This study involves the modeling of small cold-gas (N2) thrusters nozzle and plume flows, their interactions with spacecraft surfaces and the induced pressure environment. These small cold-gas thrusters were used for pitch, yaw and roll control and were mounted on the bottom of the conical Environmental Monitor Payload (EMP) suborbital spacecraft. The pitch and yaw thrusters had 0.906 mm throat diameter and 4.826 mm exit diameter, while the roll thrusters had 1.6 mm throat diameter and 5.882 mm exit diameter. During thruster firing, at altitudes between 670 km and 1200 km, pressure measurements exhibited non-periodic pulses (Gatsonis et al., 1999). The pressure sensor was located inside the EMP and was connected to it's sidewall with a 0.1-m long, 0.022-m diameter tube and the pressure pulses appeared instantaneously with the firings for thrusters without a direct line-of-sight with the sensor entrance. Preliminary analysis showed that the plume of these small EMP thrusters undergoes transition from continuous to rarefied. Therefore, nozzle and plume simulations are performed using a combination of Navier-Stokes and Direct Simulation Monte Carlo codes. This study presents first a validation of the Navier-Stokes code Rampant used for the continuous EMP nozzle and plume simulations. The first Rampant validation example involves a two-dimensional axisymetric freejet expansion and is used to demonstrate the use of Bird's breakdown parameter. Results are compared favorably with those of Bird (1980) obtained through the method of characteristics. The second validation example involves three-dimensional plume simulations of a NASA thruster. This nitrogen nozzle has a throat diameter of 3.18 mm, an exit diameter of 31.8 mm, half-angle of 20 degrees, stagnation temperature of 699 K, stagnation pressure of 6,400 Pa. Simulation results are compared favorably with previous Navier-Stokes and Direct Simulation Monte Carlo numerical work. The third validation example involves three-dimensional simulations of Rothe's (1970) nozzle that has a throat diameter of 2.5 mm, an exit diameter of 20.3 mm, half-angle of 20 degrees, operating at stagnation temperature of 300 K and pressure of 1975 Pa. Numerical results also compared favorably to experimental data. The combined Navier-Stokes/DSMC approach and the EMP simulation results are presented and discussed. The continuous part of the EMP nozzle and plume flow is modeled using the three-dimensional Navier-Stokes Rampant code. The Navier-Stokes domain includes the geometry of the nozzle and the EMP base until transition of the continuous flow established by Bird's breakdown parameter. The rarefied part of the plume flow is modeled using the Direct Simulation Monte Carlo code DAC. Flowfield data obtained inside the breakdown surface from the Navier-Stokes simulation are used as inputs to the DSMC simulations. The DSMC domain includes the input surface and the EMP spacecraft geometry. The combined Navier-Stokes/DSMC simulations show the complex structure of the plume flow as it expands over the EMP surfaces. Plume reflection and backflow are demonstrated. The study also summarizes findings presented by Gatsonis et al. (2000), where the DSMC predictions at the entrance of the pressure sensor are used as inputs to a semi-analytical model to predict the pressure inside the sensor. It is shown that the pressure predictions for the pitch/yaw thrusters are close to the measurements. The plume of a pitch or yaw thruster reaches the pressure sensor after expanding on the EMP base. The pressure predicted for the roll thruster is larger that the measured. This is attributed to the uncertainty in the roll thruster location on the EMP base resulting, in the simulation, in a component of direct flow to the sensor.

As drop-on-demand (DOD) applications continue to gain ground in desktop inkjet-printing, 3D printing, fluid mixing, and other areas the demand for higher frequency operations are beginning to push against the current physical boundaries in DOD technology. The current research is exploring the possibility of controlling drop volume and velocity at high frequency ranges where meniscus vibrations can occur between drop formations and affect drop formation characteristics. A periodic voltage is applied to a piezoelectric disk in order to generate pressure fluctuations in a single nozzle droplet generator, causing the fluid meniscus at the nozzle to vibrate. A single stronger pulse is then superimposed over the periodic waveform at different phases in order to drive drop ejection. The characteristics of the resulting drop, specifically the volume and velocity, are experimentally measured using a high speed camera with precise timing control. The results of these experiments are then compared to a lumped element model (LEM) developed for the droplet generator geometry used. Within the LEM model framework, special attention was given to the definition of a novel method by which one can measure drop volume within an electroacoustic circuit and also allow meniscus dynamics to affect present and future drop formations. Experimental results indicate a strong dependence of both drop volume and drop velocity on the phase of the vibrating meniscus at the start of drop formation. Positive meniscus displacements and momentums resulted in large drop volumes and velocities while negative displacements could reduce drop volume or altogether eliminate drop formation. Specifically, positive displacements and momentum of a vibrating meniscus could lead to drop volumes approximately 50% larger than the original drop volume without a vibrating meniscus. Meanwhile, negative meniscus displacements and momentums were shown to have the ability to completely prevent drop formation. Additional potential for drop characteristic control with a vibrating meniscus is discussed alongside observations on the stabilizing affect the vibrating meniscus appears to have on drop velocity as a function of time. Also, flow visualization of the drop formation is provided to demonstrate the added affect the meniscus vibrations have on the drop shapes and break-off profiles. The LEM model presented demonstrates qualitative agreement with the experimental model, but fails to quantitatively predict drop volumes. Sources of error for the LEM model and potential improvements are discussed. / Graduation date: 2012

Plug nozzle, a passive altitude adaptive nozzle, for futuristic SSTO applications, exhibits greater efficiency as compared to conventional nozzles over a wide range of altitudes. The plug nozzle comprises of a primary nozzle and a contoured plug; an under–expanded jet exiting the primary nozzle is allowed to further expand over the plug surface for altitude adaptation. At design condition the flow expands correctly to the ambient conditions on the full length plug surface, while at off design conditions the flow adapts to the ambient conditions through wave interactions within the nozzle core jet. Based on thrust to weight considerations, the full length plug is truncated and this results in a base flow rich in flow physics. In addition, the base flow exhibits an interesting transitional behaviour from open wake to a closed wake because of the wave interactions within the nozzle core jet. The plug surface flow can further exhibit flow complexities because of wave interactions resulting from the shear layer emanating from the splitter plates, in case of clustered plug flows. Considering these flow complexities, the design of the plug nozzles and analysing the associated flows can be a challenge to the aerodynamic community. An attempt has been made in understanding this class of flows in this thesis. This objective has been accomplished using both experimental and computational tools. In the present work, both the linear and annular plug nozzle geometries have been analysed for a wide range of pressure ratios spanning from 5to 80. The linear and annular nozzles have been designed for similar flow conditions and their respective design pressure ratios are 60and 66. From the experimental and computational results, it has been shown that the computational solver performs well in predicting the wave interactions on the plug surface. In addition the limitations of the computational solver in predicting the plug base flows in general has been brought out. This limitation in itself need not be considered as a serious handicap in the design and analysis of plug nozzle flows; this is because the plug base contribution to the thrust is very minimal, as has been brought out in this thesis. Apart from this the high quality experimental data generated is also of immense value to the CFD community as this also serves as a valuable data base for CFD code validation. For analysis, the plug flow field has been categorized into three different regimes based on the primary nozzle lip expansion fan extent. The flow field is categorised based on the reflection of the primary nozzle lip expansion fan from plug surface, base region shear layer and symmetry line downstream of the base region recirculation bubble. This flow division is particularly helpful in understanding the base wake characteristics with increasing pressure ratio. The base lip pressure and the base pressure variation have been discussed with respect to the primary nozzle lip expansion fan extent. In the open wake regime (or for low pressure ratios) the wave interactions within the core jet flow impinge on the base region shear layer. Because of these interactions it is difficult to propose an empirical model for open wake base pressure. In the closed wake regime (for higher pressure ratios), the base region recirculation bubble is completely under the shower of primary nozzle lip expansion fan. Hence the base lip pressure and base pressure are frozen with respect to stagnation conditions. Based on these insights it was possible to propose empirical models for linear and annular closed wake base pressure. Along with these, a mathematical model defining a reference pressure ratio PR∗, beyond which the closed wake base pressure is expected to be more than the ambient pressure has also been proposed. This is expected to serve as a good design parameter. In case of linear plug flows, this also serves the purpose of base wake transition, for the cases considered in this thesis. The flow expansion process or the primary nozzle lip expansion fan extent was also useful in understanding the differences between the linear and annular plug nozzle flow fields. In a linear plug nozzle, the flow expands only in the streamwise direction while in an annular plug nozzle the flow expands both along the streamwise and azimuthal directions. The flow expands at a faster rate in case of annular nozzle as against linear nozzle. Hence differences are observed between the linear and annular nozzle on plug and base surfaces. On the annular plug surface more wave interactions are observed because of faster expansion. With regard to base characteristics, faster expansion in annular plug nozzle, with respect to linear nozzle, results in a lower base lip pressure, lower base pressure and higher wake transition pressure ratio. The realistic cluster plug configurations have also been considered for the present studies. The effects of clustering on the plug nozzle flow field have been brought out by considering two different linear cluster nozzles and one annular cluster nozzle. The differences in the flow field of a simple and cluster plug nozzle has been discussed. In case of simple plug nozzle wave interactions are observed only in the stream wise direction, while in case of cluster plug nozzle three dimensional wave interactions are observed because of the splitter plates. Along the splitter plate differential end conditions introduce a curved recompression shock on the plug surface. This recompression shock in turn induces a streamwise vortex and also a secondary shock. It has been observed that differences between the simple and cluster plug surface pressure field are because of three dimensional wave interactions. Regarding the base pressure, differences between the simple and cluster geometries were observed for shorter truncation plug lengths (20% length plug). While for longer plug lengths (more than 34% length) the effects of clustering were reduced on the base pressure. Regarding the transition pressure ratio, differences were observed between simple and clustered plug nozzles for all the plug lengths considered. In addition, the performance of the plug nozzles has been carried out. From the analysis it was found that the primary nozzle and plug surface are major contributors towards thrust. The base surface contributes only about 2– 3% of the thrust at design condition. Hence, from a design point of view, a computational solver can be a useful tool considering its efficacy on the plug surface and in the primary nozzle.

Plug nozzle, a passive altitude adaptive nozzle, for futuristic SSTO applications, exhibits greater efficiency as compared to conventional nozzles over a wide range of altitudes. The plug nozzle comprises of a primary nozzle and a contoured plug; an under–expanded jet exiting the primary nozzle is allowed to further expand over the plug surface for altitude adaptation. At design condition the flow expands correctly to the ambient conditions on the full length plug surface, while at off design conditions the flow adapts to the ambient conditions through wave interactions within the nozzle core jet. Based on thrust to weight considerations, the full length plug is truncated and this results in a base flow rich in flow physics. In addition, the base flow exhibits an interesting transitional behaviour from open wake to a closed wake because of the wave interactions within the nozzle core jet. The plug surface flow can further exhibit flow complexities because of wave interactions resulting from the shear layer emanating from the splitter plates, in case of clustered plug flows. Considering these flow complexities, the design of the plug nozzles and analysing the associated flows can be a challenge to the aerodynamic community. An attempt has been made in understanding this class of flows in this thesis. This objective has been accomplished using both experimental and computational tools. In the present work, both the linear and annular plug nozzle geometries have been analysed for a wide range of pressure ratios spanning from 5to 80. The linear and annular nozzles have been designed for similar flow conditions and their respective design pressure ratios are 60and 66. From the experimental and computational results, it has been shown that the computational solver performs well in predicting the wave interactions on the plug surface. In addition the limitations of the computational solver in predicting the plug base flows in general has been brought out. This limitation in itself need not be considered as a serious handicap in the design and analysis of plug nozzle flows; this is because the plug base contribution to the thrust is very minimal, as has been brought out in this thesis. Apart from this the high quality experimental data generated is also of immense value to the CFD community as this also serves as a valuable data base for CFD code validation. For analysis, the plug flow field has been categorized into three different regimes based on the primary nozzle lip expansion fan extent. The flow field is categorised based on the reflection of the primary nozzle lip expansion fan from plug surface, base region shear layer and symmetry line downstream of the base region recirculation bubble. This flow division is particularly helpful in understanding the base wake characteristics with increasing pressure ratio. The base lip pressure and the base pressure variation have been discussed with respect to the primary nozzle lip expansion fan extent. In the open wake regime (or for low pressure ratios) the wave interactions within the core jet flow impinge on the base region shear layer. Because of these interactions it is difficult to propose an empirical model for open wake base pressure. In the closed wake regime (for higher pressure ratios), the base region recirculation bubble is completely under the shower of primary nozzle lip expansion fan. Hence the base lip pressure and base pressure are frozen with respect to stagnation conditions. Based on these insights it was possible to propose empirical models for linear and annular closed wake base pressure. Along with these, a mathematical model defining a reference pressure ratio PR∗, beyond which the closed wake base pressure is expected to be more than the ambient pressure has also been proposed. This is expected to serve as a good design parameter. In case of linear plug flows, this also serves the purpose of base wake transition, for the cases considered in this thesis. The flow expansion process or the primary nozzle lip expansion fan extent was also useful in understanding the differences between the linear and annular plug nozzle flow fields. In a linear plug nozzle, the flow expands only in the streamwise direction while in an annular plug nozzle the flow expands both along the streamwise and azimuthal directions. The flow expands at a faster rate in case of annular nozzle as against linear nozzle. Hence differences are observed between the linear and annular nozzle on plug and base surfaces. On the annular plug surface more wave interactions are observed because of faster expansion. With regard to base characteristics, faster expansion in annular plug nozzle, with respect to linear nozzle, results in a lower base lip pressure, lower base pressure and higher wake transition pressure ratio. The realistic cluster plug configurations have also been considered for the present studies. The effects of clustering on the plug nozzle flow field have been brought out by considering two different linear cluster nozzles and one annular cluster nozzle. The differences in the flow field of a simple and cluster plug nozzle has been discussed. In case of simple plug nozzle wave interactions are observed only in the stream wise direction, while in case of cluster plug nozzle three dimensional wave interactions are observed because of the splitter plates. Along the splitter plate differential end conditions introduce a curved recompression shock on the plug surface. This recompression shock in turn induces a streamwise vortex and also a secondary shock. It has been observed that differences between the simple and cluster plug surface pressure field are because of three dimensional wave interactions. Regarding the base pressure, differences between the simple and cluster geometries were observed for shorter truncation plug lengths (20% length plug). While for longer plug lengths (more than 34% length) the effects of clustering were reduced on the base pressure. Regarding the transition pressure ratio, differences were observed between simple and clustered plug nozzles for all the plug lengths considered. In addition, the performance of the plug nozzles has been carried out. From the analysis it was found that the primary nozzle and plug surface are major contributors towards thrust. The base surface contributes only about 2– 3% of the thrust at design condition. Hence, from a design point of view, a computational solver can be a useful tool considering its efficacy on the plug surface and in the primary nozzle.