This thesis aims to make advances in the accurate simulation of the ows in and around clustered module plug nozzles. The resulting simulations presented in this thesis are, as far as can be ascertained from available data, the most detailed to date in Europe. A comparison is made with results from other sources for clarication of this point. In the process of producing these solutions, two ow solvers have been developed. NSAXIMB is a general 2D multi-block ow solver,developed by the author, for the axisymmetric, Reynolds averaged Navier-Stokes equations. It was developed to allow simulation of axisymmetic plug nozzle congurations and the investigation of the effects of turbulence modelling on such ows. MERLIN is a general 3D, implicit, multi-block ow solver again for the RANS equations. MERLIN was developed by the Centre for Computational uid Dynamic at Craneld. Signicant input from this work has included a large portion of the structure of the mean ow solver and the extension of the advanced two equation turbulence modelling, incorporated in NSAX- IMB, to three dimensions. Of the turbulence models investigated the zonal models of Menter prove to be most effective in reproducing experimental results. These models out perform a more advanced non-linear eddy viscosity formulation, based on the work of Abid. In an effort to improve solution accuracy, grid adaptation software, based on node redistribution techniques has been developed for use in conjunction with the 3D ow solver. This work is demonstrated in conjunction with a basic test case before application to the clustered module plug nozzle conguration. Results for the complex block topology adopted in the 3D test case are shown to cause the adaptation process to fail. Further, it is shown that such a process may not be generalised for arbitrary topologies.

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.

abstract: The aerospike nozzle belongs to the class of altitude compensating nozzles making it a strong candidate for Space Shuttle Main Engines. Owing to their higher efficiency compared to conventional bell nozzles, the aerospike nozzles are being studied extensively and are being used for many Single State to Orbit (SSTO) designs. A rocket engine nozzle with altitude compensation, such as the aerospike, consumes less fuel than a rocket engine with a bell nozzle. Aerospike nozzles are huge and are often difficult to construct and have to be truncated in order to make them feasible for application in a rocket propulsion system. Consequently, truncation of the aerospike leads to pressure loss under the base, which in-turn decreases the overall thrust produced by the rocket nozzle. To overcome this loss, a technique called base bleed is implemented in which a secondary jet is made to flow through the base of the truncated portion. This thesis uses dynamic pressure contour plots to find out the ideal base bleed mass flow rate to avoid base recirculation in 10 %, 20 % and 30 % truncated aerospike nozzles. / Dissertation/Thesis / Masters Thesis Mechanical Engineering 2017

Supersonic micronozzles operate in the unique viscosupersonic flow regime, characterized by large Mach numbers (M>1) and low Reynolds numbers (Re<1000). Past research has primarily focused on the design and analysis of converging-diverging de Laval nozzles; however, plug (i.e. centerbody) designs also have some promising characteristics that might make them amenable to microscale operation. In this study, the effects of plug geometry on plug micronozzle performance are examined for the Reynolds number range Re = 80-640 using 2D Navier-Stokes-based simulations. Nozzle plugs are shortened to reduce viscous losses via three techniques: one - truncation, two - the use of parabolic contours, and three - a geometric process involving scaling. Shortened nozzle are derived from a full length geometry designed for optimal isentropic performance. Expansion ratio (ε = 3.19 and 6.22) and shortened plug length (%L = 10-100%) are varied for the full Reynolds number range. The performance of plug nozzles is then compared to that of linear-walled nozzles for equal pressure ratios, Reynolds numbers, and expansion ratios. Linear-walled nozzle half-angle is optimized to to ensure plug nozzles are compared against the best-case linear-walled design. Results indicate that the full length plug nozzle delivers poor performance on the microscale, incurring excessive viscous losses. Plug performance is increased by shortening the nozzle plug, with the scaling technique providing the best performance. The benefit derived from reducing plug length depends upon the Reynolds number, with a 1-2% increase for high Reynolds numbers an up to 14% increase at the lowest Reynolds number examined. In comparison to Linear-walled nozzle, plug nozzles deliver superior performance when under-expanded, however, this trend reverses at low pressure ratios when the nozzles become over-expanded.