AFOSR - Unit Combustor. Fundamental Processes that Drive Combustion Instabilities in Liquid Rocket Engines Annual Report

Transcription

1 AFOSR - Unit Combustor Fundamental Processes that Drive Combustion Instabilities in Liquid Rocket Engines Annual Report Matt Quinlan Yong Jea Kim Yedidia Neumeier Ben T. Zinn Guggenheim School of Aerospace Engineering Georgia Institute of Technology April 28th, 211

2 1 Introduction In spite of the research that has been performed over the last half century the reliable design and fundamental knowledge of liquid rocket engines (LRE) is still lacking[1]. High frequency, acoustically coupled combustion instabilities have plagued many LRE design programs leading to costly redesigns or worse, catastrophic failures[2, 3]. In a broad sense, the driving of these acoustically coupled instabilities occurs when energy from the combustion process is added to the acoustic wave in-phase and the net energy addition is greater than damping provided by, for example, viscous dissipation and convection through the nozzle. The specific mechanism for the driving of instabilities can be quite complex and involve phenomena such as acoustics, flow instabilities, interaction of coherent structures, pressure and velocity coupling of combustion, and injection system coupling. Due to the cost involved in performing full-scale hot fire testing of LRE, the in situ study of combustion stability is prohibitive. Ideally studies could be done on laboratory scale combustors, but many of the mechanisms responsible for instabilities are frequency dependent and hence depend on the physical dimensions of the engine. If a sub-scale combustor was able to exhibit many similar processes at the full-scale frequencies found in real LRE, then more economical research and development could be made. One approach to overcome the difficulty in acoustic scaling is to adjust the acoustic boundary of the sub-scale combustor. By controlling the acoustic impedance of these boundaries the combustor can, at least acoustically, appear similar to the full-scale geometry. Figure 1 shows two diagram of a typical LRE injector plate from the nozzle end, first, a fullscale LRE and second, a small sector of the same engine with two boundaries actively controlled. While this would be ideal for simulating real LRE, due to the complexity of the acoustics at the boundaries an alternative arrangement was selected. Figure 2 shows a rectangular LRE injector plate, the corresponding sector combustor, and a unit combustor with two acoustically driven walls based on the sector. At low enough frequencies the acoustics at the control boundaries are one dimensional plane waves, both analytically tractable and reproducible with the appropriate acoustic drivers. Acoustically controlled boundaries (a) Full-scale cylindrical LRE (b) Sector cylindrical LRE Figure 1: Cylindrical LRE 1

3 (a) Full-scale rectangular LRE Acoustically controlled boundaries (b) Sector rectangular LRE Combustor Acoustic drivers (c) Sector combustor Figure 2: Rectangular LRE The current work is to elucidate the driving mechanisms found in unstable LRE. For example how linear or non-linear pressure and velocity coupled combustion response is effected by the intrinsic flow instabilities in the shear layers of the injectors. Specifically the goals of the project are to develop a sub-scale tool for simulating full-scale acoustically coupled transverse instabilities found in LRE and study the associated driving mechanisms. 2 Objectives To develop a sub-scale combustor that is capable of performing testing under appropriate acoustic conditions four key tasks were identified: Identification and characterization of acoustic driving system Development of experimental rig Development of active control system Use developed system to study design parameters and operational conditions Each of these tasks will be addressed in the following sections. 2.1 Project goals Identification of acoustic driving system The acoustic boundaries of the combustor may be controlled by passive or active means. Passive control could be made through the addition of an acoustic element to change the impedance of 2

4 the system at the interface. This approach requires the addition of a different system onto the combustor for each impedance of interest. Active control may be made through the addition of an active element onto the boundary. This active element may take many forms, but the approach selected here is the use of an acoustic compression driver. After a search of available drivers the JBL Pro Audio 249H was selected, see Fig. 3. This driver has a relatively large throat diameter, 76.2mm, high power rating, 25W, good frequency response over the frequency range of interest, 15 2Hz. Figure 3: Compression driver, JBP 249H In addition to the combustor rig, an impedance tube is being developed. One of the primary reasons for this work is to allow for the proper identification of the driver current to acoustic velocity transfer function required for the controller; this will be expanded upon in subsequent sections Development of unit combustor Ideally the combustor would be a section of an actual LRE, but this would be cost prohibitive, complex, and difficult to study the fundamental phenomena within the combustor. It would be desirable to have a simple, flexible combustor that has optical access for modern laser diagnostics, such as, particle image velocimetry (PIV) and planar laser induced florescence (PLIF), the former allowing for the measurement of the velocity field and the latter allowing for the quantification of chemical species such as hydroxyl or formaldehyde. Design requirements: Active impedance control Flexible injection (liquid vs. gaseous fuel, swirl vs. shear,...) Optically accessible (PIV, PLIF,...) No cryogenic liquids Design preferences: Near atmospheric pressure operation (at least initially) 3

5 Transverse mean flow (it has been suggested that transverse mean flow may be related to the formation of spinning modes[4, 5]) Acoustic drivers located in close proximity to combustor boundary The throat diameter of the JBL 249H compression drivers is 76.2mm (3inch) so the combustor width was chosen to be on the same order, approximately 1mm. The lengths along the driver axis and injector axis, depth and height, was more flexible. It is undesirable for the fundamental acoustic frequencies in the three directions to be degenerate so differing lengths were selected, with the largest dimension being along the injector/nozzle direction allowing for longer combustion zone if desired. Acoustic drivers have been mounted in close proximity to the combustor interface to ensure very small time delays for the control system. This design consideration has driven the need to actively cool the driver. The resulting packaging may be found in Fig. 4a. Injectors have been designed to be modular, allowing for the replacement of some or all parts to achieve alternate configurations. The injector design will be addresses subsequently. A flat nozzle with relatively large open area has been selected. This allows for an outlet boundary condition that can be approximated, has simple geometry, and allows for the mean pressure in the combustor to remain nearly atmospheric. With the need for the setup to be optically accessible for laser diagnostics, a small quart window allowing for a laser sheet to be passed vertically into the combustor was incorporated in the nozzle plate. Two additional large quartz windows have been situated on the front and back walls. Figure 4b shows a cross section view of the unit combustor. Here it is clear the center injector port, of a three by three layout, has an injector installed while the remaining injector ports have been plugged. Quartz windows Nozzle Quartz windows Nozzle Drivers Water cooling Driver port Drivers (a) Overview Modular injector (b) Cross section Figure 4: Unit combustor design The modular/cartridge injector design allows for individual parts or entire injectors to be changed. This can be for reasons as simple as changing the oxidizer orifice to change the mass flow for a given supply pressure, to changing the style of injector from swirl/swirl to shear co-axial. Figure 5a shows one embodiment of the injector, in this case a counter swirling co-axial injector. The fuel, methane, enters the fuel annulus through four tangentially drilled holes. The oxidizer, air, is metered at a critical orifice, then flowing to the outer portion of the oxidizer swirler, finally 4

6 into the oxidizer post via three tangential flow passages in the swirler. For this injector the fuel and oxidizer is injected counterclockwise and clockwise respectively when viewed from above. For a slightly different visualization of the flow passage see Fig. 5b. Fuel annulus Oxidizer post Fuel inlet Fuel supply path Oxidizer swirler Oxidizer supply path Oxidizer orifice (a) Cross section (b) Flow paths Figure 5: Modular injector design Development of active control system Currently a dspace DS114 control system is being studied for use. This control system utilizes a 25MHz Power PC processor and runs a compiled version of Simulink/Matlab and C code. A simple Simulink and C code simulation was created to read in a signal on one of the eight analog inputs, modify the signal, and output the new signal on one of the analog output channels. It was found for very simple signal modification, e.g. gains and offsets, this process can be performed in real-time. The dspace control system interfaces with Simulink to provide easy transition from simulation to real-time control. The physical and control systems of interest may be modeled directly in Simulink utilizing prebuilt blocks, e.g. time delays, integrators, etc., or by custom written blocks of code. The blocks used in the latter approach are called s-functions and were employed for the current study. The simulation can be run and tested completely within the Matlab/Simulink environment. Transition from the simulation to the real-time control is simply a matter of replacing the simulation input and output blocks by the appropriate dspace blocks, building the code, compiling the code, and downloading the executable to the control board. To test the DS114 system s ability to perform input, output, and simple signal modifications, a Simulink model was built. This model first reads in an analog signal, then scales and offsets the signal utilizing a custom written C code s-function, clips the top and bottom of the signal using a prebuilt saturation block, and lastly outputs the signal. Figure 7 shows the Simulink model with the dspace input and output blocks, the ADC and DAC respectively. Once the code has been built, compiled, and downloaded to the control board, the user may interface with the control system via dspace s software package Control Desk 4.. A screen shot of this software while the controller is running the previously described model is shown in Fig. 8. The user interface here has been configured to display the input signal, the output of 5

7 Input/output breakout box RTI Data Control board Figure 6: dspace hardware ADC 1 u DS114ADC_C5 Gain1-2 Gain InOutTest Offset S-Function Builder y Saturation.1 Gain2 DAC DS114DAC_C1 Gain.1 Offset Figure 7: Simulink model the scaling/offset s-function, and the output of the saturation block, as well as the parameterized input values, such as gain, so they may be adjusted during the run. A chirp was generated by a signal generator and used as the input to the controller. For the current testing a simulation time step of 15µs was selected. It was found the time required for the DS114 to perform the required operations was approximately 6µs and the output signal lagged the input by approximately 3 to 18µs. This lag is shown in Fig. 9a. Utilizing the gain, offset, and saturation parameters the signal can be modified as desired, for example see Fig. 9b. The required computation time and step size were found to be adequate for this simple case, but further tests are needed to determine if the 25MHz processor on the DS114 board is powerful enough for future requirements. For example, combustor experiments may require acquisition of data from four pressure sensors, performing two sets of calculations based on these signals, and outputting two driver signals. Depending on the the final approach, the calculations could requirer more computations than allowed in a reasonable time step Study of driving mechanisms This work has not yet begun, see the Future work section for more details. 6

8 Figure 8: Control Desk 4. 3 Project status 3.1 Impedance tube To facilitate the identification of the acoustic driver transfer function and development of the active control system, an impedance tube was developed. To ensure the proper measurement and data reduction techniques a rigid end termination to the tube has been employed. This selection has been made for initial investigation due to the strong boundary conditions that it provides, the end reflection coefficient being equal to one (R = 1). The problem has been approached two ways, first, via a simple simulation based on traveling waves and time delays that was programed in Matlab/Simulink. Second, experimental hardware utilizing a 3inch stainless steel tube, JBL compression driver, solid end plate, and two pressure sensors. Additionally, the capability of performing hot wire anemometry measurements has been built into the tube as a secondary confirmation of impedance measurement and control techniques. Figure 1 shows a simple diagram of the impedance tube setup to be tested. The driver on the left end of the tube generates an acoustic wave that propagates down the tube hitting the target, in this case our solid steel end plate, and is reflected back with some complex reflection coefficient. There are two pressure sensors located at different distances from the target. Each of these sensors 7

9 3 dspace Testing 2.5 dspace Testing 2 2 Voltage [v] Input signal Modified output signal Time [s] 6 8 x 1 4 (a) Input/output timing Voltage [v] Input signal Modified output signal Time [s] (b) Input and modified output signals Figure 9: DS114 signal input/output testing measures the transient part of the total pressure, i.e. contributions from both the right and left traveling waves (p i and p r respectively). Figure 1: Impedance tube Theory Assuming that the distances S and L (Fig. 1) and the speed of sound are known a priori and the pressure time histories, p 1 and p 2, are measured, then the reflection coefficient of the target can be calculated. The time history data are used to find appropriate auto and cross-spectral density functions, which are twice the Fourier transforms of the auto and cross-correlation functions. R xy (τ) = 1 T Y (t) Ŷ (f) T x(t)y(t + τ) dt G xy (f) = 2 ˆR xy (f) 8

10 Next, the frequency response function (FRF) is estimated by the ratio of the cross-spectral density between the two pressure signals and the auto-spectral density of microphone number one. H 12 (f) = ˆp 2 G 12 (f) = ˆp 1 G 11 (f) This FRF is then used to find the reflection coefficient at location 1. R 1 (f) = H 12(f) e iks e iks H 12 (f) Lastly, the reflection coefficient is transfered to the target location Simulation R(f) = R 1 (f) ( e 2ikL) A simple model of the impedance tube was made by generating a driver signal that is then delayed according to the local speed of sound and distance that the traveling wave must traverse. Figure 11 shows the Simulink model employed to simulate the impedance tube. The driver signal can be a single sinusoidal signal, band-limited white noise, or a chirp. While all three methods have been employed, the discussion will be limited to the chirp input. The chirp s frequency varies linearly in time from 1Hz at the beginning of the simulation to around 24Hz at the end. Impedance Tube Simulation 4/13 /211 M. Quinlan Clock time To Workspace 2 Chirp Signal Scope P To Workspace 1 1 D-P1 P1-P2 P2-P2 Gain P2-P1 Delay Delay 1 Delay 2 Delay 3 Band -Limited White Noise Terminator Pressure 2 SD _P_sens.mat Sine Wave Terminator 1 To File 1 Pressur 1 Scope 1 Figure 11: Simulink model P1-P2 Delay 2 The simulated pressure measurements were used to post calculate the reflection coefficient Scope 2 (R = 1) to confirm both the model and data reduction technique. Figure 12a shows the calculated 2X P 1-P2 Delay 3 magnitude of R based on the simulated data. Over the frequency range of interest, 2Hz to 2Hz, the data are nearly equal to one. Over some small frequencystudent ranges Version of MATLAB the data show some error. To elucidate the reasons behind this, the frequency spectra ˆp 1 and ˆp 2 may be found in Fig. 13. Recalling the FRF used in this theory is based on the ratio of these spectra it is clear that as either signals spectrum approaches zero, H 12 approaches zero or infinity, either case subject to large numerical errors. Better approximations for R can be made with additional pressure sensors at different axial locations in the tube. Figure 12b shows the calculated phase of R, which should be zero for this case. Again, the bulk of the data agree well and discrepancies are expected over some small frequency ranges. R To Workspace 9

11 2 R 4 R Phase R Phase [rad] Frequency (Hz) (a) Magnitude of refection coefficient Frequency (Hz) (b) Phase of reflection coefficient Figure 12: Simulated reflection coefficient.14 Frequency Spectrum of p 1 (t) and p 2 (t).12.1 p1,p Frequency (Hz) Figure 13: Simulated pressure spectra - FFT of p 1 and p Experimental The experimental setup is shown in Fig. 14a. There are drivers located on both sides of the tube here, as will be the arrangement for control. Figure 14b shows the pressure sensor and hot wire block bungs with two pressure sensors and the hot wire probe mounted. A block diagram showing the signal/data flow is shown in Fig. 14c. Similarly to the Simulink model, a signal generator is used to output a chirp with constantly varying frequency from 1Hz to 25Hz. The electronic signal is amplified and supplied to the acoustic driver. Data are taken from two Kistler 211 b5 sensors, anti-aliased at 8kHz and recorded by a National Instruments data acquisition unit sampling at 2kHz for samples. These data are then processed in a similar fashion to the Simulink data except that 2 data sets are ensemble averaged to reduce random error and the pressure signals required calibration. The data show for the majority of the frequency range of interest, 2Hz to 2Hz, the magnitude and phase of the reflection coefficient are very near their theoretical values of 1 and 1

12 (a) Experimental setup (b) Pressure and velocity sensor bungs (c) System flow chart Figure 14: Experimental system respectively (see Fig. 15). The phase has a slowly increasing nature, roll, that is likely due to uncertainties in the speed of sound and distances involved. Utilizing cross correlation techniques this uncertainty might be mitigated, this will be addressed in future work. Both the magnitude and phase have poor results near 5Hz and 14Hz as expected. Current work efforts are to continue development of the velocity measurement technique via the two microphone method and confirmation by hot wire anemometry. Once velocity measurements are confirmed the driver transfer function will be found and the dspace active impedance control system work can be continued. 4 Acoustic development with heat addition In addition to the experimental work being performed a theoretical development to elucidate some fundamental mechanisms is being undertaken. The intent of the development is to show if the interaction of heat release and a bulk rotational momentum in a LRE can be responsible for the development of spinning tangential waves as some experiments indicate. To simplify the analysis, the spinning tangential waves in and cylindrical chamber are in part being represented by a large radius annular chamber where the transverse wave propagation is nearly one-dimensional. Starting from the standard Euler Equations, making some fundamental assumptions, performing a perturbation analysis, and linearizing allows for the development of a non-homogeneous wave equation that includes effects of heat addition. Then by reducing the system to a very simple case the modification of the d Alembert spinning wave solutions due to a discrete heat source can be found. 11

13 2 Ensemble Average of R 4 R Phase R Phase [rad] Frequency (Hz) (a) Magnitude of refection coefficient Frequency (Hz) (b) Phase of reflection coefficient 4.1 Governing equations Assumptions Figure 15: Measured reflection coefficient A small perturbation analysis will be performed on a set of unsteady equations that have been derived via Reynolds decomposition to get a wave equation that includes a heat source. In this development it is necessary to make some simplifying assumptions to make the problem more tractable. Some of these assumptions are: Small perturbations Steady mean properties Uniform mean properties Compact heat source (discrete source) In this case a compact heat source is one that is much smaller than the characteristic acoustic length scales and hence may be treated as a point source and zero heat addition elsewhere. Steady and uniform mean properties allow for the temporal and spatial derivatives of mean quantities to be dropped Reynolds decomposition By representing state variables by the sum of a mean and fluctuating quantity, Reynolds decomposition, will allow for the proper linearization of the governing equations. p = p + p ρ = ρ + ρ T = T + T V = V + V. 12

14 Assuming, for now, no mean velocity, V =, then the following set of equations may be found. Linearized continuity ρ t + ρ V = (1) Linearized momentum V ρ = p (2) t Linearized energy Thermal equation of state Perturbation analysis q h = ρ t + h ρ t p t + h ρ V (3) p = ρ RT (4) p = ρ RT + ρ RT (5) By assuming all fluctuating quantities are small, they then may be assumed to be on the order of or smaller than some number ɛ. Combining the equations found from Reynolds decomposition and neglecting terms of ɛ 2 and higher results in a non-homogeneous wave equation with the form: 2 p t 2 c2 2 p = (γ 1) q t Where the speed of the wave propagation is found to be governed by: (6) c 2 = γ p ρ = γrt (7) Including mean velocity a similar, but significantly more complex, wave equation may be developed. D 2 p Dt 2 c2 2 p = (8) Where D + V Dt t is the material derivative. Although similar looking, this equation is significantly more complicated. 4.2 Effect of heat source Before examining the more complex wave equation that includes mean flow, first examine Eq. 6. By reducing to a very fundamental form as a result of additional assumptions, this equation may bring to light some of the expected behavior of the system. The situation considered here is for a single point source of heat in a channel in which two one-dimensional traveling waves propagate in opposite directions through the heat addition zone. This could be representative of a rectangular combustor or a large radii annular combustor. 13

15 4.2.1 Assumptions One-dimensional acoustics Discrete heat source Heat addition zone small enough to be considered acoustically compact d Alembert traveling wave solution outside of heat addition zone q is a state variable, i.e. not a function of temporal or spatial history The resulting d Alembert wave solution with heat addition follows as: f 2 = f γ 1 q 2 c (9) g 1 = g γ 1 q 2 c (1) Here f 1 and g 2 are the incident waves, while f 2 and g 1 are the outward waves and are found to be a sum of the incident waves and a term proportional to the fluctuating heat release. f1 g1 f2 g2 Heat addition zone Figure 16: d Alembert solution with heat addition 5 Future work Driver transfer function identification Active impedance control system development Finalization of detailed design for unit combustor Manufacturing of unit combustor Acoustic equation development including both mean flow and heat sources 14

16 References [1] J. Pieper, T. Nguyen, and J. Hulka. Recent advances in spray combustion : spray atomization and drop burning phenomena. Progress in astronautics and aeronautics ;. American Institute of Aeronautics and Astronautics, Inc., Reston, Virginia :, ISBN (v. 1) (v. 2). [2] D. K. Huzel and D. H. Huang, editors. Modern engineering for design of liquid-propellant rocket engines, volume 147 of Progress in astronautics and aeronautics ;. American Institute of Aeronautics and Astronautics, Washington, DC :, rev., updated and enl. / edition, ISBN Includes index. [3] K. C. Schadow and E. Gutmark. Combustion instability related to vortex shedding in dump combustors and their passive control. Progress in Energy and Combustion Science, 18(2): , [4] T. Conrad, A. Bibik, D. Shcherbik, E. Lubarsky, and B. T. Zinn. Control of instabilities in liquid fueled combustor by modification of the reaction zone using smart fuel injector, 24. [5] O. Bibik, E. Lubarsky, D. Shcherbik, M. Hadjipanayis, and B. T. Zinn. Rotational traveling of tangential wave in multi-injectors lre combustor simulator, 7-1 January