Broadband_JJ shock_NN1 noise_NN1 reduction_NN1 in_II turbulent_JJ jets_NN2 by_II water_NN1 injection_NN1 1_MC1 ._. 
Introduction_NN1 Three_MC distinct_JJ components_NN2 of_IO noise_NN1 are_VBR present_JJ in_II supersonic_JJ jets_NN2 :_: turbulent_JJ mixing_NN1 noise_NN1 ,_, Mach_NNU wave_NN1 radiation_NN1 ,_, and_CC broadband_JJ shock_NN1 associated_JJ noise_NN1 ._. 
Generally_RR the_AT shock-associated_JJ noise_NN1 includes_VVZ both_RR broadband_JJ shock_NN1 noise_NN1 and_CC discrete_JJ screech_NN1 tones_NN2 ._. 
Both_DB2 the_AT broadband_JJ shock_NN1 noise_NN1 and_CC screech_NN1 tones_NN2 are_VBR associated_VVN with_IW imperfectly_RR expanded_JJ jets_NN2 ._. 
The_AT high_JJ noise_NN1 levels_NN2 radiated_VVD by_II launch_NN1 vehicles_NN2 at_II lift-off_JJ induce_VV0 severe_JJ vibration_NN1 on_II the_AT launch_NN1 vehicle_NN1 structure_NN1 and_CC payload_NN1 ,_, and_CC ground_NN1 support_NN1 equipment_NN1 ._. 
Consequently_RR the_AT need_NN1 to_TO reduce_VVI acoustic_JJ levels_NN2 from_II jet_NN1 exhausts_NN2 is_VBZ paramount_JJ ._. 
Water_NN1 injection_NN1 has_VHZ been_VBN traditionally_RR considered_VVN for_IF the_AT suppression_NN1 of_IO high_JJ noise_NN1 levels_NN2 from_II rocket_NN1 exhausts_VVZ in_II launch_NN1 vehicle_NN1 environments_NN2 ._. 
For_REX21 example_REX22 ,_, large_JJ amounts_NN2 of_IO water_NN1 are_VBR used_VVN for_IF the_AT suppression_NN1 of_IO ignition_NN1 overpressure_NN1 (_( IOP_NP1 )_) and_CC lift-off_JJ noise_NN1 during_II Space_NN1 Shuttle_NN1 launches_NN2 ._. 
The_AT water_NN1 mass_NN1 flow_NN1 rate_NN1 to_II the_AT SRB_NP1 exhaust_VV0 mass_JJ flow_NN1 rate_NN1 ratio_NN1 is_VBZ maintained_VVN around_RG one_MC1 to_II two_MC in_BCL21 order_BCL22 to_TO meet_VVI payload_NN1 design_NN1 requirements_NN2 of_IO 145_MC dB_NNU ._. 
Water_NN1 injection_NN1 could_VM reduce_VVI noise_NN1 by_II as_RG much_DA1 as_CSA 8-12_MCMC dB_NNU ._. 
Such_DA a_AT1 high_JJ level_NN1 of_IO reduction_NN1 includes_VVZ reductions_NN2 in_II the_AT turbulent_JJ mixing_NN1 noise_NN1 and_CC shock-associated_JJ noise_NN1 ,_, the_AT latter_DA constituting_VVG the_AT predominant_JJ component_NN1 of_IO noise_NN1 reduction_NN1 ._. 
Water_NN1 injection_NN1 mitigates_VVZ all_DB the_AT three_MC components_NN2 of_IO jet_NN1 noise_NN1 :_: the_AT turbulent_JJ mixing_NN1 noise_NN1 ,_, Mach_NNU wave_NN1 radiation_NN1 ,_, and_CC shock_NN1 noise_NN1 ._. 
Two_MC principal_JJ mechanisms_NN2 leading_VVG to_II the_AT diminution_NN1 of_IO jet_NN1 noise_NN1 by_II water_NN1 injection_NN1 are_VBR the_AT reduction_NN1 of_IO jet_NN1 velocity_NN1 and_CC jet_NN1 temperature_NN1 ._. 
The_AT decrease_NN1 of_IO jet_NN1 velocity_NN1 is_VBZ occasioned_VVN through_II momentum_NN1 transfer_NN1 between_II the_AT liquid_NN1 and_CC the_AT gaseous_JJ phases_NN2 ,_, and_CC the_AT reduction_NN1 of_IO the_AT jet_NN1 temperature_NN1 is_VBZ achieved_VVN due_II21 to_II22 partial_JJ vaporization_NN1 of_IO the_AT injected_JJ water_NN1 ._. 
The_AT effect_NN1 of_IO water_NN1 may_VM also_RR be_VBI regarded_VVN as_II effectively_RR increasing_VVG the_AT jet_NN1 density_NN1 ._. 
Important_JJ velocity_NN1 reductions_NN2 are_VBR achieved_VVN within_II a_AT1 few_DA2 diameters_NN2 of_IO the_AT nozzle_NN1 exit_NN1 ._. 
Noise_NN1 reductions_NN2 of_IO the_AT order_NN1 of_IO 10_MC dB_NNU are_VBR realized_VVN for_IF both_DB2 cold_JJ and_CC hot_JJ jets_NN2 ._. 
Several_DA2 design_NN1 parameters_NN2 influence_VV0 the_AT effectiveness_NN1 of_IO noise_NN1 reduction_NN1 by_II water_NN1 injection_NN1 ._. 
These_DD2 include_VV0 water_NN1 to_II jet_NN1 mass_NN1 flow_NN1 rate_NN1 ratio_NN1 ,_, axial_JJ injection_NN1 location_NN1 ,_, water_NN1 injection_NN1 angle_NN1 ,_, number_NN1 of_IO injectors_NN2 ,_, method_NN1 of_IO injection_NN1 (_( jet_NN1 type_NN1 or_CC spray_VV0 type_NN1 )_) ,_, droplet_NN1 size_NN1 ,_, water_NN1 pressure_NN1 ,_, and_CC water_NN1 temperature_NN1 ._. 
Optimal_JJ injection_NN1 parameters_NN2 need_VV0 to_TO be_VBI determined_VVN for_IF the_AT design_NN1 of_IO efficient_JJ water_NN1 injection_NN1 system_NN1 ._. 
Data_NN of_IO Zoppellari_NP1 &;_NULL Juve_NP1 and_CC of_IO Norum_NP1 suggest_VV0 that_CST best_JJT noise_NN1 reductions_NN2 of_IO the_AT order_NN1 of_IO 10-12_MCMC dB_NNU are_VBR obtained_VVN at_II injection_NN1 angles_NN2 of_IO 45-60&deg;_FO ,_, injection_NN1 near_II the_AT nozzle_NN1 exit_NN1 (_( especially_RR for_IF shock-containing_JJ jets_NN2 )_) ,_, and_CC high_JJ mass_JJ flow_NN1 rates_NN2 ._. 
Also_RR the_AT optimum_JJ number_NN1 of_IO injectors_NN2 appears_VVZ to_TO be_VBI around_RG eight_MC ._. 
Experiments_NN2 by_II Krothappalli_NP1 et_RA21 al_RA22 ._. 
and_CC Greska_NP1 &;_NULL Krothapalli_NP1 and_CC Arakeri_NP1 et_RA21 al_RA22 ._. 
at_II reduced_JJ water_NN1 mass_NN1 flow_NN1 rate_NN1 ratios_NN2 through_II the_AT use_NN1 of_IO microjets_NN2 show_VV0 sizable_JJ noise_NN1 reduction_NN1 for_IF application_NN1 to_II aircraft_NN jet_NN1 engines_NN2 ._. 
Experiments_NN2 with_IW water_NN1 injection_NN1 suggest_VV0 that_CST the_AT mass_JJ flow_NN1 rate_NN1 ratio_NN1 appears_VVZ to_TO be_VBI an_AT1 important_JJ parameter_NN1 ._. 
Tests_NN2 conducted_VVN with_IW water_NN1 to_II jet_NN1 mass_NN1 flow_NN1 rate_NN1 ratios_NN2 up_RG21 to_RG22 four_MC reveal_VV0 that_CST significant_JJ noise_NN1 reductions_NN2 can_VM be_VBI achieved_VVN at_II high_JJ water_NN1 flow_NN1 rate_NN1 ratio_NN1 ._. 
In_II the_AT case_NN1 of_IO cold_JJ jets_NN2 ,_, beyond_II a_AT1 critical_JJ mass_JJ flow_NN1 rate_NN1 ratio_NN1 ,_, the_AT velocity_NN1 reduction_NN1 and_CC thus_RR the_AT noise_NN1 reduction_NN1 is_VBZ small_JJ ._. 
For_IF hot_JJ jets_NN2 ,_, only_RR a_AT1 fraction_NN1 of_IO the_AT liquid_NN1 is_VBZ effective_JJ in_II reducing_VVG the_AT air_NN1 jet_NN1 velocity_NN1 due_JJ to_TO drop_VVI evaporation_NN1 ._. 
At_II low_JJ water_NN1 flow_NN1 rates_NN2 ,_, it_PPH1 is_VBZ possible_JJ to_TO reduce_VVI the_AT shock_NN1 associated_JJ noise_NN1 significantly_RR ._. 
At_II higher_JJR mass_JJ flow_NN1 rates_NN2 ,_, momentum_NN1 transfer_NN1 principally_RR affects_VVZ the_AT mixing_NN1 noise_NN1 over_II a_AT1 broad_JJ range_NN1 of_IO frequency_NN1 ._. 
At_II considerably_RR high_JJ mass_JJ flow_NN1 rates_NN2 ,_, the_AT benefit_NN1 of_IO velocity_NN1 reduction_NN1 of_IO the_AT air_NN1 jet_NN1 by_II momentum_NN1 transfer_NN1 between_II the_AT two_MC phases_NN2 is_VBZ partly_RR opposed_VVN by_II the_AT emergence_NN1 of_IO new_JJ parasitic_JJ sources_NN2 linked_VVN to_II water_NN1 injection_NN1 ,_, which_DDQ include_VV0 the_AT impact_NN1 noise_NN1 of_IO air_NN1 on_II the_AT water_NN1 jets_NN2 ,_, fragmentation_NN1 of_IO these_DD2 water_NN1 jets_NN2 ,_, and_CC unsteady_JJ movement_NN1 of_IO the_AT droplets_NN2 ._. 
A_AT1 compromise_NN1 can_VM be_VBI found_VVN between_II significant_JJ penetration_NN1 of_IO water_NN1 jet_NN1 into_II the_AT air_NN1 jet_NN1 and_CC low_JJ impact_NN1 noise_NN1 ._. 
A_AT1 significant_JJ parameter_NN1 is_VBZ the_AT velocity_NN1 component_NN1 of_IO water_NN1 jets_NN2 that_CST is_VBZ perpendicular_JJ to_II the_AT air_NN1 jet_NN1 ._. 
If_CS this_DD1 component_NN1 is_VBZ high_JJ ,_, water_NN1 penetrates_VVZ deeply_RR into_II the_AT air_NN1 jet_NN1 and_CC mixing_NN1 takes_VVZ place_NN1 rapidly_RR ._. 
If_CS this_DD1 component_NN1 is_VBZ small_JJ ,_, water_NN1 does_VDZ not_XX produce_VVI significant_JJ drag_VV0 and_CC impact_NN1 noise_NN1 ._. 
In_II31 view_II32 of_II33 the_AT importance_NN1 of_IO water_NN1 injection_NN1 in_II jet_NN1 noise_NN1 suppression_NN1 ,_, a_AT1 theoretical_JJ understanding_NN1 of_IO the_AT mechanism_NN1 of_IO noise_NN1 reduction_NN1 is_VBZ useful_JJ in_II the_AT design_NN1 and_CC optimization_NN1 of_IO water_NN1 injection_NN1 systems_NN2 for_IF launch_NN1 acoustics_NN2 application_NN1 ._. 
Based_VVN on_II control_NN1 volume_NN1 formulation_NN1 a_AT1 simple_JJ one-dimensional_JJ analytical_JJ model_NN1 has_VHZ been_VBN recently_RR reported_VVN by_II the_AT author_NN1 for_IF estimating_VVG jet_NN1 mixing_NN1 noise_NN1 suppression_NN1 due_II21 to_II22 water_NN1 injection_NN1 ._. 
The_AT method_NN1 is_VBZ based_VVN on_II the_AT conception_NN1 of_IO effective_JJ jet_NN1 properties_NN2 in_II31 conjunction_II32 with_II33 the_AT scaling_NN1 laws_NN2 developed_VVN by_II Kandula_NN1 for_IF shock-free_JJ jet_NN1 noise_NN1 ._. 
The_AT predictions_NN2 are_VBR found_VVN to_TO yield_VVI satisfactory_JJ agreement_NN1 with_IW the_AT test_NN1 data_NN for_IF hot_JJ perfectly_RR expanded_VVN supersonic_JJ jets_NN2 with_II31 regard_II32 to_II33 turbulent_JJ mixing_NN1 noise_NN1 reduction_NN1 with_IW water_NN1 injection_NN1 over_II a_AT1 wide_JJ range_NN1 of_IO water_NN1 to_II jet_NN1 mass_NN1 flow_NN1 rate_NN1 ratios_NN2 ._. 
In_II the_AT presence_NN1 of_IO water_NN1 injection_NN1 ,_, broadband_JJ shock_NN1 noise_NN1 reductions_NN2 are_VBR considerably_RR higher_JJR than_CSN those_DD2 due_II21 to_II22 turbulent_JJ mixing_NN1 noise_NN1 ._. 
Thus_RR an_AT1 accurate_JJ estimation_NN1 of_IO the_AT broadband_JJ shock_NN1 noise_NN1 reduction_NN1 is_VBZ important_JJ in_II the_AT design_NN1 of_IO the_AT water_NN1 injection_NN1 systems_NN2 for_IF jet_NN1 noise_NN1 mitigation_NN1 at_II launch_NN1 sites_NN2 ._. 
In_II this_DD1 paper_NN1 derived_VVD primarily_RR from_II ,_, the_AT method_NN1 of_IO effective_JJ jet_NN1 properties_NN2 will_VM be_VBI applied_VVN (_( extended_VVN )_) to_II the_AT prediction_NN1 of_IO broadband_JJ shock_NN1 noise_NN1 reduction_NN1 with_IW water_NN1 injection_NN1 in_II imperfectly_RR expanded_VVN supersonic_JJ jets._NNU 2_MC ._. 
Analysis_NN1 2.1_MC ._. 
Broadband_JJ shock_NN1 noise_NN1 reduction_NN1 The_AT intensity_NN1 of_IO broadband_JJ shock_NN1 noise_NN1 is_VBZ primarily_RR a_AT1 function_NN1 of_IO the_AT nozzle_NN1 pressure_NN1 ratio_NN1 and_CC largely_RR independent_JJ of_IO the_AT temperature_NN1 ratio_NN1 ._. 
Harper-Bourne_NP1 and_CC Fisher_NP1 found_VVD that_CST for_IF a_AT1 given_JJ radiation_NN1 direction_NN1 the_AT measured_JJ mean_JJ square_JJ sound_NN1 pressure_NN1 due_II21 to_II22 broadband_JJ shock-associated_JJ noise_NN1 scales_NN2 with_IW the_AT parameter_NN1 &beta;_NULL as_II :_: and_CC Mj_NP1 is_VBZ the_AT fully_RR expanded_JJ jet_NN1 Mach_NNU number_NN1 ._. 
The_AT parameter_NN1 &beta;_NULL characterizes_VVZ the_AT pressure_NN1 jump_NN1 across_II a_AT1 normal_JJ shock_NN1 with_IW an_AT1 upstream_JJ Mach_NNU number_NN1 Mj_NP1 ._. 
In_II the_AT presence_NN1 of_IO water_NN1 injection_NN1 ,_, the_AT effective_JJ jet_NN1 properties_NN2 (_( jet_NN1 velocity_NN1 ,_, temperature_NN1 ,_, Mach_NNU number_NN1 ,_, etc._RA )_) near_II the_AT exit_NN1 are_VBR obtained_VVN from_II the_AT theory_NN1 proposed_VVD in_RP ._. 
In_II the_AT present_JJ context_NN1 ,_, the_AT effective_JJ jet_NN1 Mach_NNU number_NN1 is_VBZ obtained_VVN as_II a_AT1 function_NN1 of_IO the_AT water_NN1 to_II jet_NN1 mass_NN1 flow_NN1 rate_NN1 ratio_NN1 ._. 
Thus_RR the_AT reduction_NN1 in_II the_AT overall_JJ sound_NN1 pressure_NN1 level_NN1 (_( OASPL_NP1 )_) can_VM be_VBI estimated_VVN as_CSA where_CS the_AT subscripts1_FO and_CC 2_MC respectively_RR refer_VV0 to_II the_AT original_JJ and_CC effective_JJ jet_NN1 exit_NN1 conditions_NN2 ._. 
Eq_NN1 ._. 
yields_VVZ the_AT noise_NN1 reduction_NN1 due_II21 to_II22 water_NN1 injection_NN1 as_CSA applied_VVN to_II a_AT1 single_JJ isolated_JJ shock_NN1 in_II the_AT jet_NN1 ._. 
The_AT consideration_NN1 of_IO noise_NN1 reduction_NN1 in_II the_AT multiple_JJ shock_NN1 system_NN1 is_VBZ very_RG complex_JJ ._. 
Thus_RR it_PPH1 is_VBZ assumed_VVN in_II the_AT present_JJ analysis_NN1 that_CST the_AT overall_JJ noise_NN1 reduction_NN1 is_VBZ proportional_JJ to_II the_AT number_NN1 of_IO shock_NN1 cells_NN2 downstream_RL of_IO the_AT water_NN1 injection_NN1 station_NN1 ,_, nsd_NNU ._. 
That_REX21 is_REX22 ,_, where_CS the_AT quantity_NN1 &Delta;_NULL OASPL_NN1 is_VBZ provided_VVN by_II Eq._NP1 2.2_MC ._. 
Effective_JJ jet_NN1 exit_NN1 conditions_NN2 2.2.1_MC ._. 
Effective_JJ jet_NN1 Mach_NNU number_NN1 In_II the_AT following_JJ ,_, we_PPIS2 briefly_RR review_VV0 the_AT results_NN2 for_IF the_AT effective_JJ jet_NN1 properties_NN2 derived_VVD in_RP on_II the_AT basis_NN1 of_IO a_AT1 control_NN1 volume_NN1 formulation_NN1 ._. 
An_AT1 expression_NN1 for_IF the_AT effective_JJ jet_NN1 Mach_NNU number_NN1 is_VBZ given_VVN by_II where_RRQ the_AT effective_JJ jet_NN1 velocity_NN1 and_CC jet_NN1 density_NN1 are_VBR obtained_VVN as_CSA follows._VVZ 3_MC ._. 
Results_NN2 and_CC discussion_NN1 3.1_MC ._. 
Comparisons_NN2 with_IW experimental_JJ data_NN for_IF cold_JJ over-expanded_JJ jet_NN1 For_IF comparison_NN1 purposes_NN2 ,_, we_PPIS2 consider_VV0 here_RL the_AT test_NN1 data_NN of_IO Norum_NN1 for_IF cold_JJ over-expanded_JJ jet_NN1 broadband_NN1 shock_NN1 noise_NN1 reduction_NN1 with_IW water_NN1 injection_NN1 (_( case_NN1 D_ZZ1 )_) ._. 
The_AT jet_NN1 issues_NN2 from_II a_AT1 convergent-divergent_JJ (_( CD_NN1 )_) nozzle_NN1 ._. 
For_IF the_AT cold_JJ operation_NN1 of_IO the_AT Mach_NNU 1.5_MC (_( design_VV0 Mach_NNU number_NN1 )_) CD_NN1 nozzle_NN1 ,_, the_AT highest_JJT nozzle_NN1 pressure_NN1 ratio_NN1 (_( NPR_NP1 )_) that_CST can_VM be_VBI achieved_VVN prior_II21 to_II22 the_AT onset_NN1 of_IO dominant_JJ screech_NN1 is_VBZ about_RG 2.27_MC ,_, corresponding_VVG to_II at_II which_DDQ broadband_JJ shock_NN1 noise_NN1 is_VBZ measured_VVN ._. 
Data_NN for_IF only_RR one_MC1 Mach_NNU number_NN1 is_VBZ available_JJ for_IF the_AT cold_JJ case_NN1 ._. 
Acoustic_JJ data_NN are_VBR obtained_VVN with_IW injection_NN1 angles_NN2 of_IO 45&deg;_NNU and_CC 60&deg;_NNU ,_, with_IW the_AT injection_NN1 at_II 60&deg;_NNU yielding_VVG a_AT1 somewhat_RR higher_JJR noise_NN1 reduction_NN1 ._. 
The_AT axial_JJ injection_NN1 location_NN1 is_VBZ adjusted_VVN by_II varying_VVG the_AT injector_NN1 ring_NN1 corresponding_VVG to_II known_JJ positions_NN2 of_IO the_AT shocks_NN2 in_II the_AT over-expanded_JJ jet_NN1 plume_NN1 ._. 
Maximum_JJ noise_NN1 reduction_NN1 is_VBZ achieved_VVN in_II a_AT1 direction_NN1 at_II 135&deg;_NNU to_II the_AT downstream_JJ jet_NN1 axis_NN1 ._. 
Fig._NN1 5a_FO shows_VVZ the_AT dependence_NN1 of_IO maximum_JJ SPL_NP1 reduction_NN1 with_IW the_AT water_NN1 mass_NN1 flow_NN1 rate_NN1 with_IW the_AT injection_NN1 station_NN1 upstream_RL of_IO shock_NN1 cell-1_MC1 ._. 
A_AT1 total_NN1 of_IO five_MC shock_NN1 cells_NN2 are_VBR considered_VVN here_RL ._. 
The_AT theory_NN1 shows_VVZ a_AT1 nearly_RR linear_JJ dependence_NN1 of_IO SPL_NP1 reduction_NN1 with_IW the_AT mass_JJ flow_NN1 rate_NN1 ,_, while_CS the_AT data_NN suggests_VVZ a_AT1 saturation_NN1 trend_NN1 after_II an_AT1 initially_RR linear_JJ increase_NN1 ._. 
In_II the_AT linear_JJ range_NN1 of_IO the_AT data_NN ,_, the_AT theory_NN1 suffers_VVZ a_AT1 maximum_JJ error_NN1 of_IO about_RG 2.5_MC dB_NNU ._. 
From_II the_AT preceding_JJ comparisons_NN2 ,_, it_PPH1 is_VBZ evident_JJ that_CST the_AT agreement_NN1 between_II the_AT experimental_JJ data_NN and_CC the_AT predictions_NN2 of_IO the_AT proposed_JJ model_NN1 is_VBZ good_JJ at_RR21 least_RR22 in_II the_AT linear_JJ phase_NN1 ,_, when_CS the_AT mass_JJ flow_NN1 rate_NN1 of_IO the_AT injected_JJ water_NN1 is_VBZ relatively_RR limited_VVN ._. 
For_IF higher_JJR values_NN2 of_IO water_NN1 injection_NN1 rates_NN2 ,_, there_EX is_VBZ a_AT1 definite_JJ trend_NN1 toward_II saturation_NN1 in_II the_AT experimental_JJ results_NN2 ._. 
It_PPH1 is_VBZ believed_VVN that_CST the_AT trend_NN1 towards_II saturation_NN1 in_II noise_NN1 reduction_NN1 at_II higher_JJR mass_JJ injection_NN1 rates_NN2 is_VBZ connected_VVN with_IW the_AT phenomenon_NN1 of_IO parasitic_JJ noise_NN1 (_( referred_VVN to_II in_II the_AT introduction_NN1 )_) ._. 
A_AT1 detailed_JJ theoretical_JJ modeling_NN1 of_IO this_DD1 parasitic_JJ noise_NN1 is_VBZ beyond_II the_AT scope_NN1 of_IO the_AT present_JJ investigation_NN1 ._. 
An_AT1 estimate_NN1 of_IO the_AT parasitic_JJ noise_NN1 ,_, as_CSA deduced_VVN from_II the_AT experimental_JJ data_NN ,_, is_VBZ discussed_VVN in_II the_AT following_JJ section._NNU 3.2_MC ._. 
Deduction_NN1 of_IO parasitic_JJ noise_NN1 Fig._NN1 6_MC shows_VVZ a_AT1 composite_JJ plot_NN1 for_IF the_AT case_NN1 of_IO water_NN1 injection_NN1 upstream_RL of_IO shock_NN1 cell-1_MC1 ._. 
In_II this_DD1 plot_NN1 ,_, the_AT original_JJ data_NN are_VBR resolved_VVN (_( extrapolated_JJ )_) into_II two_MC linear_JJ segments_NN2 --_NN1 curve-1_MC1 and_CC curve-2_MC ._. 
Curve-1_MC1 extrapolates_VVZ the_AT second_MD linear_JJ segment_NN1 of_IO the_AT data_NN ,_, and_CC curve-2_MC extrapolates_VVZ the_AT third_MD linear_JJ segment_NN1 of_IO the_AT data_NN ._. 
It_PPH1 is_VBZ interesting_JJ to_TO note_VVI that_CST the_AT slope_NN1 of_IO curve-2_MC is_VBZ very_RG close_JJ to_II that_DD1 predicted_VVD by_II the_AT theory_NN1 for_IF the_AT broadband_JJ shock_NN1 noise_NN1 ._. 
We_PPIS2 are_VBR inclined_JJ to_TO believe_VVI that_CST the_AT difference_NN1 between_II curve-1_MC1 and_CC curve-2_MC represents_VVZ the_AT parasitic_JJ noise_NN1 ,_, whose_DDQGE magnitude_NN1 is_VBZ reflected_VVN by_II a_AT1 separate_JJ curve_NN1 ._. 
With_IW this_DD1 conjecture_NN1 ,_, the_AT parasitic_JJ noise_NN1 seems_VVZ to_TO commence_VVI (_( manifest_VV0 itself_PPX1 )_) at_II a_AT1 mass_JJ flow_NN1 rate_NN1 ratio_NN1 beyond_II 0.22_MC ,_, and_CC increases_VVZ linearly_RR with_IW the_AT mass_JJ flow_NN1 rate_NN1 thereafter_RT ._. 
The_AT parasitic_JJ noise_NN1 increases_VVZ to_II as_RG high_JJ as_CSA 7_MC dB_NNU for_IF a_AT1 mass_JJ flow_NN1 rate_NN1 ratio_NN1 of_IO 0.5._MC 3.3_MC ._. 
Comparisons_NN2 with_IW experimental_JJ data_NN for_IF hot_JJ over-expanded_JJ jet_NN1 The_AT only_JJ hot_JJ jet_NN1 data_NN for_IF broadband_JJ shock_NN1 noise_NN1 reduction_NN1 available_JJ for_IF comparison_NN1 is_VBZ that_DD1 of_IO a_AT1 hot_JJ over-expanded_JJ supersonic_JJ jet_NN1 at_II ,_, obtained_VVN by_II Norum_NP1 ._. 
Unfortunately_RR the_AT data_NN are_VBR reported_VVN only_RR for_IF the_AT highest_JJT water_NN1 mass_NN1 flow_NN1 rate_NN1 ratio_NN1 of_IO 0.46_MC ._. 
As_CSA in_II the_AT cold_JJ jet_NN1 case_NN1 ,_, largest_JJT noise_NN1 reduction_NN1 was_VBDZ obtained_VVN at_II 135&deg;_NNU to_II the_AT downstream_JJ jet_NN1 axis_NN1 ._. 
A_AT1 maximum_JJ noise_NN1 reduction_NN1 of_IO 6.6_MC dB_NNU was_VBDZ realized_VVN in_II the_AT hot_JJ jet_NN1 case_NN1 ._. 
According_II21 to_II22 the_AT proposed_JJ theory_NN1 ,_, we_PPIS2 have_VH0 at_II a_AT1 mass_JJ flow_NN1 rate_NN1 ratio_NN1 of_IO 0.46_MC ,_, so_CS21 that_CS22 for_IF a_AT1 five-shock_JJ system_NN1 ._. 
From_II Fig._NN1 6_MC ,_, the_AT parasitic_JJ noise_NN1 at_II this_DD1 water_NN1 flow_NN1 rate_NN1 ratio_NN1 is_VBZ 6_MC dB_NNU ._. 
Thus_RR the_AT predicted_JJ broadband_JJ shock_NN1 noise_NN1 reduction_NN1 is_VBZ 7.5_MC dB_NNU ._. 
This_DD1 result_NN1 satisfactorily_RR compares_VVZ with_IW the_AT measured_JJ noise_NN1 reduction_NN1 of_IO 6.6_MC dB_NNU ._. 
The_AT reduction_NN1 in_II noise_NN1 due_II21 to_II22 water_NN1 injection_NN1 is_VBZ generally_RR much_RR larger_JJR for_IF broad_JJ band_NN1 shock_NN1 noise_NN1 than_CSN for_IF jet_NN1 mixing_NN1 noise_NN1 ._. 
When_CS the_AT jet_NN1 temperature_NN1 is_VBZ increased_VVN at_II a_AT1 given_JJ NPR_NP1 ,_, the_AT ratio_NN1 of_IO shock_NN1 noise_NN1 to_II mixing_VVG noise_NN1 decreases_VVZ in_II the_AT forward_JJ direction_NN1 ,_, and_CC the_AT OASPL_NN1 shifts_VVZ more_RRR to_II the_AT Mach_NNU wave_NN1 radiation_NN1 dominated_VVD downstream_JJ direction_NN1 ._. 
The_AT combination_NN1 of_IO these_DD2 two_MC factors_NN2 is_VBZ responsible_JJ for_IF smaller_JJR reduction_NN1 in_II broadband_JJ shock_NN1 noise_NN1 due_II21 to_II22 water_NN1 injection_NN1 for_IF the_AT hot_JJ jet_NN1 relative_II21 to_II22 the_AT cold_JJ jet._NNU 4_MC ._. 
Conclusion_NN1 An_AT1 approximate_JJ formulation_NN1 has_VHZ been_VBN developed_VVN for_IF the_AT prediction_NN1 of_IO broadband_JJ shock_NN1 noise_NN1 reduction_NN1 by_II water_NN1 injection_NN1 ._. 
The_AT proposed_JJ formulation_NN1 agrees_VVZ satisfactorily_RR with_IW the_AT test_NN1 data_NN for_IF water_NN1 injection_NN1 into_II over-expanded_JJ cold_NN1 and_CC hot_JJ supersonic_JJ jets_NN2 ._. 
The_AT results_NN2 suggest_VV0 that_CST beyond_II certain_JJ mass_JJ flow_NN1 rate_NN1 ,_, parasitic_JJ noise_NN1 due_II21 to_II22 water_NN1 impact_NN1 becomes_VVZ manifest_JJ ._. 
This_DD1 result_NN1 points_VVZ to_II the_AT possibility_NN1 of_IO the_AT existence_NN1 of_IO an_AT1 optimum_JJ injection_NN1 water_NN1 mass_NN1 flow_NN1 rate_NN1 for_IF shock_NN1 noise_NN1 reduction_NN1 purposes_NN2 ._. 
