A COMPUTATIONAL STUDY OF MIXING IN JET STIRRED REACTORS. A Thesis. Presented to. The Graduate Faculty of The University of Akron

Transcription

1 A COMPUTATIONAL STUDY OF MIXING IN JET STIRRED REACTORS A Thesis Presented to The Graduate Faculty of The University of Akron In Partial Fulfillment of the Requirements for the Degree Master of Science Michael Crawford August, 2014

2 A COMPUTATIONAL STUDY OF MIXING IN JET STIRRED REACTORS Michael Crawford Thesis Approved: Accepted: Advisor Dr. Gaurav Mittal Dean of the College Dr. George K. Haritos Faculty Reader Dr. Siamak Farhad Dean of the Graduate School Dr. George R. Newkome Faculty Reader Dr. Abhilash Chandy Date Department Chair Dr. Sergio Felicelli ii

3 ABSTRACT Jet stirred reactors (JSRs) are frequently employed for studying homogeneous gas phase chemical kinetics of fuels. The most challenging aspect of JSR is the achievement of sufficiently rapid mixing by turbulent jets so that the temperature and concentration fields inside the reactor could be considered homogeneous. However, there has not been any investigation in the literature which conclusively addresses that rapid mixing is indeed achieved. In this work, computational fluid dynamics (CFD) simulations for JSRs are conducted to gain insights into the dynamics of jet mixing. CFD simulations are conducted for some of the geometries commonly used by researchers and mixing inside the reactor is visualized by computationally tracking an inert tracer pulse. Results suggest that some of the commonly used reactors could have significant concentration non-homogeneity and therefore may not be suitable for chemical kinetic studies. For conditions when the flow in the reactor is sufficiently turbulent and recycling rate is high, back mixing can become problematic even though the concentration field is more or less homogeneous. As a consequence, the vast chemical kinetic data obtained from such facilities is questionable. Furthermore, modifications to the design of JSR are considered that could significantly improve concentration homogeneity. An alternative geometry of the reactor is evaluated and shown to be promising. A new JSR is designed and fabricated iii

4 for studying homogeneous gas phase chemical kinetics over a range of pressures from atmospheric to elevated (up to 50 bar). iv

5 DEDICATION I would like to dedicate this thesis to my parents, the most selfless and giving people I have ever met, Mike and Margaret Crawford. I would not be where I am today without their endless love and support. They have provided the perfect example of the person that I strive to be. I love you Mom and Dad. v

6 ACKNOWLEDGEMENTS I would like to sincerely thank Dr. Gaurav Mittal for advising me throughout my career at the University of Akron. This thesis would not have been possible without his guidance and support. I am grateful to have had the opportunity to work under him during the course of my graduate study. I would also like to thank Dr. Siamak Farhad and Dr. Abhilash Chandy for giving me their valuable time and serving as my thesis committee members. vi

7 TABLE OF CONTENTS Page LIST OF TABLES... x LIST OF FIGURES... xi CHAPTER I. INTRODUCTION Chemical Kinetics Practical and Surrogate Fuels Facilities for Studying Chemical Kinetics Static Reactor Flow Reactor Shock Tube Rapid Compression Machine Jet Stirred Reactor Advantages and Challenges of JSR Specific Objectives Thesis Organization II. METHODOLOGY FOR DETERMINING MIXING INSIDE JSR Historical Perspective Computational Methodology vii

8 2.2.1 Computational Geometry Governing Equations Solution Strategy III. COMPUTATIONAL RESULTS FOR MIXING IN JSR Existing Geometries Phillipe Dagaut (1986) Olivier Herbinet (2007) Renato Rota (1994) Joseph Zelina (1994) Results with Existing Geometries Cases Simulated Computational Grid Velocity and Temperature Field Tracer Injection and Evolution Characterization of Mixing Grid and Time Step Independence Summary of Simulated Cases for Reactor Nozzle of 1mm Summary of Simulated Cases for Reactor Nozzle of 0.25mm IV. ALTERNATIVE REACTOR GEOMETRY AND DESIGN OF A JSR Consideration of an Alternative Reactor Geometry Design Features of Existing JSRs viii

9 4.2.1 Phillipe Dagaut (1986) Olivier Herbinet (2007) Renato Rota (1994) Design of the Present JSR V. CONCLUSIONS AND FUTURE WORK Conclusions Future Work REFERENCES ix

10 LIST OF TABLES Table Page 3.1 Conditions Simulated Numerical results for reactor with 0.25 mm nozzles..56 x

11 LIST OF FIGURES Figures Page 1.1 Lumped kinetic scheme of the primary oxidation reactions in hydrocarbons Schematic of a static reactor A schematic of the pressurized flow reactor from Princeton University (Vermeersch et al., 1991; Kim et al., 1994) Schematic of a typical shock tube (Mertens et al., 2004) Schematic of an RCM (Mittal et al., 2007) A jet stirred reactor (Dagaut et al., 1986) Schematic of the reactor Jet circulation in a plane Reactor constraints with a residence time of 1 second at 1 atm, 800K Reactor constraints on τ vs. R plot A typical JSR reactor configuration JSR reactor design (Dagaut et al., 1986) JSR reactor (Herbinet et al., 2007) The design of Rota s reactor (Rota et al., 1994) A JSR that was built based on Zelina s design (Manzello et al., 2007) Schematic of the reactor Surface mesh xi

12 3.7 Mesh in selected planes Velocity distribution (m/s). Case Nozzle diameter = 1mm, P = 1 bar, T = 1000K, τ r = 0.09s Contours of speed (m/s) perpendicular to the selected planes. Case Nozzle diameter = 1mm, P = 1 bar, T = 1000K, τ r = 0.09s Temperature distribution in Kelvin. Case Nozzle diameter = 1mm, P = 1 bar, T = 1000K, τ r = 0.09s Evolution of tracer after injection. Normalized instantaneous mass fraction is shown. Case Nozzle diameter = 1mm, P = 1 bar, T = 1000K, τ r = 0.09s Normalized instantaneous mass fraction of tracer. Case Nozzle diameter = 1mm, P = 1 bar, T = 1000K, τ r = 0.09s % non-homogeneity. Case Nozzle diameter = 1mm, P = 1 bar, T = 1000K, τ r = 0.09s Average normalized tracer mass fraction in the reactor, Y avg, and Y out. Case Nozzle diameter = 1mm, P = 1 bar, T = 1000K, τ r = 0.09s Refined mesh in selected planes Demonstration of grid and time-step independence. % non-homogeneity. Case Nozzle diameter = 1mm, P = 1 bar, T = 1000K, τ r = 0.09s Average normalized tracer mass fraction in the reactor, Y avg, and Y out and % non-homogeneity. Case Nozzle diameter = 1mm, P = 10 bar, T = 1000K, τ r = 0.9s Average normalized tracer mass fraction in the reactor, Y avg, and Y out and % non-homogeneity. Case Nozzle diameter = 1mm, P = 10 bar, T = 1000K, τ r = 0.25s Average normalized tracer mass fraction in the reactor, Y avg, and Y out and % non-homogeneity. Case Nozzle diameter = 1mm, P = 10 bar, T = 1000K, τ r = 1s xii

13 3.20 Average normalized tracer mass fraction in the reactor, Y avg, and Y out and % non-homogeneity. Case Nozzle diameter = 0.25mm, P = 1 bar, T = 1000K, τ r = 1s Average normalized tracer mass fraction in the reactor, Y avg, and Y out and % non-homogeneity. Case Nozzle diameter = 0.25mm, P = 10 bar, T = 1000K, τ r = 1s Average normalized tracer mass fraction in the reactor, Y avg, and Y out and % non-homogeneity. Case Nozzle diameter = 0.25mm, P = 1 bar, T = 1000K, τ r = 4s Normalized instantaneous mass fraction of tracer. Case Nozzle diameter = 0.25mm, P = 10 bar, T = 1000K, τ r = 1s Alternative geometry for the reactor Normalized instantaneous tracer mass fraction % non-homogeneity for alternative reactor geometry Detailed schematic of Dagaut s JSR system (Dagaut et al., 1986) A schematic of Herbinet s JSR system (Herbinet et al., 2007) A basic schematic of Rota s JSR system (Rota et al., 1994) Cross-section views of the final reactor design and image Schematic of the reactor, heater, and pressure vessel with probes Recover of energy from exhaust gas A schematic of the flow system Image of the JSR system xiii

14 CHAPTER I INTRODUCTION 1.1 Chemical Kinetics In response to the increasing global demand for energy and emphasis on improving the efficiency and emission characteristics of practical combustors/engines, there is increased focus on developing innovative, efficient, sustainable and cleanburning approaches. Various topics of emphasis include development of new combustion technologies and use of alternative/renewable fuels. Research in the direction of development of renewable biofuels and associated combustion technologies, which promise harmonious correlation with sustainable development, energy conservation, efficiency, and environmental preservation, has become highly pronounced in the present context (Agarwal, 2007). Biofuels can decrease the dependence on petroleum and lower net emissions of greenhouse gases. Experiments using biodiesel in engines have shown decrease in emission of carbon monoxide, unburned hydrocarbons, and particulate matter, although with a slight increase in emissions of nitrogen oxides (McCormick et al., 2001; EPA report, 2002). Advanced engine combustion technologies are moving towards low-temperature strategies where engines operate with highly diluted or fuel lean charge. It is also envisioned that the next generation of clean, fuel-flexible and efficient engines could operate at pressures considerably higher than those commonly seen in engines today. 1

15 This poses significant technological challenges (US DOE Report). Operation at novel low temperature strategies becomes significantly kinetically-influenced by the complex low-temperature chemistry of fuels. Therefore, an important ingredient in the overall objective of science-based design of clean and efficient combustors, that use alternative as well as conventional fuels, is the need for understanding the chemical kinetic mechanisms of such fuels at conditions of elevated pressures and low-tointermediate temperatures. Successful integration of bio-derived fuels in the present energy scenario will require development of predictive combustion modeling capabilities to optimize the design and operation of such fuels in advanced engines for transportation application (US DOE Report). Chemical kinetics is the study of the rates of reactions and influence of various parameters on these rates. The ultimate objective of investigating chemical kinetics of fuels is to develop comprehensive kinetic mechanisms with predictive capabilities which can be integrated with Computational Fluid Dynamics (CFD). The rates of reactions and the controlling chemistry are significantly influenced by pressure and temperature. Hydrocarbon oxidation is typically divided into three temperature regimes, namely the low temperature (< 700 K), intermediate temperature ( K), and high temperature (> 1000 K) (Curran et al. 1998, 2002). The division into regimes is based on transition in the controlling chemistry. Furthermore, these temperature boundaries shift to higher temperatures as pressure increases. The reactions that control hydrocarbon oxidation at low-to-intermediate temperatures are very complex. The discussion can be simplified considerably by representing long chain fuel molecule by RH, where H is the hydrogen atom and R is the radical formed by the removal of H atom. 2

16 At low-to-intermediate temperatures, the initiation occurs through abstraction of H atom from the fuel by reaction with O 2 to produce a hydroperoxy radical (HO 2 ) and an alkyl radical (R) RH + O 2 R. + HO 2 (1) The fate of the R radical depends upon the rates of the following competing pathways. R. + O 2 RO. 2 (2) R. + O 2 olefin + HO 2 (3) Reaction 2 has low activation energy and is therefore favored at low temperatures and reaction 3 has relatively high activation energy and becomes favored at intermediate temperatures. At low temperatures, when the formation of alkyl peroxy (RO 2 ) is favored, the following reaction sequence ensues, leading to the low temperature chain branching. RO. 2 + RH ROOH + R. (4) ROOH RO. + OH (5) Hydrocarbons with C >3 can undergo internal isomerization of RO 2 to form QOOH, where Q is formed by abstracting H from R. At low temperatures, QOOH can add another O 2 molecule to yield O 2 QOOH which finally produces two OH radicals. The overall sequence is highly chain branching. As an example, the overall flux diagram for iso-octane oxidation is shown schematically in Fig As temperature increases, 3

17 the chain propagation reactions of QOOH species increase because the energy barrier to their formation is more easily overcome, leading to the formation of cyclic ether species, conjugate olefins, and -decomposition products at the expense of the chainbranching reaction pathways through O 2 QOOH (Curran et al., 1998). The shift in the controlling chemistry with temperature leads to a decrease in the reactivity of the system with increase in temperature and is referred to as the negative temperature coefficient (NTC) regime. For larger hydrocarbons, the number of potential radical sites increases, leading to enormous variety of intermediate species. With further increase in temperature in the intermediate temperature regime and beyond, -scission of R radical becomes important and chain branching through H + O 2 = OH + O plays a key role. ic 8 H 18 C 8 H 17 scission olefin + R' O 2 C 8 H 17 O 2 C 8 H 16 OOH O 2 scission C 8 H 16 + HO 2 olefin + aldehyde +OH cyclic ether + OH O 2 C 8 H 16 OOH ic 8 ket + OH chain branching Figure 1.1 Lumped kinetic scheme of the primary oxidation reactions in hydrocarbons 4

18 The difference in the chain-branching mechanisms at low and high temperatures also leads to varying reactivity, depending on the fuel to air equivalence ratio. Because the chain-branching mechanism at high temperatures is due to the H + O 2 = OH + O reaction, fuel lean mixtures are more reactive in this regime. However, at low temperatures, because chain branching is dependent on radical species formed directly from the parent fuel, fuel rich mixtures are oxidized more quickly (Curran et al., 2002). Historically, chemical kinetics of hydrocarbons has been extensively studied at low pressures and high temperatures but reaction mechanisms have not been well validated at the other extreme, namely the conditions of low temperatures and high pressures, which is very relevant to advanced combustion technologies. The investigations at such conditions are meager for all practical fuels and much research is warranted. 1.2 Practical and Surrogate Fuels Practical fuels, such as gasoline, diesel and jet fuels, consist of hundreds of hydrocarbons. A typical gasoline is composed of 4-8% n-alkanes, 25-40% isoalkanes, 20-50% aromatics, 3-7% cycloalkanes, and 2-5% olefins (cf. The kinetic mechanism for gasoline will have to have the reactions for each component and interactions between them. This is not practical. The use of surrogate fuels is a viable approach. A surrogate fuel model consists of a small number (typically less than 5) of fuel components that can be used to represent the real fuel and can predict the desired characteristics of the real fuel. The kinetic model for the surrogate can be developed and used in lieu of the practical fuel. 5

19 In order to develop the surrogate fuel composition correctly for a given application, target values of performance metrics need to be identified that the surrogate fuel should match. These targets depend on application. For example, certain fuel performance targets that are judged to be important for a spark ignition engine operation may be less important in HCCI combustion. A wide range of fuel targets have been identified, including fuel properties (chemical composition, C/H ratio, density, viscosity, distillation curve), engine characteristics (combustion phasing, bulk burn duration, emissions), and laboratory data (species evolution, flame speed, ignition delay/limit, extinction limit). The approach of application-specific surrogate development for a particular practical fuel involves identification of a small number of hydrocarbon molecules that can be blended into useful experimental fuels and modeled computationally. These surrogate formulations are required to adequately mimic the behavior of the practical fuels. This effort further necessitates the availability of experimental data of high fidelity to compare the performance of a surrogate formulation against practical fuel and then develop kinetic mechanism for the surrogate. One approach for developing a surrogate for a practical fuel is to use a single component from each hydrocarbon class in the practical fuel so that the unique molecular structure of each class is included. This approach has the advantage of representing the associated chemistry of each class of hydrocarbon, as fuel structure is known to greatly affect the combustion processes. Therefore, a surrogate fuel for gasoline can possibly include a representative component from n-alkanes (e.g. n- heptane), iso-alkanes (e.g. iso-octane), aromatics (e.g. toluene), cycloalkanes (e.g. methylcyclohexane), olefins (e.g. diisobutylene, 1-pentene), and additives (e.g. ethanol). This approach may lead to reliable predictions of many of the combustion 6

20 properties of the practical fuel. For example, Lenhert et al. (2003) designed a fourcomponent surrogate for gasoline which consisted of approximately 14% n-heptane, 49.6% iso-octane, 31.8% toluene, and 4.6% 1-pentene. All of the primary hydrocarbon classes in gasoline except cycloalkanes were included in the surrogate fuel. Development of their surrogate was based on the criteria that the components should preferably be present in the automotive gasoline, be of similar molecular weights as automotive fuels, and have been studied kinetically. Lenhert et al. showed that their gasoline surrogate matched the low- and intermediate-temperature reactivity of the full boiling range fuels. 1.3 Facilities For Studying Chemical Kinetics As mentioned above, development of surrogate fuels and their kinetic mechanisms for combustion modeling requires experimental data from a variety of experimental facilities. Next, various experimental facilities for studying homogeneous chemical kinetics at high pressures and low-to-intermediate temperatures are briefly discussed Static Reactor The static reactor is the simplest configuration for studying chemical kinetics at low temperatures. It consists of a spherical chamber containing the reactive mixture, which is heated with an oven or thermostated bath. A schematic of a basic static reactor can be seen in Fig

21 Figure Schematic of a static reactor The maximum operating temperature for a static reactor is generally around 750 K. This creates relatively slow reaction times (on the order of seconds to minutes). The test chamber is assumed to be homogeneous in temperature and reactant mixture. Slow reaction times help this assumption to remain valid. Samples are taken from the test chamber with a probe and immediately quenched. Data is also obtained by measuring the increase in pressure in the chamber. Although static reactors have problems with surface reactions in the test chamber, they can still be useful. Explosion limits for many fuel-oxidizer mixtures have been determined using the static reactor. However, due to high sensitivity to surface effects under the conditions of long reaction times, static reactor experiments are generally not as useful for quantitative analysis as alternate techniques. 8

22 1.3.2 Flow Reactor Flow reactor consists of a long tube with a homogeneous fuel-oxidizer mixture injected at one end with exhaust at the other end. A plug flow situation, where composition and temperature are uniform over the cross section of the reactor and axial diffusion is negligible, is desirable. This is achieved by diluting the homogeneous mixture with a large amount of inert gas. Sampling probes are placed in the flow path to determine concentrations of species at different axial locations. Figure 1.3 shows a schematic of the high pressure flow reactor at Princeton University. Data from the flow reactor may be influenced by experimental uncertainties. Potential problems with this technique include imperfect mixing of reactants, radial gradients of temperature and concentration and problems associated with gas sampling technique. In essence, a flow reactor offers ease of specie and temperature measurement, but is suitable for relatively slow reaction conditions under highly diluted mixture. The variable-pressure flow reactor at Princeton University can operate in the pressure range of 0.2 to 20 bar and temperature up to 1200 K (Vermeersch et al., 1991; Kim et al., 1994), which is a typical upper limit of operating conditions for flow reactor. 9

23 Electric Resistance Heater Evaporator Fuel Inlet Sample Probe Wall Heaters Slide Table Optical Access Ports Oxidizer Injector Figure A schematic of the pressurized flow reactor from Princeton University (Vermeersch et al., 1991; Kim et al., 1994) Shock Tube Shock tubes are used to study chemical kinetics up to very high pressures and intermediate-to-high temperatures. The tube is separated into two sections by a diaphragm. One section is filled with inert gasses at a high pressure (called the driver). The other is at low pressure and contains the combustible gasses. The driven section is much longer than the driver, usually measuring up to several meters in length. When the diaphragm is ruptured, the extreme pressure difference creates a shock wave that propagates into the driven section. This instantly increases the pressure and temperature to the desired values. 10

24 Figure Schematic of a typical shock tube (Mertens et al., 2004) Combustion reactions are typically observed behind the reflected shock wave. The observation times are generally short (on the order of 10 ms) due to boundary layer effects and interference from the rarefaction wave. This means that the operating temperatures and pressures are limited only to arrangements that achieve short chemical induction times and experimentation in the low temperature regime is generally difficult. Shock tubes are capable of attaining pressures up to 1000 atm and temperatures as high as 5000 K (Mertens et al., 2004). Figure 1.4 shows a schematic of a typical shock tube Rapid Compression Machine A rapid compression machine (RCM) consists of a test chamber filled with reactants at low pressure and temperature. Typically, a pneumatically driven piston compresses the reactants very quickly (20-30 ms) to a specified volume in order to increase pressure and temperature to facilitate combustion. The piston must move 11

25 very fast so that heat loss is avoided and also to keep reaction from taking place until the desired pressure and temperature are reached (Mittal and Sung, 2007). Typical operating conditions are pressures from bar and temperatures from K. RCMs are excellent tools for studying high pressure autoignition of combustible mixtures in the low-to-intermediate temperature range as they provide direct measure of ignition delay. Further, autoignition chemistry can be investigated by taking out samples from the reacting mixture during the induction time and analyzing the specie concentration (Roblee, 1961). It is, however, difficult to study heavy liquid fuels in this facility, such as biodiesel or its components, due to the associated difficulty in making a homogeneous fuel-oxidizer mixture for such liquids. Fig. 1.5 shows a schematic of an RCM from Mittal and Sung (2007). Cylinder end region Reactor with quartz window, Cylinder pressure transducer, thermocouple & gas line Hydraulic Chamber Spacers for adjusting stroke Driver Piston Shims for adjusting clearance Air line from Tank Figure Schematic of an RCM (Mittal et al., 2007) Jet-Stirred Reactor A jet stirred reactor (JSR) is a steady flow device. Perfect mixing inside the reactor is achieved by employing high velocity turbulent jets. It is a fixed volume reactor with inlet and outlet for mixtures entering and exiting, respectively. Because 12

26 of high-intensity turbulent mixing, temperature and concentrations can ideally be assumed to be homogeneously distributed. The rapid mixing results in sample conditions that are purely kinetically controlled. Because of mixing, the mixture coming out from the exhaust is at the same conditions as the reactor interior mixture. The composition of the exiting mixture can be measured as a function of the residence time in the reactor. These systems operate at constant pressure and the reactor is typically made of quartz in order to withstand high temperature and to reduce surface reactions. Reactor is also enclosed in an oven and a pressure chamber to allow operation at desired temperatures and pressures. Fuel concentration is kept highly diluted (~0.1% fuel) to minimize heat release from reaction so that the reactor may be operated at steady state and uniform temperature. Figure 1.6 shows a cross-section of a JSR from the research group of Phillipe Dagaut (1986). Dr. Dagaut has extensively used this reactor to study chemical kinetics of several hydrocarbons at pressures from atmospheric to 40 bar and temperatures from K. Most important practical problem with stirred reactors is the achievement of sufficiently rapid mixing which will be discussed in detail in due course. Further, the maximum allowable temperature for operation is less than 1400 K. Reaction time scales at higher temperatures become too short to allow sufficiently rapid mixing (Dagaut et al., 1995). 13

27 Figure A jet stirred reactor (Dagaut et al., 1986) 1.4 Advantages and Challenges of JSR A major advantage of JSR is its operation as a steady flow device. This feature allows ease of experimentation with heavy liquid fuels. Study of heavy liquid fuels, for example biodiesel which consists of C >16 hydrocarbons, is almost impossible in most of the facilities discussed above. This is simply because the preheating required to obtain homogeneous fuel oxidizer mixture for heavy liquids is high and the preheated fuel-oxidizer mixture may undergo reactions in the mixing vessel itself. No wonder that so far only JSR has been used to study real biodiesel fuels (Dagaut et al., 2007). Other practical liquid fuels, which are not as heavy as biodiesel (for example 14

28 gasoline, diesel and jet fuel), and which may be studied in other facilities, are also much more easily investigated in JSR. Another advantage of JSR is that it can be used to obtain detailed speciation data over the entire low-to-intermediate temperature regime and pressures from atmospheric to high (~ 50 bar). The reacting mixture in the JSR is typically extracted and quenched by using a sonic probe and then analyzed using Gas Chromatography (GC). Detailed speciation data is necessary for assessment and optimization of chemical kinetic mechanisms and the data from the JSR allows rigorous performance analysis of kinetic mechanism and provides much needed insights into chemical kinetic pathways (Dagaut et al., 2007). JSR also offers ease of modeling. Since the conditions inside of the reactor are assumed to be steady and homogeneous, the governing equations become very simple. The concentration of species in the reactor can be computed from a balance between the net rate of production of each species during the chemical reaction and the difference between the inlet and exit flow rates. An expression for the balance can be written as ( Yout, i Yin, i m )/ V R i where Y out,i and Y in,i are the mass fractions of species i at reactor inlet and exit respectively, m is the mass flow rate, V is the volume of the reactor and R i is the mass production rate of species i per unit volume of reactor from all reactions. R i is a function of reactor pressure, temperature and mass fractions, Y out,j of all species. For a given reactor pressure, temperature, volume and mass fractions at the inlet, the set of coupled equations can be solved to yield Y out for all species. The residence time is 15

29 defined as V / m. Reactants are easily followed from low conversion to high conversion by varying the residence time. Despite of the important advantages offered by JSR in terms of ease of experimentation and modeling, the most important challenge is the achievement of sufficiently rapid mixing. An implicit assumption is that the time scale for mixing is much shorter than the chemical reaction time scales and the residence time of the reacting mixture in the reactor. In experimental situations, departure from this behavior may exist. Interestingly, there is no investigation in the literature which conclusively addresses that rapid mixing is indeed achieved. Experimental determination of homogeneity inside the reactor is possible only by laser diagnostics, which has not been attempted. Measurements by using sampling probes at various locations in the reactor have indicated homogeneity (Dagaut et al., 1986). However, the sampled compositions only represent average quantities because the sampling time period is long and therefore no conclusion can be made about the mixing inside the reactor. Recognizing the importance of addressing the issue of mixing, in this work CFD simulations are used to understand jet mixing inside the reactor, highlight the adequacy/inadequacy of the popular reactor geometries and present an alternative geometry with improved mixing characteristics. 1.5 Specific Objectives Acquisition of benchmark experimental data for developing and validating chemical kinetic mechanisms requires well-characterized experimental facilities that have minimum deviation from the desirable ideal behavior. As mentioned above, the 16

30 most important practical consideration for JSR is the achievement of sufficiently rapid mixing with high velocity turbulent jets from nozzles which enable recycling of gases. The objective of this work is to address this issue through CFD simulations. The key components of the work are as follows. a) Characterization of jet mixing inside the commonly used reactor geometries through CFD simulations. It will be shown in due course that the mixing inside the widely accepted geometries is extremely poor and the vast chemical kinetic data obtained from those is questionable. b) Conceive an alternative geometry which could provide improved mixing. c) Design and fabricate a JSR with the alternative geometry for chemical kinetic studies over a range of pressures from atmospheric to elevated. 1.6 Thesis Organization Chapter 2 of this thesis presents the methodology for determining jet dynamics inside JSR. Historical perspective is discussed along with the computational methodology for the present study. Chapter 3 presents computational results for existing geometries and highlights the problems. An alternative JSR reactor geometry is considered in Chapter 4 along with the discussion of design of a JSR. The thesis ends with Chapter 5 in which conclusions and recommendations for future work are discussed. 17

31 CHAPTER II METHODOLOGY FOR DETERMINING MIXING INSIDE JSR 2.1 Historical Perspective As discussed in Chapter 1, the greatest challenge for JSR is to ensure sufficiently rapid mixing. The criteria for the construction of JSR, that could enable rapid mixing, were deduced long ago by David and Matras (1975), namely 1) jets should be turbulent for micro-mixing, 2) the gas velocity at nozzle exits should not exceed sonic velocity and 3) the internal recycling rate should be greater than 30. These rules are discussed briefly below and they lead to relations between the residence time and the dimensions of the reactor that must be satisfied in order to achieve satisfactory mixing. The following analysis is for a spherical reactor with four nozzles arranged on a cross in the equatorial plane of the sphere. The jets issuing from the nozzles are shown as arrows (Fig. 2.1) and allow mixing and recycling of gases in the reactor. In this arrangement, the reactor can be described as the two cross-currents of recycling in perpendicular planes. Jet circulation by two nozzles in a plane is shown in Fig

32 Figure 2.1 Schematic of the reactor Figure 2.2 Jet circulation in a plane After issuing from the nozzle, the jet becomes cone shaped while curving along a circumference passing through the other nozzle. This jet can be assumed free if it satisfies the following criteria. u R

33 where, u 0 is the jet speed at nozzle exit, R is the radius of the reactor, ρ is the density of the fluid and µ is viscosity. Since u 0 4Q d 0 2 4R 3 d 3 2 where Q 0 is the volume flow rate through one nozzle, d is the diameter of the nozzle and is residence time in the reactor, we get 2 R 3 d 3 2 R for a free jet. For the case of JSRs, this condition is always realized. A gas jet entrains surrounding gas and the volume flow rate at a distance x from the nozzle can be obtained by integrating across the cross section of the jet at that location. This integration yields 3 x x R Q Qo A A d d 3 Where Q is the volume flow rate at distance x from nozzle exit and A depends on the jet cone angle. The first requirement is that the jets in the reactor should be turbulent to allow good micromixing. Reynolds number at an axial location on the jet, based on the local jet diameter, is given by 3 (4Q) 4AR Re 2x tan 6d tan Where β is the half cone angle of the jet. The condition of turbulence requires Re > 800, leading to the following relation 20

34 d 3 R c 1 (1) Where c 1 depends on the nature of the gas, pressure and temperature. This is the first criterion. The next criterion is to ensure that the gas velocity at the nozzle exit is subsonic, which imposes the following constraint. u o 4Q d o 2 4 R R c 3 d 2 2 (2) where c 2 is the speed of sound. The last creation is regarding the recycling of gases in the reactor. Turbulence alone is not sufficient and the entire volume of the reactor must be recycled several times within the residence time. According to David and Matras, the internal recycling rate of gases should be greater than 30. Recycling rate is determined by comparing the time required for the gases introduced by the jet to entrain the entire volume of the reactor, t, with the residence time,, in the reactor. V t 4Q n 1 3 2d R 3 Q0 AR Where Q n is the total flow from one nozzle due to entrainment as the jet traverses half circle and reaches the next nozzle. The recycling rate can be given by AR 30 t 2d (3) Which is the third criterion. 21

35 d (mm) N 2, 1000 K, 1 atm = 1s 1 Recycling Sonic Turbulence R(cm) Figure Reactor constraints with a residence time of 1 second at 1 atm, 800 K These three constraints can be plotted on a R vs d plot for a given residence time, pressure and temperature. A plot for nitrogen at 1000 K, 1 atm and = 1s is shown in Fig The criteria for mixing are satisfied in the triangular zone. An alternative way to present these criteria is to represent it on a vs R plot for given R/d, temperature and pressure, as shown in Fig The requirement of recycling allows R/d only greater than 64. The residence times available for a given geometry are represented by a vertical segment between the boundaries. These simplistic relations have been extremely useful as the basis for the design of several JSRs (Dagaut et al., 1986; Herbinet et al, 2007; Rota et al., 1994) that have been used for homogeneous gas phase chemical kinetic studies. 22

36 (s) 1 N 2, 1000 K, 1 atm R/d = 65 Turbulence Accessible residence time Sonic R(cm) Figure Reactor constraints on vs R plot These relations, however, fail to provide a complete description of the dynamics of the jet mixing and effect of various parameters including reactor geometry, positioning of nozzles, number of nozzles etc. on mixing. For example, there is no way to know if there are possible dead zones, the areas that are not affected by the main flow in the reactor. In this regard, CFD can significantly aid in understanding the dynamics of mixing and arriving at optimum configuration of the reactor. CFD been used widely in the design and improvement of industrial reactors. Many industrial storage tanks must be routinely stirred. This is commonly achieved with side entry of jet or jet mixers where the fluid is drawn out of the tank using a pump and returned as a high-velocity jet (Patwardhan, 2001). An example of the usefulness of CFD is the study of the hydrodynamics of jet mixing in a vessel by Jayanti (1999). From CFD simulations, it was noted that the cylindrical geometry with flat bottom 23

37 had significant dead volume and a conical bottom greatly improved the mixing (Jayanti, 2001). It is noted that such CFD simulations, while widely used in the design of industrial chemical reactors, have not been conducted for the analysis of JSRs for studying homogeneous gas phase chemical kinetics. In this work, CFD simulations are conducted for JSR. 2.2 Computational Methodology The computation methodology and specification, along with the solution strategy are detailed in this section Computational Geometry The reactor portion of a typical JSR is shown in Fig Preheated fuel+diluent mixture and oxidizer+diluent mixture are delivered to the inlet of the nozzle assembly through separate flow paths without mixing. The mixing of the fuel and oxidizer takes place inside the nozzle assembly and premixed reactants are issued from the nozzles as high velocity turbulent jets. The time duration for mixing within the nozzle assembly is kept negligible in comparison to the residence time in the reactor. The combustion products exit from the bottom cone. As an example, the reactor of Dagaut et al. (1986) consists of a sphere of diameter 4 cm and has 4 nozzles, 1 mm each. 24

38 Oxidizer +inert Fuel +inert Exit Figure A typical JSR reactor configuration In order to minimize computational time, flow through the oxidizer and fuel inlets is not included in the computational domain and nozzle exits are taken as mass flow inlets with specified stagnation temperature. The three dimensional computational domain includes the geometry of the nozzle assembly, grids inside the reactor, exit cone and the exit tube. The exit at the end of the tube is specified as pressure outlet. Details of the computational grid and grid independence of solution will be discussed in the next chapter. All walls are specified as adiabatic with no slip boundary condition. The details of the governing equations are presented in the following section. 25

39 2.2.2 Governing Equations The Fluent CFD package is used for simulations. Favre-Averaged-Navier Stokes equations, wherein velocities represent density averaged quantities, are solved in conjunction with the RNG based k-ε turbulence model. The RNG k-ε model is derived using a rigorous statistical technique called renormalization group theory (Yakhot and Orszag, 1986). It is similar in form to the standard k-ε model but includes refinements that significantly improve the accuracy for rapidly strained flows and takes into account the effect of swirl on turbulence. Therefore, the RNG k-ε model is known to provide significantly improved results where the geometry has strong curvature, and there is a large amount of swirl in the fluid (Secchiaroli et. al., 2009; Jawarneh, 2008). Favre-Averaged-Navier Stokes equations for averaged properties in Cartesian tensor form can be written as t x i u~ 0 i t ~ ~ ~ ~ p ij ij u '' '' i uiu j ui u j x j x i x j x j x j along with the ideal gas law p R T 26

40 27 Where j i i j ij k k ij x u x u x u ~ ~ ~ 3 2 ~ and the contribution from the second term on the RHS is negligible. In the above relations, an over bar indicates the mean value relative to the Reynolds averaging operation. The tilde symbol represents Favre s averaging, and the fluctuation around these values is represented by a double prime. Based on the Boussinesq hypothesis (Hinze, 1975) the Reynolds stress is related to the mean velocity gradients as follows, where t is the eddy viscosity. ij k k ij i j j i t j i k x u x u x u u u 3 2 ~ 3 2 ~ ~ '' '' The RNG based equations for the transport of turbulent kinetic energy, k, and dissipation, ε, are as follows. The overbar is removed here for convenience. k M k j eff k j i i S Y G x k x ku x k t S R k C G k C x x u x t k j eff j i i where G k represents the generation of turbulent kinetic energy due to the average velocity gradients and is modeled consistent with the Boussinesq hypothesis. i j j i k x u u u G ~ ~ ~ ' ' '' Y M represents the contribution of the fluctuating dilatation in compressible turbulence to the overall dissipation rate. It is modeled as 2 2 t M M Y based on Sarkar (1990),

41 k where M t is the turbulent Mach number. Here α 2 k and α ε are the inverse Prandtl a numbers for k and ε, respectively, computed using the following formula derived analytically by the RNG theory mol where α 0 = 1. o o eff The user-defined source terms are S k and S ε. The model constants based on RNG theory are C , C The scale elimination theory in the RNG method adds a differential equation for the turbulent viscosity as follows. d 2 k 1.72 v ˆ dˆ v v ˆ 3 1 C v where ˆ eff and C v 100 This formulation for viscosity allows better handling of low-reynolds-number and near-wall flows and approaches the standard k- model in the limit of high Reynolds number. The RNG model also provides an option to account for the effects of swirl or rotation by modifying the turbulent viscosity appropriately as follows. t to f s,, k 28

42 where μ t0 is the turbulent viscosity calculated without the swirl modification, α s is a swirl constant, set to 0.07 for moderately swirling flows, and Ω is a characteristic swirl number. The main difference between the RNG and standard k models lies in the additional term in the equation given by where Sk/, o =4.38, =0.012, C = and S is the modulus of the mean rate-of-strain tensor, defined as S 2S S ij. In comparison with the standard k ij model, this term modifies k, and effective viscosity in response to rapid strain and streamline curvature, yielding superior performance of the RNG model. The turbulent heat transport is modeled using the concept of Reynolds' analogy to turbulent momentum transfer. The modeled energy equation is as follows. The overbars are dropped for convenience. t x i keff u i ij eff x j x j E u E p i T where E is the total energy and viscous heating and is defined as eff ij is the deviatoric stress tensor representing u ui j 2 uk ij eff eff ij x j xi 3 xk 29

43 For the RNG k model, the effective thermal conductivity is Keff c p eff. Where is calculated from with 1/ Pr k / c. 0 p mol, but o o eff Turbulent flows are significantly affected by the presence of walls. The k models are primarily valid for the turbulent core. The near-wall treatment significantly impacts the fidelity of the numerical solutions. Standard wall functions for near-wall treatment require near-wall nodes to be placed in the fully turbulent region so that the wall function may adequately bridge the viscosity-affected region between the wall and the fully-turbulent region. Excessive error may occur if the near wall nodes are placed in the viscous sublayer or in the blending region between the viscous sublayer and the turbulent core. This imposes significant restriction for the near-wall grid, especially for complex flow situations. Use of enhanced wall treatment mitigates this problem for complex flows and allows improved solution for coarse as well as fine near-wall meshes. In enhanced wall treatment, the near-wall modeling is done by combining a two-layer model with an enhanced wall function. In the two-layer formulation, the whole domain is subdivided into a viscosity-affected region and a fully-turbulent region. The demarcation of the two regions is determined by a wall-distance-based turbulent Reynolds number. In the fully-turbulent region, the selected turbulence model is used and in the viscosity-affected near-wall region, a different model (Wolfstein, 1969) is used to describe turbulent viscosity. The near-wall definition of turbulent viscosity is smoothly blended with the high Reynolds number definition from the outer region by 30

44 using a blending function. The two-layer model is used in conjunction with an enhanced wall function. The enhanced wall function is attained by blending the laminar and turbulent laws of wall to obtain a single law for the entire near-wall region (Kader, 1981). The result of this treatment is that, for fine near-wall meshes, the enhanced wall treatment becomes identical to the traditional two-layer zonal models and in addition, excessive error is avoided for coarse meshes. Therefore, enhanced wall treatment is used in this work Solution Strategy The simulation strategy to determine mixing inside the reactor is as follows. The steady-state solution for the flow of air is first obtained for the given geometry and boundary conditions for specified reactor temperature, pressure and residence time. The abovementioned Favre-Averaged-Navier-Stokes, RNG k- ε and energy equation, along with the ideal gas equation of state are first solved to obtain the steady state solution using ANSYS FLUENT. ANSYS FLUENT uses a control-volume-based technique to convert the governing transport equations to algebraic equations that can be solved numerically. This control volume technique consists of integrating the transport equations about each control volume, yielding discrete equations that express the conservation laws on a control-volume basis. The governing equations for flow, turbulence and energy are discretized using the second-order upwind scheme and solved using the segregated implicit solver. SIMPLE algorithm is used for pressure-velocity coupling. At nozzle inlet, mass flow rate, stagnation temperature and turbulence intensity are specified and reactor outlet is specified as pressure outlet along with turbulence intensity and stagnation temperature for back flow. All walls are considered adiabatic. 31

45 The steady-state solution is subsequently used for the transient calculations of jet mixing inside the reactor. A tracer is injected in the flow field by specifying the tracer mass fraction as unity at the nozzle inlets for a very small duration (typically about 0.05% the residence time). The evolution of the tracer is then monitored by solving the transient scalar transport equation with the known flow-field. The transient calculations use second-order implicit formulation. The scalar transport equation is given as t Y Y Yu i Deff xi x j x j Where the effective turbulent diffusivity for mass transfer is calculated in a manner that is analogous to the method used for the heat transport. The value of 0 in Equation mol is 0 1/ Sc, where Sc is the o o eff molecular Schmidt number. Then Deff eff /. 32

46 CHAPTER III COMPUTATIONAL RESULTS FOR MIXING IN JSR 3.1 Existing Geometries This section will discuss existing geometries that were used for experimentation in the past. These geometries were used as a basis for the CFD study Phillipe Dagaut (1986) The JSR designed by Phillipe Dagaut and coworkers (1986) has been used for numerous chemical kinetic studies. This design is also often the basis for new JSR designs. Figure 3.1 shows the basic configuration of the reactor portion of their design. Figure JSR reactor design (Dagaut et al, 1986) 33

47 The entire reactor is made out of quartz due to its resistance to surface reactions and low thermal expansion. The spherical chamber is 40 mm in diameter, and the nozzles have 1 mm inner diameter. Reactants and carrier gases flow into the top of the sphere through the conical inlet. A wire heater is coiled around the inlet tube to preheat the gases before entering the reactor. The two opposing nozzles then create a counter clockwise flow in the horizontal plane, while the other two nozzles create a clockwise flow in the vertical plane. The gases mix in the spherical reactor for a residence time of seconds. A thermocouple probe and a sampling sonic quartz probe is inserted into the reactor along the axis of the exit tube. This probe can then be moved up and down to take samples and measurements at different locations using a system probe position adjuster. The measured temperature distribution inside of the reactor using a thermocouple showed temperature uniformity. Dagaut s JSR has been used for many years and has been the basis of many chemical kinetics studies (Dagaut et al., 1986) Olivier Herbinet (2007) Olivier Herbinet used a quartz JSR that was developed by Matras and Villermaux, who, as was mentioned earlier, developed the criteria to achieve sufficiently rapid mixing in a JSR. Figure 3.2 shows the reactor portion of their JSR. It is very similar to Dagaut s design. The spherical portion has a diameter of 50 mm, while the nozzles have a much smaller inner diameter of 0.3 mm. The nozzles have the same shape as Dagaut s, and create a similar flow pattern. Another difference in Herbinet s design is the annular preheating zone, seen in Fig This consists of two concentric tubes 0.5 mm from one another. The gases flow between these two tubes while a 34

48 Thermocoax heating resistance material is rolled up around the walls. Herbinet s reactor has been used for thermal decomposition studies of heavy liquid hydrocarbon fuels (Herbinet et al., 2007). Figure JSR reactor (Herbinet et al., 2007) Renato Rota (1994) The design of Renato Rota s JSR is also very similar to Dagaut (1986) and Herbinet (2007). It is made of quartz, and has a nozzle assembly closely resembling that of Dagaut et al. The spherical test chamber has a diameter of 40 mm and nozzle diameters of 1 mm. A major change in the design, however, can be seen in Fig Instead of exiting through the bottom of the reactor, the exhaust gasses exit through a tube on top that surrounds the fuel inlet tube. The burned gasses preheat the incoming gasses to the desired temperature for testing. The reactor residence time is also much 35

49 shorter than the previous designs, which was approximately 0.1 s. There are probe ports on the bottom of the reactor that allow for the sampling of species and temperature measurement, similar to Dagaut et al. Figure The design of Rota s reactor (Rota et al., 1994) Joseph Zelina (1994) Joseph Zelina et al. (1994) described a toroidal jet stirred reactor as shown in figure 3.4. The reactor is a 250 ml volume toroidal chamber made of silicon carbide. There are 48 nozzles, each with a diameter of 1 mm, located around the outside of the reactor. Gases exit the reactor through holes in the center of the toroidal chamber. It has residence times ranging from 5-12 ms (Manzello et al., 2007). This design has been used for the examination of PAH and soot formation in the combustion of 36

50 hydrocarbons (Stouffer et al., 2005). The large amount of swirl that is created by this design allows for very accurate simulation of turbine engines. This has led to many studies of synthetic jet fuels using this toroidal design (Ballal, 2008). Figure A JSR that was built based on Zelina s design (Manzello et al., 2007) 3.2 Results with Existing Geometries This section details the CFD study results obtained from the geometries and cases that closely reflect the experimental data from the existing JSRs mentioned above Cases Simulated The reactor of Dagaut et al. has been used most extensively over the past 3 decades for generating extensive data for chemical kinetic mechanism development 37

51 and validation. Most of these studies were conducted at residence time range of s at 1 atm, or residence time of 0.5-1s at 10 atm reactor pressure (Dagaut et al., 2006). Therefore, it was decided to characterize the mixing inside this geometry at relevant experimental conditions through CFD simulations. The geometry is shown in Fig The spherical reactor has 4 cm diameter. The nozzles in the reactor are situated on a cross, radially 1 cm from the center of the sphere. The cone at the exit of the sphere has height of 8 mm and diameter of 16 mm and 8 mm at the base and top, respectively. The exit tube has diameter of 2.6 cm and is 12 cm long. For convenience, only a part of the exit tube is shown. Table 3.1 presents the summary of the simulated conditions along with the evaluation of critical parameters based on the criteria of David and Matras (1975). The first four rows correspond to the reactor of Dagaut et al. and the last three have a smaller nozzle diameter of 0.25 mm to allow assessment at increased cycling rate as with the geometry of Herbinet et al. Figure 3.5 Schematic of the reactor The failure of David and Matras criteria is also highlighted in the table. It is noted that, contrary to the claims of the designers, the reactor of Dagaut et al. does not 38

52 satisfy the requirement of minimum cycling rate of 30 as well as the requirement of Reynolds number for micromixing at certain conditions. Table 3.1 Conditions simulated Critical parameters based on David and Matras criteria Nozzle diameter (mm) Reactor Diameter (cm) Residence time (s) P(bar) T (K) Reynolds # Mach # Cycling rate

53 3.2.2 Computational Grid Figure Surface mesh Figure 3.6 shows a typical surface mesh and grid distribution in selected planes is shown in Fig Grid distribution is fine inside the reactor and the cone and relatively coarser in the exit tube. The base mesh had around 17 million tetrahedral cells. In order to establish grid independence, the base grid was adaptively refined in the region of large velocity gradient and curvature. Refined grid distribution will be shown in due course. 40

54 Figure Mesh in selected planes Velocity and Temperature Field In the following, the Case with nozzle diameter = 1 mm, P = 1 bar, T = 1000 K and r = 0.09 s is first discussed in detail with respect to velocity and temperature field. 41

55 Figure Velocity distribution (m/s). Case Nozzle diameter = 1 mm, P = 1 bar, T = 1000 K, r = 0.09 s. 42

56 z-velocity x-velocity Figure Contours of speed (m/s) perpendicular to the selected planes. Case Nozzle diameter = 1 mm, P = 1 bar, T = 1000 K, r = 0.09 s. 43

57 The velocity vectors in the planes of nozzles are shown in Fig The circulation set by the jets is evident. It is also worth noticing that the downward pointing jet leads to large velocity at the exit of the sphere and may lead to short circuiting of some of the reactants without recycling. Back flow in the exit cone is also noted and it indicates the possibility of back mixing as well as turbulent diffusion at the exit of the reactor due to large gradients at the location. Fig. 3.9 presents contours of velocities perpendicular to the selected planes, i.e. z- velocity component is shown for the x-y plane and x-velocity component for the y-z plane. These contours indicate that the positioning of jets in two planes, two horizontal and 2 vertical, leads to circulation about an inclined axis. The temperature distribution in Fig is noted to be homogeneous. Figure Temperature distribution in Kelvin. Case Nozzle diameter = 1 mm, P = 1 bar, T = 1000 K, r = 0.09 s. 44

58 3.2.4 Tracer Injection and Evolution As mentioned previously, the steady-state solution was subsequently used for the transient calculations of jet mixing inside the reactor. A tracer was injected in the flow field by specifying the tracer mass fraction as unity at the nozzle inlets for a very small duration (typically about 0.05% the residence time). The evolution of the tracer was then monitored by solving the transient scalar transport equation with the known flow-field. Contours of normalized tracer mass fraction after injection are shown in Fig for the case corresponding to nozzle diameter = 1 mm, P = 1 bar, T = 1000 K, r = 0.09 s. For these simulations, time step was s. Time step independence will be presented in due course. Here short circuiting of the tracer injected by the downward pointing jet is clearly visible. The evolution of the tracer at various time steps is shown in Fig Significant non-homogeneity can be seen even at 20% residence time. The distribution at 9.77% of residence time also shows that the fluid exiting the reactor is relatively rich in tracer. Therefore, we expect to see oscillations in the tracer mass fraction at exit up to the time the tracer is not mixed reasonably well as tracer rich fluid near the exit will manifest increased outflow of tracer and tracer lean fluid near the exit will manifest decreased outflow. 45

59 Time/τ r = Figure 3.11 Evolution of tracer after injection. Normalized instantaneous mass fraction is shown. Case Nozzle diameter = 1 mm, P = 1 bar, T = 1000 K, r = 0.09 s. 46

60 Time/τ r = Figure 3.12 Normalized instantaneous mass fraction of tracer. Case Nozzle diameter = 1 mm, P = 1 bar, T = 1000 K, r = 0.09 s. 47

61 3.2.5 Characterization of Mixing In order to characterize the extent of mixing inside the reactors at various times, %-non-homogeneity can be defined as follows. dmy Yavg % non homogeneity x100 MY avg Where the summation is over all the computational cells inside the reactor, Y avg is average mass fraction of tracer inside the reactor, and M is the total mass inside the reactor. A plot for %-non-homogeneity is shown in Fig It shows the nonhomogeneity is considerable even up to duration of 20 % of the residence time. In the presence of reaction, the chemistry during this non-homogeneous phase will introduce further complications for later time. These calculations suggest that for the case under consideration (Nozzle diameter = 1 mm, P = 1 bar, T = 1000 K, r = 0.09 s), the reactor may not be considered as well stirred. Despite of that, there is plenty of experimental data at such conditions that is being used for kinetic mechanism development and validation. More insights into mixing can be obtained by looking at the evolution of the average tracer mass fraction inside the reactor. This is presented in Fig The average mass fraction is normalized with respect to the mass fraction at the end of tracer injection. In the absence of any non-idealities, the average tracer mass fraction is expected to follow an exponential decay after the injection pulse that is given by Y avg Y avg,0 e ( t / ) r, Where r is the theoretical residence time. However, deviation from such an exponential decay will be observed in the presence of non-idealities such as short-circuiting, back-mixing and non-homogeneity inside the reactor. 48

62 % non-homogeneity (time / r ) Figure % non-homogeneity. Case Nozzle diameter = 1 mm, P = 1 bar, T = 1000 K, r = 0.09 s. Further, in the absence of back-mixing and non-homogeneity, the rate of tracer outflow from the reactor would be m Yavg, where m is the mass flow rate at reactor inlet and Y avg is the average tracer mass fraction in the reactor. However, due to nonidealities, the actual outflow of tracer given by the rate of change of tracer mass in the dm reactor, tracer, can be different. A comparison of both of these mass flow rates, dt normalized by m, is also shown in Fig Here Y out, is evaluated as Y dmtracer ( 1/ m. dt out ) Large oscillations are seen in Y out that decay in amplitude and persist up to 40% of the residence time. These oscillations are due to considerable non-homogeneity in the reactor. Whenever, tracer rich fluid comes near the reactor exit, Y out shoots up and it goes down as tracer lean fluid follows. Subsequently, when the reactor is reasonably 49

63 Normalized mass fraction well mixed, Y avg and Y out follow closely as seen for time greater than 40% of the residence time. For this case, the exponential decay of the reactor mass fraction, based on Y avg, will appear to follow the correct exponential decay despite of improper mixing Y out / Y avg,0 1 Y avg / Y avg, (time / r ) Figure 3.14 Average normalized tracer mass fraction in the reactor, Y avg, and Y out. Case Nozzle diameter = 1 mm, P = 1 bar, T = 1000 K, r = 0.09 s Grid and Time Step Independence The grid was adaptively refined in the region of large velocity gradient, the refined grid for the case discussed above is shown in Fig It has approximately 4.2 million cells. The computations were performed on this grid as well and negligible quantitative differences were observed. Figure 3.16 illustrates %-non-homogeneity by using different time steps and grid distribution, demonstrating independence with respect to grid and time step. For computations of all cases, a time step of 50

64 approximately τ r /2000 was chosen and time step independence was checked for selected cases. Figure Refined mesh in selected planes 51

65 % non-homogeneity s - base grid s - base grid s - refined grid (time / r ) Figure 3.16 Demonstration of grid and time-step independence. % nonhomogeneity. Case Nozzle diameter = 1 mm, P = 1 bar, T = 1000 K, r = 0.09 s Summary of Simulated Cases for Reactor Nozzle of 1mm Results from simulations of other cases from Table 3.1 for the reactor with 1 mm nozzle are shown in Figs , and similar behavior is noted in terms of nonhomogeneity and mass fraction. 52

66 % non-homogeneity Normalized mass fraction Y out / Y avg,0 1 Y avg / Y avg, (time / r ) (time / r ) Figure 3.17 Average normalized tracer mass fraction in the reactor, Y avg, and Y out and % non-homogeneity. Case Nozzle diameter = 1 mm, P = 10 bar, T = 1000 K, r = 0.9 s. 53

67 % non-homogeneity Normalized mass fraction Y out / Y avg,0 1 Y avg / Y avg, (time / r ) (time / r ) Figure 3.18 Average normalized tracer mass fraction in the reactor, Y avg, and Y out and % non-homogeneity. Case Nozzle diameter = 1 mm, P = 10 bar, T = 1000 K, r = 0.25s 54

68 % non-homogeneity Normalized mass fraction Y out / Y avg,0 1 Y avg / Y avg, (time / r ) (time / r ) Figure 3.19 Average normalized tracer mass fraction in the reactor, Y avg, and Y out and % non-homogeneity. Case Nozzle diameter = 1 mm, P = 1 bar, T = 1000 K, r = 1 s. 55

69 3.2.8 Summary of Simulated Cases for Reactor Nozzle of 0.25mm Results for the reactor with 0.25 mm nozzles are presented in Figs and table 3.2. In contrast to 1 mm nozzle, these cases show significantly enhanced mixing and % non-homogeneity is less than 5% within 5% of the residence time. This is due to increased cycling rate. However, despite of better mixing, the cases in Figs and 3.21 show that Y out is greater than Y avg initially and less at later times. This behavior is most pronounced in Fig. 3.21, which is the case with maximum turbulence of all the cases simulated here due to higher pressure and lower residence time. A piecewise exponential decay fit to Y avg gives the following r / fit, where fit is the residence time based on the fitting and r is the theoretical residence time. Table 3.2 Numerical results for reactor with 0.25 mm nozzles. Time range (time/ r ) r / fit <

70 % non-homogeneity Normalized mass fraction 1.5 Y out / Y avg, Y avg / Y avg, (time / r ) (time / r ) Figure 3.20 Average normalized tracer mass fraction in the reactor, Y avg, and Y out and % non-homogeneity. Case Nozzle diameter = 0.25 mm, P = 1 bar, T = 1000 K, r = 1 s. 57

71 % non-homogeneity Normalized mass fraction Y out / Y avg,0 0.5 Y avg / Y avg, (time / r ) (time / r ) Figure 3.21 Average normalized tracer mass fraction in the reactor, Y avg, and Y out and % non-homogeneity. Case Nozzle diameter = 0.25 mm, P = 10 bar, T = 1000 K, r = 1s. 58

72 % non-homogeneity Normalized mass fraction 1.5 Y out / Y avg,0 1 Y avg / Y avg, (time / r ) (time / r ) Figure 3.22 Average normalized tracer mass fraction in the reactor, Y avg, and Y out and % non-homogeneity. Case Nozzle diameter = 0.25 mm, P = 1 bar, T = 1000 K, r = 4 s. 59

73 Time/τ r = Figure 3.23 Normalized instantaneous mass fraction of tracer. Case Nozzle diameter = 0.25 mm, P = 10 bar, T = 1000 K, r = 1 s. 60

74 Clearly, the exponential decay characterized by a single residence time is not valid despite of well-mixedness of the reactor. The reason for this is back-mixing and turbulent diffusion at the exit of the reactor. This effect is demonstrated by presentation of the tracer mass fraction in Fig Up to the time the tracer mass fraction in the reactor is greater than the mass fraction in the exit tube, the effect of back-mixing and turbulent diffusion at reactor exit is to provide additional outflow of tracer and Y out > Y avg. Whereas the trend reverses as the tracer mass fraction in the reactor becomes less than the mass fraction in the exit tube. This is the scenario for a non-reactive tracer. In case of reaction, back-mixing can modify the species concentrations in the reactor in a complicated manner. From the results presented in this chapter, it is clear that there are concerning issues with widely used reactor geometries. Primarily, the jet mixing may not be adequate and back-mixing can lead to additional mass flux and complications compromising the quality of acquired chemical kinetics data. 61

75 CHAPTER IV ALTERNATIVE REACTOR GEOMETRY AND DESIGN OF A JSR 4.1 Consideration of an Alternative Reactor Geometry After computational investigations of the popular reactor geometries described in Chapter 3, it was determined that they did not perform optimally. An alternative geometry, as shown in Fig. 4.1 was considered. The goal of this geometry was to eliminate the undesirable behavior shown by other geometries. Figure Alternative geometry for the reactor The reaction chamber consists of an annular region contained between the outside sphere of diameter 4 cm and an inside cylinder of diameter 1.5 cm. It has 4 nozzles. To capitalize on the increased mixing due to increased nozzle velocity, a nozzle 62

76 diameter of 0.25 mm was chosen. The nozzles were positioned on two different horizontal planes to point in the same flow direction circumferentially. The arrows in the Fig. indicate the directions of jets from the nozzles. These were oriented in a manner that promoted flow rotation about the central axis of the reactor. To eliminate the low-velocity, low-mixing area near the axis of rotation, a cylindrical section was used. It was positioned on the central vertical axis of the reactor. The gap at the bottom of cylinder allows exit of the reaction products. Exit cone and tube remained identical to the geometries discussed in Chapter 3. Figure Normalized instantaneous tracer mass fraction 63

77 Similar to the investigations in chapter 3, CFD simulation of the alternative geometry was done. The results for the tracer distribution for a residence time of 1 s at 10 bar reactor pressure are shown in Fig The tracer distribution become homogeneous rapidly. A plot of %-non-homogeneity vs. time also shows greatly improved results in Fig This geometry also avoids short circuiting of reactants that happen with a downward pointing jet. Figure % non-homogeneity for alternative reactor geometry In order to minimize the surface area to volume ratio to minimize the effect of surface reactions, a scaled version of this reactor was fabricated. The scaled version used inside sphere diameter of 6.5 cm, central cylinder diameter of 1.5 cm and 6 nozzles, each of 0.2 mm diameter. Apart from the reactor itself, the design of the present reactor system (including flow lines, pressure vessel, heating etc) was based on existing designs. 64

78 4.2 Design Features of Existing JSRs In this section, the design features of the existing JSRs are presented. These were used as the basis for the JSR designed in this work Phillipe Dagaut (1986) A detailed schematic of the entire system can be seen in Fig. 4.4 Figure Detailed schematic of Dagaut s JSR system (Dagaut et al., 1986) 65

79 The fused silica reactor portion is enclosed in a stainless steel high-pressure chamber. This allows for testing at pressures of up to 40 atm. To balance the pressure inside the quartz reactor, four holes are drilled at the bottom of its exhaust tube. Pressure is kept constant in the system with the use of a pressure regulator on the exhaust line. A safety valve prevents an unsafe pressure rise in the system. The pressure chamber is maintained at a safe temperature by use of water-cooling in the flanges. The reactor is also enclosed in a heating resistor to keep the test chamber at the desired reaction temperature. It is capable of reaching temperatures of up to 1200 K. An electrically insulated heating resistor is coiled around the inlet tube to pre-heat the fuel, oxidizer, and inert gasses to the desired temperature. The flow of fuel and oxidizer into the reactor are measured and regulated by thermal mass-flow controllers. The diluent flow is measured with flow rotameters. Fuel and oxidizer flow into the reactor separately and are mixed just before entering the nozzle portion. This is done to reduce pyrolysis or oxidation of the fuel before issuing from the nozzles (Dagaut et al., 1986). Data is obtained from the reactor by use of a chromel-alumel thermocouple probe and a sampling sonic quartz probe. They are inserted into bottom of the pressure chamber through the exhaust tube. They both can be moved vertically throughout the test chamber by means of a system probe position adjuster. The thermocouple wires are enclosed in a double-core alumina tube. This is done to protect the thermocouple from the high temperatures in the test chamber. That tube is attached to the sampling probe and both are encased in a quartz tube. The probes are sealed to prevent leaks with Araldite glue. Samples from the sonic probe are analyzed by gas chromatography (Dagaut et al., 1986). 66

80 4.2.2 Olivier Herbinet (2007) The reactor portion of Herbinet s JSR is very similar to that of Dagaut (1986), but there are major differences between them when the entire system is considered. Herbinet s JSR was designed to study heavy liquid hydrocarbon fuels. High pressures were not required for his design, so the operating pressure is near atmospheric (~106 kpa). The pressure is maintained manually via a control valve in the JSR s exhaust tube. The liquid hydrocarbon fuels are prepared for testing using a controlled mixer and evaporator. A schematic of Herbinet s flow and sampling system can be seen in Fig Figure A schematic of Herbinet s JSR system (Herbinet et al., 2007) 67

81 It can be seen from the figure that there are liquid and gas mass flow controllers in the system upstream from the controlled mixer and evaporator. The liquid mass flow controller can be adjusted to allow between 1 and 50 g/h of hydrocarbon fuel to flow into the system. The gas mass flow controller holds the flow rate constant (Herbinet et al., 2007). Liquid reactant and nitrogen is prepared for experimentation in a pressurized vessel. Here, oxygen traces are removed through nitrogen bubbling and vacuum pumping. From the controlled mixer and evaporator, the mixture flows into the reactor. Another major difference in this design from Dagaut s is that there are no sampling probes inside the reactor. Type K thermocouples measures the temperature of the flow before entering the reactor. The lighter samples are taken from the exhaust and are frozen in an ice bath. Heavier species are quenched in a liquid nitrogen bath. Analysis of these samples is done on-line with two gas chromatographs set in parallel. This JSR is capable of operating at temperatures of K, with residence times between 1 and 5 s (Herbinet et al., 2007) Renato Rota (1994) Rota s JSR system is similar to the previous examples in that it consists of three main sections. First, the fuel, oxidizer and inert gasses are prepared for testing. They are combined and react inside of the reactor portion, and finally samples are taken to be analyzed using gas chromatography. Fuel, air, and nitrogen are stored separately. Mass flow controllers regulate the flow of each. Prior to flowing into the reactor, the fuel is diluted with nitrogen. The diluted fuel then flows into the reactor separately from the air to be pre-heated. The 68

82 fuel and air are mixed just before entering the nozzle arrangement. As shown in Fig. 4.6, the reactor portion of Rota s design is enclosed in an oven. A chromel-alumel thermocouple is used to measure temperature in the reactor. It is necessary to correct the measurements for radiant heat exchange effects since the temperature of the surroundings are higher than inside the reactor. The JSR can operate at temperatures of K (Rota et al, 1997). fuel + N 2 fuel air air probe water N 2 N 2 vacuum mass flow controller GC Figure A basic schematic of Rota s JSR system (Rota et al., 1994) Samples are taken from the reactor using a sonic quartz probe. A vacuum pump creates very low pressures inside of the sampling probe to allow samples to be taken. The entire probe is jacketed with cooling water in order to freeze the samples taken to 69

83 instantly stop reactions. These samples are then analyzed in a gas chromatograph (Rota et al, 1997). A unique feature of this design is heat recovery flow system in which hot exhaust from reactor is used to partially heat the incoming reactants. 4.3 Design of the Present JSR Fig. 4.7 shows the cross sectional view of a 3D model of the reactor portion as well as an image of the actual reactor that was fabricated at The University of Akron. 70

84 Figure Cross-section views of the final reactor design and image The reactor is made of fused silica with a nozzle assembly for the entry of the reactants. The reaction chamber consists of the annular region contained between the fused silica sphere (inside diameter 6.5 cm) and an inside cylinder (diameter 1.5 cm). There are six nozzles, each with a diameter of 0.2 mm, to provide circulation in horizontal plane. 71

85 A concern of this design was surface reactions in the test chamber. To reduce the effects of surface reactions, a sphere diameter of 6.5 cm was used, compared to Dagaut s sphere diameter of 4 cm. This was done to increase the volume-to-wall area ratio. It was also previously determined that at temperatures below 700 o C, surface reactions on quartz and fused silica are almost negligible (Deal et al., 1965). Impurities on the quartz surface can lead to increased wall reactions, but the material properties of quartz give an apparent zero porosity, meaning that it is very easy to clean. The two holes shown at the bottom of the sphere in Fig. 4.7 are for the thermocouple and sampling probes. The attached cones simply aid in assembly by directing the probes into the holes. A cylindrical quartz rod is attached to the bottom of the reactor to support it inside of the pressure chamber and heating oven. Preheated fuel+diluent mixture and oxidizer+diluent mixture are delivered to the inlet of the nozzle assembly through separate flow paths without mixing (see Figs. 4.7 and 4.8). The mixing of the fuel and oxidizer takes place inside the nozzle assembly and premixed reactants are issued from the nozzles as high velocity turbulent jets. The stirring of the reactants inside the reactor by high velocity turbulent jets from nozzles enables recycling of gases within the reactor. In order to perform experiments at elevated pressures, the reactor is enclosed inside a 303 stainless steel pressure chamber. The section view of the pressure chamber is shown in Fig The pressure chamber consists of a tube with 10 inch inside diameter and ½ inch thickness that is 3 feet long. Two 2.5 inch thick square stainless steel flanges seal the tube on each end. Flow channels are machined in the metal flanges to allow water-cooling. Operation at high pressures (up to 50 bar) is made possible by means of pressure balancing inside and outside of reactor. 72

86 oxygen+inert fuel+inert cooling water exhaust ceramic heater pressure vessel sampling probe thermocouple probes Figure Schematic of the reactor, heater, and pressure vessel with probes The reactor is surrounded by a high temperature 1250 W ceramic radiant heater that maintains it at constant temperature up to 1400 K. Three thermocouple probes are used for temperature measurement and control. One is inserted into the spherical reactor. The other two are positioned outside of the reactor but inside the ceramic heater. Ceramic fiber insulation is placed below the heater as well as at the top to 73

87 insulate the bottom and top flanges of the pressure vessel. In addition, the top flange is cooled with water-cooling channels, as shown in Fig The design incorporates recovery of energy from the exhaust gases to aid in preheating of the reactants, which is similar to Rota s design (1994). It can be seen in Fig. 4.7 and also in 4.9 that the hot gases exit the reactor (shown in orange in Fig. 4.9) through a hole at its top that surrounds the tube containing the incoming reactants. The exhaust flows between two tubes that have incoming reactants for approximately 0.57 m. Figure 4.9 shows that the inner tube containing the incoming reactants is connected to the outermost tube. This allows the reactants to flow through both tubes (shown in blue) while the hot exhaust (orange) gases flow between them. The flow through the inner reactant tube is much smaller than the outer tube. Apart from heat recovery, sufficient heating is also achieved by ceramic heaters surrounding the reactor. The schematic of the flow system is shown Fig Oxygen and diluting nitrogen are stored in tanks and their flow is controlled with pressure regulators. Sonic nozzles calibrated by using a wet gas meter are placed in the lines to ensure that a constant metered flow of oxygen and nitrogen is achieved. The nitrogen flow is split to mix partially with fuel and oxygen. Fuel is stored in a precision syringe pump to ensure that the correct amount of fuel is being introduced into the system. Heated nitrogen is used to vaporize fuel injected in a heated chamber. Heating ropes are used to maintain fuel+inert flow at high temperatures to avoid condensation in line. After reaction in the reactor, the exhaust flow is cooled in a water bath and a back pressure regulator is used to maintain the desired pressure in the pressure vessel and the reactor. 74

88 The complete reactor system, shown in Fig. 4.11, was completely designed, fabricated and assembled as part of this thesis. No investigations with the fabricated reactor could be conducted though. 75

89 Figure Recovery of energy from exhaust gas 76

90 pressure gauge O 2 sonic nozzle N 2 pressure regulator heater syringe pump fuel + inert back cooling pressure regulator heating rope reactor Figure A schematic of the flow system 77

91 Figure 4.11 Image of the JSR system 78