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Nozzle configuration has been defined through a numerical campaign with the aim to verify the influence of convergent length, convergent angle, radius of curvature at the throat and divergent angle on the overall performaces and wall heat flux. More than 30 configurations have been analysed; results for three meaningful configurations are shown in Figure 10. Wall heat flux determined on these configurations is shown in Figure 11: the analysis shows that the highest peak of heat flux has been obtained for test case 1, where the convergent is characterized by the smallest length. The lowest peaks are associated to the longest convergent, but in this case the highest average and integral values is

Figure 10 Nozzle configuration has been defined through a numerical campaign with the aim to verify the influence of convergent length, convergent angle, radius of curvature at the throat and divergent angle on the overall performaces and wall heat flux. More than 30 configurations have been analysed; results for three meaningful configurations are shown in Figure 10. Wall heat flux determined on these configurations is shown in Figure 11: the analysis shows that the highest peak of heat flux has been obtained for test case 1, where the convergent is characterized by the smallest length. The lowest peaks are associated to the longest convergent, but in this case the highest average and integral values is

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A typical architecture for the thruster has been considered, with liquid oxidizer and solid fuel presented in Figure | and a cylindrical port has been chosen. The rocket is constituted by a solid grain enveloped in an external metallic case, the injection head providing the injection of the oxidizer into the combustion chamber at suitable conditions, and the expansion nozzle. Along the feeding line, connecting the thrust chamber to the tank, oxidizer regulation valve for mass flow rate control are located. The 30 kN demonstrator has been preliminary sized using an in-house developed design tool composed by twc modules: trade-off module, which carries out the preliminary sizing of the solid grain by varying geometriacal anc operational parameters of the engine, and performance module which evaluates the performances of the selectec configuration. The procedure that has been definedis schematically shown in Figure 2: the first step of the numerica procedure of the trade off module relies with the interface Rocket Propulsion Analysis [8] used to evaluat theoretical 0-D rocket performance, optimal mixture ratio to maximize the specific impulse. Trade off module i: able to analyze several configurations by varying grain length, port diameter, oxidizer mass flow rate, regression rate model and chamber pressure and to evaluate for each of them the main performance parameters (Thrust, Isp, Tc, Pc O/F, etc.). As the mass flow rate is updated with the grain consumption (taken into account by implementing different regression rate models) the tool updates the main parameters with time by reading a proper externa database.
A typical architecture for the thruster has been considered, with liquid oxidizer and solid fuel presented in Figure | and a cylindrical port has been chosen. The rocket is constituted by a solid grain enveloped in an external metallic case, the injection head providing the injection of the oxidizer into the combustion chamber at suitable conditions, and the expansion nozzle. Along the feeding line, connecting the thrust chamber to the tank, oxidizer regulation valve for mass flow rate control are located. The 30 kN demonstrator has been preliminary sized using an in-house developed design tool composed by twc modules: trade-off module, which carries out the preliminary sizing of the solid grain by varying geometriacal anc operational parameters of the engine, and performance module which evaluates the performances of the selectec configuration. The procedure that has been definedis schematically shown in Figure 2: the first step of the numerica procedure of the trade off module relies with the interface Rocket Propulsion Analysis [8] used to evaluat theoretical 0-D rocket performance, optimal mixture ratio to maximize the specific impulse. Trade off module i: able to analyze several configurations by varying grain length, port diameter, oxidizer mass flow rate, regression rate model and chamber pressure and to evaluate for each of them the main performance parameters (Thrust, Isp, Tc, Pc O/F, etc.). As the mass flow rate is updated with the grain consumption (taken into account by implementing different regression rate models) the tool updates the main parameters with time by reading a proper externa database.
Figure 2 - Design and performance tool procedure
Figure 2 - Design and performance tool procedure
Figure 3 - Thrust vs grain length. The performed choice of length is, moreover, in the region diagram (see Figure 3) where the variation of thrust with port dimeter is negligible (about 1%), therefore as the firing time increases the thrust is constant with the grain consumption and, as the nominal thrust is not effected by re-ignition, at least from a theoretical point of view.
Figure 3 - Thrust vs grain length. The performed choice of length is, moreover, in the region diagram (see Figure 3) where the variation of thrust with port dimeter is negligible (about 1%), therefore as the firing time increases the thrust is constant with the grain consumption and, as the nominal thrust is not effected by re-ignition, at least from a theoretical point of view.
As clear from the previous diagrams, there is a certain region in terms of grain length where performances are quite insensitive to port diameter, that means constant along the burning time. This is is part due to the selected regression model due to Grosse, experimentally determined for the same paraffin considered in the present work, but also to the fact that for these values some different effects on engine performances vary and partially compensate each other. It is know that in hybrid engines, O/F ratio decreases with time due to the increasing of grain port diameter and the decreasing of regression rate, and therefore fuel mass flow, while oxidizer mass flow is often kept as constant. This means that combustion paramaters, as chamber temperature, thrust coefficient and characteristic velocity, also vary during the burning time and follow the theoretical values shown in Figure 5; the maximum of the three curves reported in this figure takes place at different values of O/F ratio therefore there is a range of O/F variation where the variation of chamber temperature, thrust coefficient and characteristic velocity partially compensates to provide an almost constant thrust and specific impulse.
As clear from the previous diagrams, there is a certain region in terms of grain length where performances are quite insensitive to port diameter, that means constant along the burning time. This is is part due to the selected regression model due to Grosse, experimentally determined for the same paraffin considered in the present work, but also to the fact that for these values some different effects on engine performances vary and partially compensate each other. It is know that in hybrid engines, O/F ratio decreases with time due to the increasing of grain port diameter and the decreasing of regression rate, and therefore fuel mass flow, while oxidizer mass flow is often kept as constant. This means that combustion paramaters, as chamber temperature, thrust coefficient and characteristic velocity, also vary during the burning time and follow the theoretical values shown in Figure 5; the maximum of the three curves reported in this figure takes place at different values of O/F ratio therefore there is a range of O/F variation where the variation of chamber temperature, thrust coefficient and characteristic velocity partially compensates to provide an almost constant thrust and specific impulse.
The present configuration has been analyzed in terms of performance parameters as function of burning time. Ir particular, as already underlined, a negligible decrease (about 1%) of thrust and chamber pressure is predictec during the burning time (see Figure 6 and Figure 7) and also specific impulse is almost constant as shown in Figure 8). It is worth to underline that present results do not consider throat regression due to ablation that will cause ¢ stronger decrease of chamber pressure with time and a consequently decay of all performance parameters.
The present configuration has been analyzed in terms of performance parameters as function of burning time. Ir particular, as already underlined, a negligible decrease (about 1%) of thrust and chamber pressure is predictec during the burning time (see Figure 6 and Figure 7) and also specific impulse is almost constant as shown in Figure 8). It is worth to underline that present results do not consider throat regression due to ablation that will cause ¢ stronger decrease of chamber pressure with time and a consequently decay of all performance parameters.
American Institute of Aeronautics and Astronautics
American Institute of Aeronautics and Astronautics
Figure 8 - Isp vs time B. HRE DEMONSTRATOR SUB-SYSTEMS
Figure 8 - Isp vs time B. HRE DEMONSTRATOR SUB-SYSTEMS
This preliminary design has been also verified through detailed numerical analyses carried out in cavitating conditions with Open Foam solver [12]; numerical results are close to the prediction of the engineering method, with an error on the estimated mass flow rate through the single injector less than 5%. Numerical computations highlighted that the cavitation starts the injector inlet, with a steep phase change at the injector exit as shown in Figure 9 where density contours for one of the analysed configuration are reported.
This preliminary design has been also verified through detailed numerical analyses carried out in cavitating conditions with Open Foam solver [12]; numerical results are close to the prediction of the engineering method, with an error on the estimated mass flow rate through the single injector less than 5%. Numerical computations highlighted that the cavitation starts the injector inlet, with a steep phase change at the injector exit as shown in Figure 9 where density contours for one of the analysed configuration are reported.
Figure 11 Heat flux distribution along the nozzle wall determined. The selected configuration (id. 25), characterized by a divergent angle of the conical part equal to 18 deg, represents a compromise between two opposite effects: higher throat heat fluxes with lower total thermal loads and lower throat heat fluxes with higher total thermal loads. It is well known that in hybryd and solid propulsion systems, nozzle erosion will cause a decay of performances. The performance tool is able predict this decay considering the enlargement of the throat are with respect the initial design value. A conservative value throat erosion for a graphite made nozzle has been used (r= 0.025 m/s), from [3]. FBionure 19 chawe nozzle nrofile withoit eroacdoan (hinino time t = (0) ¢) and at the end af the firino time (ie t= 35
Figure 11 Heat flux distribution along the nozzle wall determined. The selected configuration (id. 25), characterized by a divergent angle of the conical part equal to 18 deg, represents a compromise between two opposite effects: higher throat heat fluxes with lower total thermal loads and lower throat heat fluxes with higher total thermal loads. It is well known that in hybryd and solid propulsion systems, nozzle erosion will cause a decay of performances. The performance tool is able predict this decay considering the enlargement of the throat are with respect the initial design value. A conservative value throat erosion for a graphite made nozzle has been used (r= 0.025 m/s), from [3]. FBionure 19 chawe nozzle nrofile withoit eroacdoan (hinino time t = (0) ¢) and at the end af the firino time (ie t= 35
A strong decrease of chamber pressure (see Figure 13) is predicted with respect the no throat regression case (about 35%), in both cases (with and without nozzle erotion) the throat has been verified to be chocked (M.= 2.73 and 2.95 respectively).
A strong decrease of chamber pressure (see Figure 13) is predicted with respect the no throat regression case (about 35%), in both cases (with and without nozzle erotion) the throat has been verified to be chocked (M.= 2.73 and 2.95 respectively).
Figure 14 Nozzle throat erosion; Thrust A sensible variation of thrust is predicted (about 8%) but still within the thrust requirement (see Figure 14)and a low variation Isp is predicted ( see Figure 15) with respect the no throat regression case (about 5%). Anyway, Isp and thrust vary in percentage less than Pc in 0-D approach.
Figure 14 Nozzle throat erosion; Thrust A sensible variation of thrust is predicted (about 8%) but still within the thrust requirement (see Figure 14)and a low variation Isp is predicted ( see Figure 15) with respect the no throat regression case (about 5%). Anyway, Isp and thrust vary in percentage less than Pc in 0-D approach.
Figure 15 Nozzle throat erosion; Specific Impulse
Figure 15 Nozzle throat erosion; Specific Impulse
Figure 13 Nozzle throat erosion; Chamber Pressure
Figure 13 Nozzle throat erosion; Chamber Pressure
I. NUMERICAL VERIFICATION
I. NUMERICAL VERIFICATION
Figure 17 Temperature contours in the combustion chamber In Figure 17, temperature contours in the combustion chamber and nozzle are shown; the flame is closed on the axis at the throat location. Predicted chamber pressure is equal to 36.6 bar, slightly below the design value (equal to 40 bar).
Figure 17 Temperature contours in the combustion chamber In Figure 17, temperature contours in the combustion chamber and nozzle are shown; the flame is closed on the axis at the throat location. Predicted chamber pressure is equal to 36.6 bar, slightly below the design value (equal to 40 bar).
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