overview Outline Validation of the Numerical Procedure Introduction Numerical method Unsteady Reynolds Averaged Navier-Stokes equations (URANS) SST k ω turbulent model Transport equations for the SST k ω model Time-step calculation Computational domain and boundary conditions Results and discussion Planar Backward Facing Steps Nozzle 33 viii

9 3.1 Introduction Numerical method Computational domain and boundary conditions Results and discussion Side loads D Results for Axisymmetric Backward Facing Steps Nozzle and Dual-bell Nozzle Introduction Numerical method Computational domain and boundary conditions Results and Discussion Side loads calculation D Axisymmetric Parametric Studies on Backward Facing Steps Nozzle Introduction Numerical method Computational domain and boundary conditions Results and Discussion Equal length backward facing steps Equal length steps Vs. variable length steps Temperature distributions Extendable Backward Facing Steps Nozzle Introduction Numerical methods Computational domain and boundary conditions Results and Discussion BFSN Two-modes 7-BFSN Backward Facing Steps Application for Full-Scale Nozzle Introduction ix

10 7.2 Numerical method Computational domain and boundary conditions Numerical results Flight performance Conclusions and Future Work Conclusions Future work Bibliography 100 x

11 List of Figures 1.1 Rocket nozzle FFS in over-expanded nozzle RSS on over-expanded nozzle Nozzles contours and as-designed wall pressure Relative side loads of TIC and PAR nozzles Typical side load magnitude for LE-7 and LE-7A nozzles during start up operation Jump of the separation point at LE-7A Side loads generated during separation point jump Mach number contours from SSME simulation comparing free shock separation (upper) and restricted shock separation (lower) Trip rings nozzle Vented nozzle Nozzle with ow injection Nozzle with ejectable insert Nozzle with consumable insert New nozzle prole Computed pressure contours for PR=37 without secondary ow Computed pressure contours for PR=37 with secondary ow Wall Pressure prole for PR=37 without secondary ow Wall Pressure prole for PR=37 with secondary ow Sketch of the dual-bell nozzle Operatioal modes of the dual-bell nozzle Specic impulse of the DBN in comparison with base and extension nozzles Schlieren observation of shock system within a dual-bell nozzle ow transition. 18 xi

12 1.24 Side load generation during a typical test run Normalized side loads measured during experimental work D schematic diagrams of the nozzles physical models Computational domain boundaries Computational domain at the mid-plane section Cross section (A) zoomed at nozzle geometry Y+ at the mid-plane upper wall for DBN, PR= Wall pressure distribution at PR= Wall pressure distribution at PR= Dual-bell nozzle geometry DBN upper wall pressure distribution at dierent planes PR= DBN upper wall pressure distribution at dierent planes for PR= Side loads variation with time D schematic diagrams of the nozzles physical models Computational domain at the mid-plane section Cross section (A) zoomed at BFSN geometry Y+ at the mid-plane upper wall for BFSN Upper wall pressure distribution at dierent planes Upper and lower wall pressure distribution at BFSN plane of symmetry for PR= Upper and lower wall pressure distribution at BFSN plane C for PR= BFSN upper wall pressure distribution at dierent planes for PR= Upper and lower wall pressure distribution at BFSN plane of symmetry for PR= Upper and lower wall pressure distribution at BFSN plane C for PR= Mach contours at BFSN mid-plane for PR= Mach contours at BFSN plane C for PR= Mach contours at BFSN mid-plane for PR= Mach contours at BFSN plane C for PR= Velocity vectors at plane of symmetry zoomed near second step edge (PR=30.83) 42 xii

13 3.16 Velocity vectors at plane of symmetry zoomed near second step edge (PR=45.5) Side loads over the BFSN walls as function of the ow time Side loads comparison between the BFSN and the DBN D schematic diagrams of the nozzles physical models Cross-section shows the computational domain and the boundary conditions Computational grid inside the BFSN at mid-plane section Computational grid inside the DBN at mid-plane section Wall pressure distribution at dierent azimuth angels for PR= Wall pressure distribution at dierent azimuth angels for PR= Wall pressure distribution at dierent azimuth angles for PR= Wall pressure distribution at dierent azimuth angles for PR= Isosurface for wall xial shear stress equal to or less that zero for DBN at PR=400_xy view Isosurface for wall xial shear stress equal to or less that zero for DBN at PR=600, x-y view Isosurface for wall axial shear stress equal to or less that zero for BFSN at PR=600, x-y view Isosurface for wall axial shear stress equal to or less that zero for BFSN at PR=800, x-y view Mach contours at x-y plane of symmetry for PR= Mach contours at x-y plane of symmetry for PR= Mach contours at x-y plane of symmetry for PR=800 zoomed at 1st step Mach contours at x-y plane of symmetry for PR= Mach contours at x-y plane of symmetry for PR= Axial-velocity contours for PR= Axial-velocity contours for PR= Axial-velocity contours at eective exit area for DBN at PR= BFSN with 2, 4, and 6 backward facing steps BFSN with 20 and 40 backward facing steps BFSN adjusted step cross-sectional area xiii

14 5.4 Mach contours for 2-BFSN at PR= Mach contours for 4-BFSN at PR= Mach contours for 6-BFSN at PR= Mach contours for 20-BFSN at PR= Mach contours for 40-BFSN at PR= Thrust Curves for the BFSN with two steps and the DBN with respect to PR Mach contours of 2-BFSN at dierent PRs Mach contours of 2-BFSN at dierent PRs Thrust curve for 6-BFSN with equal steps length Vs. 6-BFSN with adjusted length Static temperature contours in the 2-BFSN at dierent pressure ratios Static temperature contours in the 6-BFSN at dierent PRs Dierent operating modes of 2-BFSN computational grid of the 2-BFSN in mode Mach contour for 2-BFSN transition from mode-1 to mode Mach contour for 2-BFSN transition from mode-2 to mode Thrust curve for 2-BFSN xed steps Vs. 2-BFSN extendible steps Mach contour for 7-BFSN transition from mode-1 to mode Thrust comparison between 6-BFSN and 2-modes_7-BFSN Conventional bell shape nozzle contour Designed parabolic conventional nozzle AR= BFSN with AR= Computational domain for conventional bell nozzle and BFSN Mach contours for classical bell nozzle at dierent altitudes Mach contours for BFSN at dierent altitudes Thrust coecient for classical bell nozzle and BFSN as a function of altitude Thrust coecient Vs. nozzle area ratio Nozzles mounted in rocket base Flight performance comparison between conventional nozzle and BFSN xiv

15 List of Tables 2.1 Grid dependence study Grid dependence study Grid dependency study Grid dependency study Flow parameters comparison between 3-D and 2-D simulations Side load values for DBN and BFSN Thrust values for BFSNs and DBN at PR= Basic rocket parameters xv

16 Chapter 1 Introduction The main system which is used for space propulsion is the rocket a device that stores its own propellant mass and induce thrust. This thrust is produced by the rocket engine, by accelerating the combustion gases to the desired velocity and direction, and the nozzle is that part of the rocket engine extending beyond the combustion chamber, see Figure 1. Typically, the combustion chamber is a constant diameter ductwhere the propellants are injected, mixed and burned. Its length is sucient to allow a complete combustion of the propellants before the nozzle accelerates the gas products. The nozzle is said to begin at the point where the chamber diameter begins to decrease. The ow area is rst reduced giving a subsonic (Mach number < 1) acceleration of the gas. The area decreases until the minimum or throat area is reached. Here the gas velocity corresponds to a Mach number of one. Then the nozzle accelerates the ow supersonically (Mach number > 1) by providing a path of increasing ow area. The nozzle exit velocity that can be achieved is governed by the nozzle area ratio which is commonly called the expansion ratio, ε. 1

17 Figure 1.1: Rocket nozzle 1.1 Flow separation in rocket nozzles In today's launch vehicles, the main engine usually operates from take o at sea level up to high altitudes with variable ambient pressures. To get an optimum performance over the whole trajectory, the nozzle is usually designed for an intermediate operating PR, at which the exhaust ow is adapted to the ambient pressure [1]. That leads to over-expansion conditions when the nozzle operates at low altitudes. When the supersonic ow exposed to an adverse pressure gradient, it adapted to the higher pressure by means of a shock wave system. Basically, the separation occurs when the turbulent boundary layer cannot withstand the adverse pressure gradient imposed upon it. Thus, the ow separation in any supersonic ow is a process involving complex shock wave boundary layer interactions [2]. This condition occurs when a nozzle is operating under strongly over-expanded conditions. As soon as the exit nozzle wall pressure is slightly lower than the ambient pressure, an oblique shock system is formed from the trailing edge of the nozzle wall due to induced adverse pressure gradient [2]. When the 2

18 nozzle wall pressure is further reduced, the viscous layer cannot sustain the adverse pressure gradient imposed upon it by the inviscid ow, and the boundary layer separates from the wall. Summereld criterion [3] predicts that the ow in a nozzle separates when the ratio of the wall pressure to the ambient pressure is less than or equal to 0.4. Many experimental studies carried out on sub-scale nozzle [4, 5, 6] or full scale nozzle [4] and dierent numerical studies [7, 8, 9, 10, 11] demonstrated the existence of two dierent types of ow separation. The rst type is called Free Shock Separation (FSS) where the ow is separated from the nozzle wall and never reattaches as shown in Figure (1.2). The second type is called Restricted Shock Separation (RSS) which is characterized by a closed recirculation bubble downstream of the separation point with reattachment on the wall as shown in Figure (1.3). The RSS mainly appears in the parabolic contour nozzle [2] because of presence of internal shock due to due to non ideal nozzle wall curvature just downstream of the throat [12]. If the internal shock is strong, its interaction with the Mach disk can cause the ow to deect outward and reattach the nozzle wall which results in a recirculation bubble [12]. Figure 1.2: FFS in over-expanded nozzle 3

19 Figure 1.3: RSS on over-expanded nozzle 1.2 Side loads Many experiments have been carried out to study the side loads generated in rocket nozzles for full scale and sub-scale nozzles, see reference [13, 14, 15, 16, 17, 18, 19, 12]. Flow separation in rocket nozzles is considered undesirable because of the asymmetry in the ow separation locations which lead to asymmetrical pressure distribution over the nozzle wall that can cause a high side loads, which may damage the nozzle structure [20]. The structural damage caused by the transient nozzle side loads during testing at sea level has been found for almost all rocket engines during their initial development [21]. Many examples for the nozzle failure caused by side loads are mentioned in references [22, 23, 14, 24]. As a result, whether during sea-level testing or in ight, transient nozzle side loads have the potential of causing real systems failure [21]. In 2004, marshal Space Flight Center (MSFS) began an experimental study to quantify the relative magnitude of the side loads on two dierent types of nozzle contours, ideal contour and parabolic contour, [12]. They found that, the maximum side loads measured in the truncated ideal contour nozzle is 45% of that measured in the parabolic contour nozzle. They gured out the reason of that is because of the ow transition between FSS and RSS in the parabolic nozzle [12]. Figure (1.4) shows the the nozzles contours and the as-designed wall pressure distribution, 4

20 while Figure (1.5) shows the side loads measured in both nozzles. Further support to the analysis of the ow separation behavior has been provided by means of numerical simulations, see references [25, 26, 9, 27, 28, 21, 29]. Figure 1.4: Nozzles contours and as-designed wall pressure Figure 1.5: Relative side loads of TIC and PAR nozzles Many examples for the nozzle failure caused by side loads are mentioned in references [22, 23, 14, 24, 12]. Y. Watanabe et al. in 2002 [23] presented a study on the LE-7A engine (the rst stage main engine of the Japanese H-IIA launch vehicle) separation problem which caused a large side loads and a failure in the cooling tubes. The LE-7 A nozzle consists of two parts, the upper part is assembled from cooling tubes and the lower part is made from forging material that needs to be cooled by injecting a lm cooling, a contour discontinuity exists between the upper and the lower parts of the nozzle. They found that the there are two kinds of side loads that have dierent origins. The rst side load is due to the transition of the ow separation from FSS to RSS during start up and shut down the engine. The second side 5

21 load is due to the sudden movement/jump of the ow separation point. Figure (1.6) shows the side loads magnitude level in LE-7 and the modied LE-7A nozzles. Figure 1.6: Typical side load magnitude for LE-7 and LE-7A nozzles during start up operation During the start up, the ow separation is located at the contour discontinuity until the PR is increased high enough. The stagnation separation point jumps suddenly to the nozzle exit lib. The separation point motion is asymmetric around the nozzle circumference which caused a very large side loads that is responsible of the structural failure of the nozzle[23]. Figures (1.7) to (1.8) show the asymmetrical jump of the separation point from the step to the nozzle end and the side loads generated. Figure 1.7: Jump of the separation point at LE-7A 6

22 Figure 1.8: Side loads generated during separation point jump The Space Shuttle Main Engine (SSME) also suered from nozzle side loads in terms of low cycle fatigue crack which caused a damages in the nozzle [14]. SSME has performed reliably and safely for more than 25 space shuttle mission. However, until 1987, four failures have occurred during launches or launch attempts[22]. In 2012, Eric L. Blades et al. [30] carried out a numerical study to investigate the side loads in the SSME. Figure (1.9) demonstrates both modes in which the ow can separate in the SSME nozzle. The upper half of the gure illustrates a free shock separation (FSS) structure, and the lower half illustrates a restricted shock separation (RSS) structure. In the FSS mode, the ow separates from the wall and continues as a free stream. Since the SSME is a thrust-optimized/parabolic nozzle, an internal shock forms due to the curvature discontinuity where the wall contour transitions from a circular arc contour to a parabolic contour. As the chamber pressure increases, the internal shock interacts with the Mach disk (the normal shock identied in Figure 1), causing the annular supersonic plume to deect outward and reattach to the nozzle wall. This reattachment creates a local recirculation region that is restricted in location between the separation location and the reattachment location. The transition from FSS to RSS creates a signicant side load. As the chamber pressure increases further, the RSS reattachment location moves further downstream, closer to the end of the nozzle. As it approaches the nozzle exit plane, the plume oscillates between FSS and RSS, creating additional side loads [30]. 7

23 Figure 1.9: Mach number contours from SSME simulation comparing free shock separation (upper) and restricted shock separation (lower) High side loads also resulted in the failure of the gimbal block retaining bolts for the J-2 engine [14]. The J-2X engine, which is currently under development as an upper-stage engine for NASA's next heavy-lift launch vehicle, is a derivative of the J-2 engine and will likely experience side loads similar to its predecessors, the J-2 and J-2S [30]. Thus, accurate prediction of nozzle side loads is of great interest for current and future nozzle designs. Recent rocket nozzle failure due to the side loads is occurred with the Ariane 5 ECA launcher [24]. An intensive engineering and testing program are carried out by Volvo Aero Corporation to reinforce the Vulcain 2 Nozzle extension. It was formed that the ight loads had been much higher than expected which led to a failure of the nozzle [24]. One possible solution to avoid side loads generation is to adapt the nozzle contour during ight to changes of ambient pressure. Several methods to adapt the nozzle during ight are exist either mechanically or non-mechanically. For the mechanically methods, the weight and mechanical complexities of such devices are a big issue [1]. For the non-mechanically methods, many techniques have been used to control the ow separation and reduce the side loads generated due to asymmetrical ow separation. 1.3 Flow separation control A nozzle capable of varying eective expansion area ratio can optimize delivered impulse over the entire ight trajectory, resulting in enhanced performance gain. The ideal altitude com- 8

24 pensating nozzle would continuously vary nozzle exit area ratio such that the nozzle is always pressure matched. Theoretically, if the nozzle is available to change its exit area continuously with altitude, the over-expanded operating condition can be avoided. That means the ow will not separates from the nozzle wall and no side loads would be generated. In real life, the ideal altitude compensating nozzle doe not exist. Instead, a one- or multi-step altitude adapting nozzles are used to adapt the nozzle exit area by forcing the ow to separate at certain locations related to the operating altitude. Many studies [2, 31, 32, 33, 34, 35, 36, 37, 38, 39] have been carried out with a main objective of controlling the ow separation and/or the unsteady motion of the separation front to reduce the side loads aecting the nozzle structure. The main ideas used to control the ow separations are presented as follows: Trip rings The main concept of using a trip rings inside a bell nozzle, Figure (1.10), is to disturb the turbulent boundary layer and force the ow to separate at certain locations (ring location) in symmetrically way to decrease the side loads aecting the nozzle wall. At high altitudes, the ow reattaches to the nozzle wall behind the trip ring, and a full owing nozzle is achieved. Using several rings mounted after each others, several altitude adaptation can be achieved. However, this will results in performance loss at high altitudes [32]. The main problem with this concept is the performance losses and the ring resistance in high temperature boundary layers and also the uncertainty in transition between low altitude mode to high altitude mode [33, 34]. Figure 1.10: Trip rings nozzle 9

25 1.3.2 Vented nozzle In the vented nozzle concept [35], a section of the nozzle wall has slots or holes opened to the atmospheric surrounding, Figure (1.11). At low altitudes, these slots or holes allow adequate passive inow to sustain a symmetrical and stable ow separation. By closing the holes at high altitude, the full owing nozzle is achieved. The main disadvantages of this nozzle concept is that the number and position of the holes limit the altitude range of the nozzle operation because the concept is built on the condition that the pressure within the nozzle must be lower than the ambient pressure. The second disadvantage is that the mechanism required to close the slots or holes at high altitude will increase the rocket engine mass and reduce the reliability. Figure 1.11: Vented nozzle Active uid injection The concept is to force the ow to separate by injecting a second ow into the nozzle, normal or at angle from the nozzle wall, at certain locations, Figure (1.12). Experience on this concept [36]shows that a large amount of the secondary ow injection is required to induce signicant ow separation. Figure 1.12: Nozzle with ow injection 10

26 1.3.4 Nozzles with temporary insert This concept is based on controlling the ow separation using a temporary inserts inside the nozzle and remove them at high altitude, Figure (1.13). These inserts can be either consumable or ejectable. Previous studied on this nozzle concept [37, 38]showed that the nozzle operation at low altitudes resulting in a slightly performance loss compared to the equivalent bell shape nozzle. It should be stressed that the ejectable concept is highly depends on the ejection mechanism which have to provide a sudden and symmetrical detachment of the insert. Another issue to concern about is that during the ejection process, the insert acts as an obstacle in a supersonic ow, which will induce shocks that will interact with the nozzle wall and increase the pressure loads [2]. The nonsymmetrical ejection will lead to high side loads. furthermore, the danger of collision with the nozzle wall arises because the inserts might experience a transversal momentum toward the nozzle wall [2]. Figure 1.13: Nozzle with ejectable insert Another method to remove the insert is to use an ablative or combustible insert [38, 39], Figure (1.14). During the ascent of the nozzle through the atmosphere, the size of the insert is continuously decreased until its complete consumption. This will results in a full owing bell nozzle at high altitudes. The main uncertainties of this concept are the stability and the surface regression rate of the consumable insert. Furthermore, a symmetrical and homogenous consumption must be guaranteed to avoid the side loads generation [2]. 11

27 Figure 1.14: Nozzle with consumable insert A new nozzle concept Another method to overcome the side loads that found in the literature is presented by Luca et al. [31] in 2008 by introducing a new nozzle concept that eliminates the physical cause of the ow separation. The new concept is based on generating a second annular ow at the nozzle lip to act as an aerodynamic barrier to prevent the ambient air from going inside the nozzle Figure (1.15). That will decrease the local pressure in the recirculation region and will remove the adverse pressure gradient. Figure 1.15: New nozzle prole Luca at al. carried out a series of numerical and experimental tests to conrm his new nozzle concept in preventing the ow separation. 2-D and 3-D with 18 degree annular sector numerical solutions are obtained at dierent PRs. The numerical results showed that the ow separation did not occured when the secondary ow is injected. Figures (1.17) and (1.16) show the numerical results of the Mach contours with and without the secondary ow respectively. Experimental results for pressure distribution over the nozzle wall for PR 37 with and without the secondary ow showed that the ow separation is prevented with the presence of the secondary ow and the pressure keep decreasing as going towards the nozzle exit as shown in Figure (1.19) and Figure (1.18). 12

28 Figure 1.16: Computed pressure contours for PR=37 without secondary ow Figure 1.17: Computed pressure contours for PR=37 with secondary ow Figure 1.18: Wall Pressure prole for PR=37 without secondary ow 13

29 Figure 1.19: Wall Pressure prole for PR=37 with secondary ow In my point of view, although this new concept prevented the ow separation which lead to decrease the side loads, the pressure distribution over the inner and outer walls of the spike (secondary jet nozzle) showed a non symmetrical values as appeared in the pressure distribution curve in Figure (1.19). This can lead to a side loads over the spike nozzle Dual-bell nozzle One of the most promising non-mechanical altitude compensating nozzles is the DBN [40, 41, 42], Figure (1.20). It was rst studied at the Jet Propulsion Laboratory by Foster and Cowles in 1949 [43]. This nozzle concept is patented in late of 1960s by Rocketdyne. The main advantage of the DBN is the one step altitude adaptation achieved only with presence of a wall inection and therefore the absence of any movable parts which leads to a high reliability [44]. 14

30 Figure 1.20: Sketch of the dual-bell nozzle Dual-bell nozzle is a combination of two bell nozzles with dierent geometric area ratios. Compared with single-bell nozzles, it has advantages of providing a stable separated ow at low altitudes and high specic impulses at high altitudes [45]. Figure (1.21) shows schematics of ow patterns in a dual-bell nozzle at low- and high-altitude operation modes. At the lowaltitude operation mode, the wall inection yields stable and symmetrical ow separation. This results in a smaller eective area ratio and in small side loads. At the high-altitude operation mode, high specic impulse is obtained with the larger area ratio of the nozzle throat and the nozzle exit. As shown in Figure (1.22), however, there are three instances of performance loss during the low-altitude operation mode, the operation mode transition, and the high-altitude operation mode. During low altitude operation, the pressure in the separated ow region of the extension part becomes lower than the ambient pressure, and the drag force called aspiration drag acts on the wall of the extension part [45]. At the transition between the low- and the highaltitude operation modes, the specic impulse decreases because the transition occurs at a lower altitude than the optimum [45, 46]. The dual-bell contour is designed just as a combination of two bell nozzles; therefore, the combined contour is not optimized, and the specic impulse becomes smaller at the high-altitude operation mode. Although the mentioned disadvantages should be improved, the dual-bell nozzle has a simpler nozzle structure without any moving parts and is more lightweight in comparison with other altitude compensation concepts, such as an extendible nozzle, an expansion deection nozzle, or an aerospike nozzle. 15

31 Figure 1.21: Operatioal modes of the dual-bell nozzle Figure 1.22: Specic impulse of the DBN in comparison with base and extension nozzles In recent years, several experimental and computational studies on dual-bell nozzles have provided insight [47, 48, 49, 50, 51, 52, 53, 54] into the ow phenomenon under dierent operating conditions, varying from sea level to high altitude. Of prime interest are transient studies, especially those that aim to address the parameters that inuence the 1) transition nozzle pressure ratio (PR) and transition duration, 2) transition stability, and 3) the associated side-load activity. At sea level, the contour inection in the dual-bell nozzle wall forces the ow to separate controlled and symmetrically. The base nozzle ows full and the extension is separated, the dual bell is operating in sea level mode. Because of a smaller eective area ratio the sea level, 16

32 the specic impulse increases compared with a conventional nozzle. At the designed altitude the ow attaches abruptly to the wall of the extension down to the exit plane. This transition to high-altitude mode results in a short time specic impulse loss but later on in a higher vacuum performance. The transition from one operating mode to the other is particularly of interest as the ow potentially separates asymmetrically within the extension as shown in Figure (1.23), resulting in a strong side load peak[46]. Hagemann et al. [41] presented an experimental work including cold as well as hot ow studies with respect to side load generation. He found that depending on the type of nozzle contour used in the dual-bell nozzle extension, a sudden transition from sea level to altitude mode can be achieved. One remarkable fact is that the side load peak during re-transition (while the nozzle is shut down) was shown to be signicantly higher than during transition [41] as shown in Figure (1.25). An opposite result is given in studies performed by Hieu et al. [55], where the transition to high altitude mode generates higher side loads. The experimental cold ow results were recalculated at DLR, German Aerospace Center by Karl and Hannemann [56] using the in-house code TAU. The transient simulations showed that the calculated side load peak during transition mainly depended on the nozzle pressure ratio gradient. The side load generation was studied in a numerical parametric study by Martelli et al. [49] as a function of the wall pressure gradient, the base length, the Reynolds number, and the contour inection angle.the eect of a cooling lm applied on full scale hot ow dual bell nozzles is presented in [57]. The dual bell nozzle principle was found to improve the lm cooling eciency compared with conventional nozzles. The side loads generated during the transition increase with increasing lm mass ow. Chloe Genin at al. [46] introduced the phenomenology of side load generation in dual bell nozzles and gave a detailed experimental parametric study. The cold ow experimental study has shown the dierent phases of operation of dual bell nozzles and the side load generation corresponding to each phase. In its operating modes, a dual bell nozzle produces smaller side loads than a conventional TIC nozzle. However, the transition goes ahead with a short time side load peak that must be taken into account to avoid harm to the engine structure, Figure (1.24). 17

33 Figure 1.23: Schlieren observation of shock system within a dual-bell nozzle ow transition Figure 1.24: Side load generation during a typical test run Figure 1.25: Normalized side loads measured during experimental work 18

34 1.4 Dissertation Overview The goal of this dissertation is development and assessment a new altitude adjustable area nozzle using backward facing steps to force the ow to separate at certain symmetrical locations, with specic aims of: Stationary adaptive nozzle geometry Dynamically adaptive nozzle geometry Hybrid adaptive nozzle geometry These goals are achieved by controlling the ow separation passively using a backward facing steps nozzle geometry. The nozzle contour is replaced by a number of backward facing steps to force the ow to separate at certain locations (steps edges). A symmetrical ow separation can be guaranteed and side loads can be avoided which will increase the nozzle life time and safety margin. The assessment of the BFSN performance is done numerically using uent code. The numerical procedure is validated rst by simulating a planar dual-bell nozzle and the results are compared with experimental data. Dual-bell nozzle is chosen as a reference nozzle to assess the performance of the new developed BFSN. Backward facing steps approach is applied on both planar and axisymmetric nozzles geometries with cold ow in the planar nozzle and hot ow in the axisymmetric nozzle. 3-D solutions for both BFSN and the DBN at dierent PRs show that the ow is axisymmetric in the BFSN at all PRs with symmetrical ow separation locations. While the ow in the DBN is naturally asymmetric with dierent separation locations over the nozzle circumference. Further conrmation for the ow symertical behavior in the BFSN are carried out by the 2-D axisymmetrical simulation of the BFSN at derent PRs and comparing the results of the ow parameters with the results of the 3-D solutions. The comparison showed that the maximum dierence in the ow parameters at the nozzle exit section is less than 1%. The conrmation of the axisymmetrical nature of the ow in the BFSN is a very important nding which has the following implications: 1) two dimensional solution can be used to analyze the BFSN, nozzle thrust, ow exit velocity, etc, 2) unsteady ow solution are now possible because of the major reduction of the CPU time for 2D solutions compared to 3D solutions, and 3) the axi-symmetric solution is suitable for design practices. 19

35 Parametric studies on the BFSN are carried out in two ways. First, changing the number of backward facing steps with keeping their length to be equal. Second, choosing a certain number of backward facing steps and changing their length based on the ideal exit areas (area corresponding to fully expands) suitable for dierent altitudes. For the rst parameter, the BFSN is simulated with 2, 4, 6, 20, 40 backward facing steps. A high PR is chosen as a design point and all BFSNs thrust values are calculated and compared to each other and to the DBN. The BFSNs with two and six backward facing steps are chosen (as a lower and medium number of backward facing steps) and their performance in terms of thrust are obtained for a wide range of PR and compared to the DBN. For the second parameter, the BFSN with six backward facing steps is chosen and the steps are redesigned so that each step local cross-sectional area present an ideal area suitable for specic PR (altitude). The BFSN with ideal backward facing steps cross-sectional area is simulated for the all PRs and compared to the BFSN with equal six backward facing steps. Expandable capability of the BFSN is studied in two dierent approaches. First, the BFSN can be contracted at sea level and the steps starts to expand one after other as the rocket ascent through the atmosphere. This approach is studied using the BFSN with two backward facing steps. At sea level, the two steps are contracted and the BFSN operates with its base section only limiting the nozzle expansion area to the base nozzle exit area (mode-1). As the PR increases, the rst step expands and BFSN expansion area increased to the rst step crosssectional area (mode-2). At high altitude, the second step expands and the BFSN operates with its nal expansion area which is the second step cross-sectional area (mode-3). Second, the BFSN can operates with certain number of xed and contracted backward facing steps to sustain its length to be equal to the DBN (as a comparable reference nozzle) until it reach a designed high altitude. For a higher altitudes, this nozzle can be expanded to a higher expansion area ratio and operates eciently using a contracted backward facing steps. 1.5 Outline This thesis consists of eight chapters. The rat chapter is the introduction. The second chapter is numerical procedure validation. The third chapter is the planar backward facing steps nozzle. The fourth chapter is 3-D numerical simulations for the axisymmetric backward facing steps 20

36 nozzle and the dual-bell nozzle. The fth chapter is parametric studied for the BFSN. The sixth chapter is the expandable BFSN. The seventh chapter is a full sclae nozzle application. Finally, the eighth chapter is the conclusions. 21

37 Chapter 2 Validation of the Numerical Procedure 2.1 Introduction This chapter presents three-dimensional unsteady solutions and two-dimensional time dependent solutions of turbulent ow in a planar DBN as shown in Figure (2.1). The two- and the three-dimensional numerical results of the DBN are validated by comparing with an available numerical results and experimental data respectively in ref [58]. The three-dimensional unsteady numerical results showed a high side load value for the dual-bell nozzle. The twodimensional time dependent results showed a high uctuated side load values in the dual-bell nozzle during the transition from low to high altitude modes. (a) DBN Figure 2.1: 3-D schematic diagrams of the nozzles physical models 22

38 2.2 Numerical method The commercial CFD software, Ansys Fluent, is used to simulate the turbulent ow of the sub-scale BFSN and the DBN shown in Figures (4.1-a) and (4.1-b). The SST k ω is used to predict the turbulence quantities of the ow eld behavior. It was chosen due to its accuracy in computing the ow separation from smooth surface and predicting the details of the wall layer characteristics [59]. Second order accuracy upwind scheme is used which accurately predicts the interaction between the oblique shock and the turbulent boundary layer. Ideal air is modeled as the driving gas at constant inlet pressure and temperature. Varied ambient pressure is specied at the far downstream boundary condition. The three-dimensional computations are done using parallel processing on eighteen node cluster at OSC (Ohio Super Computer). Each node is a 2.5 GHz processor Unsteady Reynolds Averaged Navier-Stokes equations (URANS) In turbulent ows, the randomly changing ow variables of the conventional Reynolds decomposition are replaced by two parts: 1) a steady quantity time average, 2) its uctuation quantity. More details about turbulent decomposition, dierent forms for RANS and boundary layer equations are available in references [59, 60]. The system of turbulent ow governing equations for a single-component uid, written to describe the mean ow properties, is cast in integral Cartesian form for an arbitrary control volume V with dierent surface area da as follows: ˆ W.dV + t V ˆ [F G].dA = V H.dV (2.1) where the vectors W,F,and G are dened as ρ ρv 0 ρu ρvu + p i τ xi W = { ρv }, F = { ρvv + p j }, G = { τ yi } (2.2) ρw ρvw + p k τ zi ρe ρve + pv τ ij v j + q and the vector H contains source terms such as body forces and energy sources. 23

39 2.2.2 SST k ω turbulent model The shear-stress transport (SST) k ω model was developed by Menter [61] to eectively blend the robust and accurate formulation of k ω model in the near-wall region with the free-stream independence of the k ε model in the far eld. To achieve this, the k ε model is converted into k ω formulation. More details of the standard k ωturbulent model can be found in [62]. The SST k ω model is similar to the standard k ω model, but includes the following renements: The standard k ω model and the transformed k ε model are both multiplied by a blending function and both models are added together. The blending function is designed to be one in the near-wall region, which activates the standard k ω model, and zero away from the surface, which activates the transformed k ε model. The SST model incorporates a damped cross-diusion derivative term in the ω equation. The denition of the turbulent viscosity is modied to account for the transport of the turbulent shear stress. The modeling constants are dierent. These features make the SST k ω model more accurate and reliable for a wider class of ows (for example, adverse pressure gradient ows, airfoils, transonic shock waves) than the standard k ω model Transport equations for the SST k ω model The SST k ω model has a similar form to to the standard k ω model: and t (ρk) + (ρku i ) = x i k (Γ k ) + x j x j G k Y k + S k (2.3) t (ρω) + x j (ρωu j ) = ω (Γ ω ) + G ω Y ω + D ω + S ω (2.4) x j x j In these equations, Gk represents the generation of turbulence kinetic energy due to mean velocity gradients, calculated from G k and dened in as: 24