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The piston-driven oscillator is traditionally modeled by directly applying boundary conditions to the acoustic wave equations; with better models re-deriving the wave equations but retaining nonlinear and viscous effects. These better models are required as the acoustic solution exhibits singularity near the natural frequencies of the cavity, with an unbounded (and therefore unphysical) solution. Recently, a technique has been developed to model general pressure oscillations in propulsion systems and combustion devices. Here, it is shown that this technique applies equally well to the piston-driven gas-column oscillator; and that the piston experiment provides strong evidence for the validity of the general theory. Using a modified piston-tube apparatus, agreement between predicted and observed limit-cycle amplitudes is observed to be on the order of 1%.

The flow-reversal elliptical cylindrical end chamber mufflers of short length are used often in the modern day automotive exhaust systems. The conventional 1-D axial plane wave theory is not able to predict their acoustical attenuation performance in view of the fact that the chamber length is not enough for the evanescent 3-D modes generated at the junctions to decay sufficiently for frequencies below the cut-off frequency. Also, due to the large area expansion ratio at the inlet, the first few higher order modes get cut on even in the low frequency regime. This necessitates a 3-D FEM or 3-D BEM analysis, which is cumbersome and time consuming. Therefore, an ingenious 1-D transverse plane wave theory is developed by considering plane wave propagation along the major-axis of the elliptical section, whereby a 2-port axially short elliptical and circular chamber muffler is characterized by means of the transfer matrix [T] or impedance matrix [Z]. Two different approaches are followed: (1) a numerical scheme such as the Matrizant approach, and (2) an analytical approach based upon the Frobenius series solution of the Webster’s equation governing the transverse plane wave propagation. The convective effects of mean flow are neglected; however the dissipative effects at the ports are taken into account. The TL predicted by this 1-D transverse plane wave analysis is compared with that obtained by means of the 3-D analytical approach and numerical (FEM/BEM) methods. An excellent agreement is observed between this simplified 1-D approach and the 3-D approaches at least up to the cut-on frequency of the (1, 1) even mode in the case of elliptical cylindrical chambers, or the (1, 0) mode in the case of circular cylindrical chambers, thereby validating this 1-D transverse plane wave theory. The acoustical attenuation characteristics of such short chamber mufflers for various configurations are discussed, qualitatively as well as quantitatively. Moreover, the Frobenius series solution enables one to obtain non-dimensional frequencies for determining the resonance peak and trough in the TL graph. The use of this theory is, however, limited to configurations in which both the ports are located along the major axis in the case of elliptical chambers and along the same diameter for circular chambers. The method of cascading the [T] matrices of the 2-port elements cannot be used to analyze a network arrangement of 2-port elements owing to the non-unique direction of wave propagation in such a network of acoustic elements. Although, a few papers are found in the literature reporting the analysis of a network of 2-port acoustic elements, no work is seen on the analysis of a network of multi-port elements having more than two external ports. Therefore, a generalized algorithm is proposed for analyzing a general network arrangement of linear multi-port acoustic elements having N inlet ports and M outlet ports. Each of these multi-port elements constituting the network may be interconnected to each other in an arbitrary manner. By appropriate book-keeping of the equations obtained by the [Z] matrix characterizing each of the multi-port and 2-port elements along with the junction laws (which imply the equality of acoustic pressure and conservativeness of mass velocity at a multi-port junction), an overall connectivity matrix is obtained, whereupon a global [Z] matrix is obtained which characterizes the entire network. Generalized expressions are derived for the evaluation of acoustic performance evaluation parameters such as transmission loss (TL) and insertion loss (IL) for a multiple inlet and multiple outlet (MIMO) system. Some of the characteristic properties of a general multi-port element are also studied in this chapter. The 1-D axial and transverse plane wave analysis is used to characterize axially long and short chambers, respectively, in terms of the [Z] matrix. Different network arrangements of multi-port elements are constructed, wherein the TL performance of such MIMO networks obtained on the basis of either the 1-D axial or 1-D transverse plane wave theory are compared with 3-D FEA carried on a commercial software. The versatility of this algorithm is that it can deal with more than two external or terminal ports, i.e., one can have multiple inlets and outlets in a complicated acoustic network. A generalized approach/algorithm is presented to characterize rigid wall reactive multi-port chamber mufflers of different geometries by means of a 3-D analytical formulation based upon the modal expansion and the uniform piston-driven model. The geometries analyzed here are rectangular plenum chambers, circular cylindrical chamber mufflers with and without a pass tube, elliptical cylindrical chamber mufflers, spherical and hemispherical chambers, conical chamber mufflers with and without a co-axial pass tube and sectoral cylindrical chamber mufflers of circular and elliptical cross-section as well as sectoral conical chamber mufflers. Computer codes or subroutines have been developed wherein by choosing appropriate mode functions in the generalized pressure response function, one can characterize a multi-port chamber muffler of any of the aforementioned separable geometrical shapes in terms of the [Z] matrix, subsequent to which the TL performance of these chambers is evaluated in terms of the scattering matrix [S] parameters by making use of the relations between [Z] and [S] matrices derived earlier. Interestingly, the [Z] matrix approach combined with the uniform piston-driven model is indeed ideally suited for the 3-D analytical formulation inasmuch as regardless of the number of ports, one deals with only one area discontinuity at a time, thereby making the analysis convenient for a multi-port muffler configuration with arbitrary location of ports. The TL characteristics of SISO chambers corresponding to each of the aforementioned geometries (especially the elliptical cylindrical chamber) are analyzed in detail with respect to the effect of chamber dimensions (chamber length and transverse dimensions), and relative angular and axial location of ports. Furthermore, the analysis of SIDO (i.e., single inlet and double outlet) chamber mufflers is given special consideration. In particular, we examine (1) the effect of additional outlet port (second outlet port), (2) variation in the relative angular or axial location of the additional or second outlet port (keeping the location of the inlet port and the outlet ports of the original SISO chamber to be constant) and (3) the effect of interchanging the location of the inlet and outlet ports on the TL performance of these mufflers. Thus, design guidelines are developed for the optimal location of the inlet and outlet ports keeping in mind the broadband attenuation characteristics for a single inlet and multiple outlet (SIMO) system. The non-dimensional limits up to which a flow-reversal elliptical (or circular) cylindrical end chamber having an end-inlet and end-outlet configuration is acoustically short (so that the 1-D transverse plane wave theory is applicable) and the limits beyond which it is acoustically long (so that the 1-D axial plane wave theory is applicable) is determined in terms of the ratio or equivalently, in terms of the ratio. Towards this end, two different configurations of the elliptical cylindrical chamber are considered, namely, (1) End-Offset Inlet (located along the major-axis of the ellipse) and End-Centered Outlet (2) End-Offset Inlet and End-Offset Outlet (both the ports located on the major-axis of the ellipse and at equal offset distance from the center). The former configuration is analyzed using 3-D FEA simulations (on SYSNOISE) while the 3-D analytical uniform piston-driven model is used to analyze the latter configuration. The existence of the higher order evanescent modes in the axially long reversal chamber at low frequency (before the cut-on frequency of the (1, 1) even mode or (1, 0) mode) causes a shift in the resonance peak predicted by the 1-D axial plane wave theory and 3-D analytical approach. Thus, the 1-D axial plane wave analysis is corrected by introducing appropriate end correction due to the modified or effective length of the elliptical cylindrical chamber. An empirical formulae has been developed to obtain the average non-dimensional end correction for the aforementioned configurations as functions of the expansion ratio, (i.e., ), minor-axis to major-axis ratio, (i.e., ) and the center-offset distance ratio, (i.e., ). The intermediate limits between which the chamber is neither short nor long (acoustically) has also been obtained. Furthermore, an ingenious method (Quasi 1-D approach) of combining the 1-D transverse plane wave model with the 1-D axial plane wave model using the [Z] matrix is also proposed for the end-offset inlet and end-centered outlet configuration. A 3-D analytical procedure has also been developed which also enables one to determine the end-correction in axially long 2-port flow-reversal end chamber mufflers for different geometries such as rectangular, circular and elliptical cylindrical as well as conical chambers, a priori to the computation of TL. Using this novel analytical technique, we determine the end correction for arbitrary locations on the two end ports on the end face of an axially long flow-reversal end chamber. The applicability of this method is also demonstrated for determination of the end corrections for the 2-port circular cylindrical chamber configuration without and with a pass tube, elliptical cylindrical chambers as well as rectangular and conical chambers.

The piston-driven oscillator is traditionally modeled by directly applying boundary conditions to the acoustic wave equations; with better models re-deriving the wave equations but retaining nonlinear and viscous effects. These better models are required as the acoustic solution exhibits singularity near the natural frequencies of the cavity, with an unbounded (and therefore unphysical) solution. Recently, a technique has been developed to model general pressure oscillations in propulsion systems and combustion devices. Here, it is shown that this technique applies equally well to the piston-driven gas-column oscillator; and that the piston experiment provides strong evidence for the validity of the general theory. Using a modified piston-tube apparatus, agreement between predicted and observed limit-cycle amplitudes is observed to be on the order of 1%.

The re-entry space vehicles encounter high temperatures when they enter the earth atmosphere and the high temperature air in the shock layer around the body undergoes partial dissociation. Also, the gas molecules injected into the shock layer from the ablative thermal protection system (TPS) undergo pyrolysis which helps in reducing the net heat flux to the vehicle surface. The chemical species due to the pyrolysis add complexity to the stagnation flow chemistry (52 chemical reactions) models which include species like NOx, CO and hydrocarbons (HCs). Although the ablative TPS is responsible for the safety of re-entry space vehicle, the induced chemical species result in variety of adverse effects on environment such as global warming, acid rain, green house effect etc. The well known three-way-catalyst (TWC) involves simultaneous removal of all the three gases (i.e, NOx, CO, Hydrocarbons) present in the shock layer. Interaction of such three-way-catalyst on the heat shield materials or on the wall of the re-entry space vehicle is to reduce the heat flux and to remove the gases in the shock layer, which is an important issue. For the re-entry vehicle the maximum aerodynamic heating occurs at an altitude ranging about 68 to 45 km during which the vehicle is surrounded by high temperature dissociated air. Then the simplest real gas model of air is the five species model which is based on N2, O2, O, NO and N. This five species model assumes no ionization and no pyrolysis gases are emitted from the heat shield materials. The experimental research work presented in this thesis is directed towards the understanding of catalytic and non-catalytic surface reactions on high temperature materials in presence of strong shock heated test gas. We have also explored the possibility of using shock tube as a high enthalpy device for synthesis of new materials. In the first Chapter, we have presented an overview of re-entry space vehicles, thermal protection system (TPS) and importance of real gas effects in the shock layer. Literature survey on TPS, ablative materials and aerothermochemistry at the stagnation point of reentry capsule, in addition to catalytic and non-catalytic surface reactions between the wall and dissociated air in the shock layer are presented. In Chapters 2 and 3, we present the experimental techniques used to study surface reactions on high temperature materials. A brief description of HST2 shock tunnel is presented and this shock tunnel is capable of generating flow stagnation enthalpies ranging from 0.7 to 5 MJ/kg and has an effective test time of ~ 800 µs. High speed data acquisition system (National Instruments and Yokogawa) used to acquire data from shock tube experiments. The experimental methods like X-ray Photoelectron Spectroscopy (XPS), Scanning Electron Microscopy (SEM), X-ray diffraction (XRD), Raman and FTIR spectroscopy have been used to characterize the shock-exposed materials. Preliminary research work on surface nitridation of pure metals with shock heated nitrogen gas is discussed in Chapter 2. Surface nitridation of pure Al thin film with shock heated N2 is presented in Chapter 3. An XPS study shows that Al 2p peak at 74.2 eV is due to the formation AlN on the surface of Al thin film due to heterogeneous non-catalytic surface reaction. SEM results show changes in surface morphology of AlN film due to shock wave interaction. Thickness of AlN film on the surface increased with the increase in temperature of the shock heated nitrogen gas. However, HST2 did not produce sufficient temperature and pressure to carry out real conditions of re-entry. Therefore design and development of a new high enthalpy shock tunnel was taken up. In Chapter 4, we present the details of design and fabrication of free piston driven shock tunnel (FPST) to generate high enthalpy test gas along with the development of platinum (Pt) and thermocouple sensors for heat transfer measurement. A free piston driven shock tunnel consists of a high pressure gas reservoir, compression tube, shock tube, nozzle, test section and dump tank connected to a vacuum pumping system. Compression tube has a provision to fill helium gas and four ports, used to mount optical sensors to monitor the piston speed and pressure transducer to record pressure at the end of the compression tube when the piston is launched. Piston can attain a maximum speed of 150 m/s and compress the gas inside the compression tube. The compressed gas bursts the metal diaphragm and generates strong shock wave in the shock tube. This tunnel produces total pressure of about 300 bar and temperature of about 6000 K and is capable of producing a stagnation enthalpy up to 45 MJ/kg. The calibration of nozzle was carried out by measuring the pitot tube pressure in the dump tank. Experimentally recorded P5 pressure at end of the shock tube is compared with Numerical codes. Calibrated pressure P5 values are used to calculate the temperature T5 of the reflected shock waves. This high pressure and high temperature shock heated test gas interacts with the surface of the high temperature test materials. For the measurement of heat transfer rate, platinum thin film sensors are developed using DC magnetron sputtering unit. Hard protective layer of aluminum nitride (AlN) on Pt thin film was deposited by reactive DC magnetron sputtering to measure heat transfer rate in high enthalpy tunnel. After the calibration studies, FPST is used to study the heat transfer rate and to investigate catalytic/non-catalytic surface reaction on high temperature materials. In Chapter 5, an experimental investigation of non-catalytic surface reactions on pure carbon material is presented. The pure carbon C60 films and conducting carbon films are deposited on Macor substrate in the laboratory to perform shock tube experiments. These carbon films were exposed to strong shock heated N2 gas in the shock tube portion of the FPST tunnel. The typical shock Mach number obtained is about 7 with the corresponding pressure and temperature jumps of about 110 bar and 5400 K after reflection at end of the shock tube. Shock exposed carbon films were examined by different experimental techniques. XPS spectra of C(1s) peak at 285.8 eV is attributed to sp2 (C=N) and 287.3 eV peak is attributed to sp3 (C-N) bond in CNx due to carbon nitride. Similarly, N(1s) core level peak at 398.6 eV and 400.1 eV observed are attributed to sp3-C-N and sp2-C=N of carbon nitride, respectively. SEM study shows the formation of carbon nitride crystals. Carbon C60 had melted and undergone non-catalytic surface reaction with N2 while forming carbon nitride. Similar observations were made with conducting carbon films but the crystals were spherical in shape. Micro Raman and FTIR study gave further evidence on the formation of carbon nitride film. This experimental investigation confirms the formation of carbon nitride in presence of shock-heated nitrogen gas by non-catalytic surface reaction. In Chapters 6 and 7, we present a novel method to understand fully catalytic surface reactions after exposure to shock heated N2, O2 and Ar test gas with high temperature materials. We have employed nano ZrO2 and nano Ce0.5Zr0.5O2 ceramic high temperature materials to investigate surface catalytic reactions in presence of shock heated test gases. These nano crystalline oxides are synthesized by a single step solution combustion method. Catalytic reaction was confirmed for both powder and film samples of ZrO2. As per the theoretical model, it is known that the catalytic recombination reaction produces maximum heating on the surface of re-entry space vehicles. This was demonstrated in this experiment when a metastable cubic ZrO2 changed to stable monoclinic ZrO2 phase after exposure to shock waves. The change of crystal structure was seen using XRD studies and needle type monoclinic crystal growth with aspect ratio (L/D) more than 15 was confirmed by SEM studies. XPS of Zr(3d) core level spectra show no change in binding energy before and after exposure to shock waves, confirming that ZrO2 does not change its chemical nature, which is the signature of catalytic surface reaction. When a shock heated argon gas interacted with Ce0.5Zr0.5O2 compound, there was a change in colour from pale yellow to black due to reduction of the compound, which is the effect of heat transfer from the shock wave to the compound in presence of argon gas. The reduction reaction shows the release of oxygen from the compound due to high temperature interaction. The XPS of Ce(3d) and Zr(3d) spectra confirm the reduction of both Ce and Zr to lower valent states. The oxygen storage and release capacity of the Ce0.5Zr0.5O2 compound was confirmed by analyzing the reduction of Ce4+ and Zr4+ with high temperature gas interaction. When Ce0.5Zr0.5O2 (which is same as Ce2Zr2O8) in cubic fluorite structure was subjected to strong shock, it changed to pyrochlore (Ce2Zr2O7) structure by releasing oxygen and on further heating it changed to Ce2Zr2O6.3 which is also crystallized in pyrochlore structure by further releasing oxygen. If this heating is carried out in presence of argon test gas, fluorite structure can easily change to pyrochlore Ce2Zr2O6.3 structure, which is a good electrical conductor. Due to its oxygen storage capability (OSC) and redox (Ce4+/Ce3+) properties, Ce0.5Zr0.5O2 had been used as oxygen storage material in three-way-catalyst. Importance of these reactions is that the O2 gas released from the compound will react with gas released from the heat shield materials, like NOx, CO and hydrocarbon (HCs) species which results in reduction of temperature in the shock layer of the re-entry space vehicle. The compound Ce0.5Zr0.5O2 changes its crystal structure from fluorite to pyrochlore phase in presence of shock heated test gas. The results presented in these two Chapters are first of their kind, which demonstrates the surface catalytic reactions. In Chapter 8, we present preliminary results of the oxygen recombination on the surface of heat shield material procured from Indian Space Research Organization (ISRO) used as TPS in re-entry space capsule (Space capsule Recovery Experiment SRE-1) and on thin film SiO2 deposited on silicon substrate. The formation of SiO between the junctions of SiO2/Si was confirmed using XPS study when shock exposed oxygen reacted on these materials. The surface morphology of the ablated SiO2 film was studied using SEM. The damage induced due to impact of shock wave in presence of oxygen gas was analyzed using Focused Ion Beam (FIB) microscope. The results reveal the damage on the surface of SiO2 film and also in the cross-section of the film. We are further investigating use of FIB, particularly related to residual stress developed on thin films due to high pressure and high temperature shock wave interaction. In Chapter 9, conclusions on the performance of FPST, synthesis of high temperature materials, catalytic and non-catalytic surface reactions on the high temperature material due to shock-heated test gases are presented. Possible scope for future studies is also addressed in this Chapter.

One of the characteristics of the high speed ows over blunt bodies is the detached shock formed in front of the body. The distance of the shock from the stagnation point measured along the stagnation streamline is termed as the shock stand o distance or the shock detachment distance. It is one of the most basic parameters in such ows. The need to know the shock stand o distance arises due to the high temperatures faced in these cases. The biggest challenge faced in high enthalpy ows is the high amounts of heat transfer to the body. The position of the shock is relevant in knowing the temperatures that the body being subjected to such ows will have to face and thus building an efficient system to reduce the heat transfer. Despite being a basic parameter, there is no theoretical means to determine the shock stand o distance which is accepted universally. Deduction of this quantity depends more or less on experimental or computational means until a successful theoretical model for its predictions is developed. The experimental data available in open literature for spherical bodies in high speed ows mostly lies beyond the 2 km/s regime. Experiments were conducted to determine the shock stand o distance in the velocity range of 1-2 km/s. Three different hemispherical bodies of radii 25, 40 and 50 mm were taken as test models. Since the shock stand o distance is known to depend on the density ratio across the shock and hence gamma (ratio of specific heats), two different test gases, air and carbon dioxide were used for the experiments here. Five different test cases were studied with air as the test gas; Mach 5.56 with Reynolds number of 5.71 million/m and enthalpy of 1.08 MJ/kg, Mach 5.39 with Reynolds number of 3.04 million/m and enthalpy of 1.42 MJ/kg Mach 8.42 with Reynolds number of 1.72 million/m and enthalpy of 1.21 MJ/kg, Mach 11.8 with Reynolds number of 1.09 million/m and enthalpy of 2.03 MJ/kg and Mach 11.25 with Reynolds number of 0.90 million/m and enthalpy of 2.88 MJ/kg. For the experiments conducted with carbon dioxide as test gas, typical freestream conditions were: Mach 6.66 with Reynolds number of 1.46 million/m and enthalpy of 1.23 MJ/kg. The shock stand o distance was determined from the images that were obtained through schlieren photography, the ow visualization technique employed here. The results obtained were found to follow the same trend as the existing experimental data in the higher velocity range. The experimental data obtained was compared with two different theoretical models given by Lobb and Olivier and was found to match. Simulations were carried out in HiFUN, an in-house CFD package for Euler and laminar own conditions for Mach 8 own over 50 mm body with air as the test gas. The computational data was found to match well with the experimental and theoretical data