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Investigation of effects of convergence and divergence half-angles on the performance of a nozzle for different operating conditions

  • M. H. Hamedi-Estakhrsar
  • H. Mahdavy-Moghaddam
  • M. Jahromi
Technical Paper
  • 51 Downloads

Abstract

The effects of convergence and divergence half-angles on the performance of a nozzle at the different pressure ratios are investigated numerically. SST k − ω turbulence model is applied to simulate the compressible gas flow inside the nozzle and its exhaust plume. Exhaust nozzle performance parameters have been calculated and compared with available experimental data to show the validity of the simulations. For this purpose, different nozzle pressure ratios for various operating conditions including over-expanded, under-expanded and design condition are considered. The effects of the nozzle geometry (convergence and divergence half-angle) on the velocity coefficient (Cv), discharge coefficient (Cd), gross thrust coefficient (Cfg) and nozzle adiabatic efficiency (ηn) are investigated. Predicted results show that for a given nozzle pressure ratio, by increasing the divergence angle from 5 to 20, there is about 3% loss in the gross thrust coefficient and also by increasing this angle from 20° to 40°, the value of the Cv and ηn will decrease 5 and 10%, respectively. Increasing the convergence angle reduces the discharge coefficient about 6% and causes a 3% penalty in nozzle gross thrust coefficient.

Keywords

Convergence half-angle Divergence half-angle Gross thrust coefficient Discharge coefficient Velocity coefficient Nozzle efficiency 

List of symbols

Athroat

Nozzle throat area (m2)

Aeff

Nozzle effective area (m2)

CA

Divergence loss factor

Cd

Discharge coefficient

Cfg

Gross thrust coefficient

Cv

Velocity coefficient

Cw

Dimensionless shear stress

F

Thrust (N)

Fg−ideal

Isentropic thrust (N)

Fg−Actual

Actual thrust (N)

Gk

Production of k

Gω

Production of ω

k

Turbulent kinetic energy (m2/s2)

L

Length of nozzle (m)

\(\dot{m}_{{}}\)

Actual mass flow rate (kg/s)

\(\dot{m}_{\text{ideal}}\)

Isentropic mass flow rate (kg/s)

NPR

Nozzle pressure ratio (Pinlet/Pambient)

Pa

Ambient pressure (Pa)

P0

Back pressure (Pa)

Pe

Exit pressure (Pa)

Pti

Inlet stagnation pressure (Pa)

Ptt

Throat stagnation pressure (Pa)

Pte

Exit stagnation pressure (Pa)

R

Gas constant (kj/kg K)

Sk

User-defined source term

Sω

User-defined source term

Tt

Stagnation temperature (K)

Ve−ideal

Isentropic exit velocity (m/s)

Ve

Exit velocity (m/s)

\(\bar{u}\)

Average gas velocity (m/s)

u

Fluctuating velocity component (m/s)

β

Divergence half-angle (degree)

Yk

Dissipation of k

Yω

Dissipation of ω

Γk

Diffusion coefficient of k

Γω

Diffusion coefficient of ω

γ

Specific heat ratio

ηn

Nozzle efficiency (%)

θ

Convergence half-angle (degree)

μ

Dynamic viscosity(Pa s)

μt

Turbulent dynamic viscosity (Pa s)

ρ

Flow field density (kg/m3)

σk

Turbulent Prandtl numbers for k

σω

Turbulent Prandtl numbers for ω

τw

Wall shear stress

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Copyright information

© The Brazilian Society of Mechanical Sciences and Engineering 2018

Authors and Affiliations

  • M. H. Hamedi-Estakhrsar
    • 1
  • H. Mahdavy-Moghaddam
    • 1
  • M. Jahromi
    • 2
  1. 1.Faculty of Aerospace EngineeringK. N. Toosi University of TechnologyTehranIran
  2. 2.Faculty of Aerospace EngineeringMalek-Ashtar University of TechnologyTehranIran

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