scholarly journals Design of Minimum Length Supersonic Nozzle using the Method of Characteristics

2019 ◽  
Vol 9 (2) ◽  
pp. 1370-1374
Keyword(s):  
Mach Number ◽  
Combustion Chamber ◽  
Method Of Characteristics ◽  
Supersonic Nozzle ◽  
Minimum Length ◽  
Convergent Nozzle ◽  
The Method Of Characteristics ◽  
Inlet Conditions ◽  
The Given ◽  
Nozzle Inlet

The work focuses upon design of minimum length supersonic nozzle, using the method of characteristics, for the given combustion chamber conditions, which are going to serve as nozzle inlet conditions. It is assumed that the flow has somehow been accelerated to the sonic value through a suitable convergent nozzle and from that point; the divergent portion of the nozzle is to be designed using the method of characteristics. The optimum exit area and hence, the Mach number are predicted and this Mach number is the value for which the nozzle has to be designed. The results obtained are validated with the results obtained by validation in ANSYS and based on the observation, followed by a discussion on the optimisation of results.

Analytical and Numerical Design of a High Performance Double–Throated Supersonic Blowdown Windtunnel

2016 ◽  
Author(s):  
Philipp Epple ◽  
Michael Steppert ◽  
Michael Steber
Keyword(s):  
Mach Number ◽  
Wind Tunnel ◽  
Design Process ◽  
Test Section ◽  
Method Of Characteristics ◽  
Design Procedure ◽  
Optimum Shape ◽  
Supersonic Wind Tunnel ◽  
Convergent Nozzle ◽  
The Method Of Characteristics

In this publication the focus lies on the design process of the full supersonic double throated wind tunnel. Starting with the fundamental equations of gas dynamics in combination with an analytical model of the pressure reservoir, the area of the throat at the nozzle and the runtime of the blowdown wind tunnel were computed. Based on these results, the shape of a shock free nozzle was calculated by the method of characteristics. For this purpose, a nozzle design program was developed using Python. In order to validate the results of the method of characteristics program, these results were compared with the area-Mach number relation, which is the exact analytical solution of the isentropic flow through supersonic nozzles. The convergent part of the nozzle, which initially accelerates the flow to sonic speed, cannot be calculated by the method of characteristics, since it applies to supersonic flows only. Hence the subsonic convergent section of the nozzle was designed directly with 2D CFD using CD Adapco Star-CCM+ v. 10.06. A parametric model of the convergent nozzle section was used to find the optimum nozzle shape, i.e. a nozzle which results in a maximum mass flow rate in order to have an undisturbed flow field and Mach number in the following test section. In order to decelerate the flow again from supersonic to subsonic flow after the test section and minimize the total pressure losses, an oblique shock diffuser was used [1]. As for the convergent subsonic nozzle, the optimum shape of a diffusor was found by 2D CFD analysis. Putting all these elements together, i.e. nozzle, test section and diffuser the optimum supersonic wind tunnel shape was found. Finally, a full 3D simulation of the supersonic wind tunnel was performed in order to validate the complete design procedure and computations and also to include the viscous effect of the side walls. These results and the whole design process are presented and analyzed in the paper.

Non-symmetric flow in Laval type nozzles

1972 ◽  
Vol 273 (1232) ◽  
pp. 185-235 ◽  
Keyword(s):  
Steady State ◽  
Combustion Chamber ◽  
Method Of Characteristics ◽  
Three Dimensions ◽  
Symmetric Flow ◽  
Gaseous Flow ◽  
The Method Of Characteristics ◽  
Lateral Forces

The equations of the steady state, compressible inviscid gaseous flow are linearized in a form suitable for application to nozzles of the Laval type. The procedure in the supersonic phase is verified by comparing solutions so obtained with those derived by the method of characteristics in two and three dimensions. Likewise, the solutions in the transonic phase are com pared with those obtained by other investigators. The linearized equation is then used to investigate the nat re of non-symmetric flow in rocket nozzles. It is found that if the flow from the combustion chamber into the nozzle is non-symmetric, the magnitude and direction of the turning couple produced by the emergent jet is dependent on the profile of the nozzle and it is possible to design profiles such that the turning couples or lateral forces are zero. The optimum nozzle so designed is independent of the pressure and also of the magnitude of the non-symmetry of the entry flow. The formulae by which they are obtained have been checked by extensive static and projection tests with simulated rocket test vehicles which are described in this paper.

scholarly journals Solutions of problems for the wave equation with conditions on the characteristics

2021 ◽  
Vol 57 (2) ◽  
pp. 148-155
Author(s):  
V. I. Korzyuk ◽  
O. A. Kovnatskaya
Keyword(s):  
Wave Equation ◽  
Analytical Solution ◽  
Classical Solution ◽  
Method Of Characteristics ◽  
Matching Conditions ◽  
One Dimensional ◽  
The Method Of Characteristics ◽  
The One ◽  
The Given ◽  
Dimensional Wave

In this paper we obtain a classical solution of the one-dimensional wave equation with conditions on the characteristics for different areas this problem is considered in. The analytical solution is constructed by the method of characteristics. In addition, the uniqueness of the obtained solution is proved. The necessity and sufficiency of the matching conditions for given functions of the problem are proved. When these conditions are satisfied and the given functions are smooth enough, the classical solution of the considered problem exists.

Design and Verification of Minimum Length Nozzles with Specific/Variable Heat Ratio Based on Method of Characteristics

2016 ◽  
Vol 13 (06) ◽  
pp. 1650034 ◽  
Author(s):  
Lei Fu ◽  
Shuai Zhang ◽  
Yao Zheng
Keyword(s):  
Mach Number ◽  
Flow Field ◽  
Method Of Characteristics ◽  
Wave Theory ◽  
Minimum Length ◽  
Two Dimensional ◽  
Conservation Of Mass ◽  
Novel Technique ◽  
Field Uniformity ◽  
Exit Mach Number

Two-dimensional (2D) and axisymmetric minimum length nozzles (MLN) with constant and variable specific heat were strictly designed using the method of characteristics. Requirements for the exit Mach number and flow field uniformity were proposed for the nozzles design. In solutions to kernel zone flow field reported previously, violent vibrations of upper wall discrete points at the inlet were observed. Meanwhile, slight compressions could be observed in the flow field of axisymmetric nozzles designed by those methods. In this study, we proposed a novel technique in which the inlet grid is intensified to overcome the limitations mentioned above. Additionally, methods based on conservation of mass and eliminating wave theory were proposed to determine the contour of the nozzle’s upper wall. Inviscid numerical simulations by CFD revealed that the proposed nozzle could meet the requirements for exit Mach number and flow field uniformity in various situations, and axisymmetric nozzles designed from eliminating wave theory exhibited better flow field compared with those designed from conservation of mass.

Lift Characteristics of Asymmetric Exhaust Nozzles at High Flight Speeds

1966 ◽  
Vol 70 (671) ◽  
pp. 1036-1040 ◽  
Author(s):  
W. G. E. Lewis ◽  
R. J. Herd ◽  
M. V. Herbert
Keyword(s):  
Theoretical Analysis ◽  
Lift Force ◽  
Method Of Characteristics ◽  
Supersonic Nozzle ◽  
Two Dimensional ◽  
The Method Of Characteristics

SummaryIf a supersonic nozzle is designed for less than complete expansion of the flow, some lift force can be produced without downwards deflection of the nozzle. A theoretical analysis has been made, by the method of characteristics, for a two-dimensional nozzle consisting of an upper wedge and lower parallel shroud. General trends of lift performance with the main variables have been obtained.

Boundary Layer Closure and Heat Transfer in Constant Base Pressure and Simple Wave Guns

1978 ◽  
Vol 100 (4) ◽  
pp. 690-696 ◽  
Author(s):  
A. D. Anderson ◽  
T. J. Dahm
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Layer Thickness ◽  
Boundary Layer Thickness ◽  
Method Of Characteristics ◽  
Simple Wave ◽  
Momentum Equation ◽  
Base Pressure ◽  
Two Dimensional ◽  
The Method Of Characteristics

Solutions of the two-dimensional, unsteady integral momentum equation are obtained via the method of characteristics for two limiting modes of light gas launcher operation, the “constant base pressure gun” and the “simple wave gun”. Example predictions of boundary layer thickness and heat transfer are presented for a particular 1 in. hydrogen gun operated in each of these modes. Results for the constant base pressure gun are also presented in an approximate, more general form.

Integrated Large Eddy Simulation of Combustor and Turbine Interactions: Effect of Turbine Stage Inlet Condition

2017 ◽  
Author(s):  
Florent Duchaine ◽  
Jérôme Dombard ◽  
Laurent Gicquel ◽  
Charlie Koupper
Keyword(s):  
Large Eddy Simulation ◽  
Combustion Chamber ◽  
Rotor Blade ◽  
Turbine Stage ◽  
High Pressure Turbine ◽  
Eddy Simulation ◽  
Large Eddy ◽  
Stator Vane ◽  
Specific Configuration ◽  
Inlet Conditions

To study the effects of combustion chamber dynamics on a turbine stage aerodynamics and thermal loads, an integrated Large-Eddy Simulation of the FACTOR combustion chamber simulator along with its high pressure turbine stage is performed and compared to a standalone turbine stage computation operated under the same mean conditions. For this specific configuration, results illustrate that the aerodynamic expansion of the turbine stage is almost insensitive to the inlet turbulent conditions. However, the temperature distribution in the turbine passages as well as on the stator vane and rotor blade walls are highly impacted by these inlet conditions: underlying the importance of inlet conditions in turbine stage computations and the potential of integrated combustion chamber / turbine simulations in such a context.

Sign in / Sign up

Export Citation Format

Share Document