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Transient three-dimensional startup side load analysis of a regeneratively cooled nozzle

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Abstract

The objective of this effort is to develop a computational methodology to capture the side load physics and to anchor the computed aerodynamic side loads with the available data by simulating the startup transient of a regeneratively cooled, high-aspect-ratio nozzle, hot-fired at sea level. The computational methodology is based on an unstructured-grid, pressure-based, reacting flow computational fluid dynamics and heat transfer formulation, and a transient inlet history based on an engine system simulation. Emphases were put on the effects of regenerative cooling on shock formation inside the nozzle, and ramp rate on side load reduction. The results show that three types of asymmetric shock physics incur strong side loads: the generation of combustion wave, shock transitions, and shock pulsations across the nozzle lip, albeit the combustion wave can be avoided with sparklers during hot-firing. Results from both regenerative cooled and adiabatic wall boundary conditions capture the early shock transitions with corresponding side loads matching the measured secondary side load. It is theorized that the first transition from free-shock separation to restricted-shock separation is caused by the Coanda effect. After which the regeneratively cooled wall enhances the Coanda effect such that the supersonic jet stays attached, while the hot adiabatic wall fights off the Coanda effect, and the supersonic jet becomes detached most of the time. As a result, the computed peak side load and dominant frequency due to shock pulsation across the nozzle lip associated with the regeneratively cooled wall boundary condition match those of the test, while those associated with the adiabatic wall boundary condition are much too low. Moreover, shorter ramp time results show that higher ramp rate has the potential in reducing the nozzle side loads.

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Abbreviations

C 1, C 2, C 3, C μ :

Turbulence modeling constants, 1.15, 1.9, 0.25, and 0.09

C p :

Heat capacity

D :

Diffusivity

F yz :

Integrated force in the lateral direction

H :

Total enthalpy

K :

Thermal conductivity

k :

Turbulent kinetic energy

p :

Pressure

Q :

Heat flux

T :

Temperature

t :

Time

u i :

Mean velocities in three directions

x :

Cartesian coordinates

α :

Species mass fraction

\({\varepsilon}\) :

Turbulent kinetic energy dissipation rate

θ :

Energy dissipation contribution

μ :

Viscosity

μ t :

Turbulent eddy viscosity \({(=\rho{C}_{\mu }{k}^{2}/\varepsilon}\))

Π:

Turbulent kinetic energy production

ρ :

Density

σ :

Turbulence modeling constants

τ :

Shear stress

ω :

Chemical species production rate

r:

Radiation

t:

Turbulent flow

w:

Wall

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Authors and Affiliations

  1. Fluid Dynamics Branch, NASA Marshall Space Flight Center, Huntsville, AL, 35812, USA

    Ten-See Wang

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  1. Ten-See Wang
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Correspondence to Ten-See Wang.

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Communicated by A. Hadjadj.

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Wang, TS. Transient three-dimensional startup side load analysis of a regeneratively cooled nozzle. Shock Waves 19, 251–264 (2009). https://doi.org/10.1007/s00193-009-0201-2

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  • DOI: https://doi.org/10.1007/s00193-009-0201-2

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