attention to ablation protection treatment. The theoretical results in this part are in
agreement with the experimental results. The results can be used as a theoretical
basis for the structure and process design of Laval nozzle.
10.2.1 Flow Field Analysis of Laval Nozzle
10.2.1.1 Physical Model
Because the Laval nozzle is a circular section pipe, its three-dimensional flow can
be simplified to two-dimensional axisymmetric flow. The double arc method is used
to design the profile of axisymmetric nozzle. The design dimensions include the
angle a between the straight line and the vertical line of the contraction section, the
radius R 1 of the small arc at the throat, the radius R 2 of the large arc at the expansion
section, the angle b between the common tangent of the large arc and the small arc
and the horizontal line, the radius r i of the entrance section, the radius r
à of the
throat section, the radius r e of the exit section, and the total length l of the nozzle.
10.2.1.2 Boundary Conditions for Throttle Ports
The gas flow through Laval nozzle accelerates from subsonic to supersonic, and the
velocity increases gradually, while the pressure, temperature, and density decrease
gradually. It is a compressible flow. The entrance boundary condition is set to the
entrance pressure, and the total pressure and other scalar values of the entrance
boundary are given at the entrance boundary. The pressure entrance boundary is
suitable for compressible flow. The outlet boundary condition is set to the pressure
outlet, and the static pressure of the flow outlet is specified. The density coupling
algorithm for compressible flow is adopted, and the velocity component and density
are taken as basic variables. The S-A one-equation turbulence model is chosen to
simulate the flow with wall confinement.
10.2.1.3 Basic Equation of Fluid
Fluid flow obeys the laws of mass conservation, momentum conservation, and
energy conservation. The flow of nozzle gas is in turbulent state, and the governing
equation includes turbulent equation.
(1) Mass Conservation Equation
The increase of mass in a fluid element per unit time is equivalent to the net mass
flowing into the element at the same time interval. The equation of mass conservation is
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10 Application of Aerodynamic Technology in Attitude Control …
agreement with the experimental results. The results can be used as a theoretical
basis for the structure and process design of Laval nozzle.
10.2.1 Flow Field Analysis of Laval Nozzle
10.2.1.1 Physical Model
Because the Laval nozzle is a circular section pipe, its three-dimensional flow can
be simplified to two-dimensional axisymmetric flow. The double arc method is used
to design the profile of axisymmetric nozzle. The design dimensions include the
angle a between the straight line and the vertical line of the contraction section, the
radius R 1 of the small arc at the throat, the radius R 2 of the large arc at the expansion
section, the angle b between the common tangent of the large arc and the small arc
and the horizontal line, the radius r i of the entrance section, the radius r
à of the
throat section, the radius r e of the exit section, and the total length l of the nozzle.
10.2.1.2 Boundary Conditions for Throttle Ports
The gas flow through Laval nozzle accelerates from subsonic to supersonic, and the
velocity increases gradually, while the pressure, temperature, and density decrease
gradually. It is a compressible flow. The entrance boundary condition is set to the
entrance pressure, and the total pressure and other scalar values of the entrance
boundary are given at the entrance boundary. The pressure entrance boundary is
suitable for compressible flow. The outlet boundary condition is set to the pressure
outlet, and the static pressure of the flow outlet is specified. The density coupling
algorithm for compressible flow is adopted, and the velocity component and density
are taken as basic variables. The S-A one-equation turbulence model is chosen to
simulate the flow with wall confinement.
10.2.1.3 Basic Equation of Fluid
Fluid flow obeys the laws of mass conservation, momentum conservation, and
energy conservation. The flow of nozzle gas is in turbulent state, and the governing
equation includes turbulent equation.
(1) Mass Conservation Equation
The increase of mass in a fluid element per unit time is equivalent to the net mass
flowing into the element at the same time interval. The equation of mass conservation is
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10 Application of Aerodynamic Technology in Attitude Control …