Stagnation pressure effect on the supersonic flow parameters with application for air in nozzles

2016 ◽  
Vol 120 (1224) ◽  
pp. 313-354 ◽  
Author(s):  
Merouane Salhi ◽  
Toufik Zebbiche ◽  
Abderrahmane Mehalem
Keyword(s):  
Supersonic Flow ◽  
Supersonic Nozzle ◽  
Molecular Size ◽  
State Equation ◽  
Stagnation Pressure ◽  
Design Parameters ◽  
Perfect Gas ◽  
Thrust Coefficient ◽  
Real Gas ◽  
Flow Parameters

ABSTRACTWhen the stagnation pressure of a perfect gas increases, the specific heat and their ratio do not remain constant anymore and start to vary with this pressure. The gas doesn't stay perfect. Its state equation changes and it becomes a real gas. In this case, the effects of molecular size and intermolecular attraction forces intervene to correct the state equation. The aim of this work is to determine the effect of stagnation pressure on the thermodynamic, physical and geometrical supersonic flow parameters in order to find a general form for real gas. With the assumptions that Berthelot's state equation accounts for molecular size and intermolecular force effects, expressions are developed for analysing the supersonic flow for thermally and calorically imperfect gas lower than the dissociation molecules threshold. The design parameters of the supersonic nozzle-like thrust coefficient depend directly on the stagnation parameters of the combustion chamber. The application made for air. A computation of error was made in this case to give a limit of the perfect gas model compared to the real gas model.

Stagnation pressure effect on Prandtl Meyer function for air

2016 ◽  
Vol 231 (2) ◽  
pp. 326-337 ◽  
Author(s):  
Merouane Salhi ◽  
Toufik Zebbiche ◽  
Abderrahmane Mehalem
Keyword(s):  
High Temperature ◽  
Pressure Effect ◽  
Molecular Size ◽  
State Equation ◽  
Stagnation Pressure ◽  
Intermolecular Force ◽  
Perfect Gas ◽  
Real Gas ◽  
New Form ◽  
Made In

When the stagnation pressure of a perfect gas increases, the specific heat and their ratio do not remain constant anymore and start to vary with this pressure. The gas does not stay perfect. Its state equation change and it becomes for a real gas. In this case, the effects of molecular size and intermolecular attraction forces intervene to correct the state equation, the thermodynamic parameters and the value of Prandtl Meyer function. The aim of this work is developing a new form of Prandtl Meyer function based on those assumptions; and determining the effect of stagnation pressure on this function. With the assumptions that Berthelot’s state equation accounts for molecular size and intermolecular force effects, expressions are developed for analysing the supersonic flow for thermally and calorically imperfect gas lower than the dissociation molecules threshold. The supersonic parameters depend directly on the stagnation parameters of the combustion chamber. The application is for air. A computation of error was made in this case to give a limit of the perfect gas and the high temperature models compared to the real gas model.

scholarly journals Effect of stagnation temperature on supersonic flow parameters application for air in nozzles

2007 ◽  
Vol 111 (1115) ◽  
pp. 31-40 ◽  
Author(s):  
T. Zebbiche ◽  
Z. Youbi
Keyword(s):  
Supersonic Flow ◽  
Supersonic Nozzle ◽  
Stagnation Temperature ◽  
Algebraic Equations ◽  
Perfect Gas ◽  
State Equations ◽  
Specific Heats ◽  
Flow Parameters ◽  
Analytical Functions ◽  
Dissociation Threshold

Abstract When the stagnation temperature of a perfect gas increases, the specific heats and their ratio do not remain constant and start to vary with the temperature. The gas remains perfect; its state equations remain valid, so it can be named as calorifically imperfect gas. The aim of this research is to develop the necessary thermodynamic and geometrical equations and to study the supersonic flow at high temperature, lower than the dissociation threshold. The results are found by the resolution of nonlinear algebraic equations and integration of complex analytical functions where the exact calculation is impossible. The dichotomy method is used to solve the nonlinear equations and Simpson’s algorithm for the numerical integration applied. A condensation of the nodes is used. The functions to be integrated have a high gradient at the extremity of the interval of integration. The comparison is made with the calorifically perfect gas to determine the error. The application is made for air in a supersonic nozzle.

Validation of a 3D RANS Solver With a State Equation of Thermally Perfect and Calorically Imperfect Gas on a Multi-Stage Low-Pressure Steam Turbine Flow

2005 ◽  
Vol 127 (1) ◽  
pp. 83-93 ◽  
Author(s):  
Piotr Lampart ◽  
Andrey Rusanov ◽  
Sergey Yershov ◽  
Stanislaw Marcinkowski ◽  
Andrzej Gardzilewicz
Keyword(s):  
Steam Turbine ◽  
Low Pressure ◽  
State Equation ◽  
Linear Functions ◽  
Perfect Gas ◽  
Specific Heats ◽  
Flow Parameters ◽  
Imperfect Gas ◽  
Multi Stage ◽  
Pressure Steam

A state equation of thermally perfect and calorically imperfect gas is implemented in a 3D RANS solver for turbomachinery flow applications. The specific heats are assumed as linear functions of temperature. The model is validated on a five-stage low-pressure steam turbine. The computational results exhibit the process of expansion in the turbine. The computed and measured distributions of flow parameters in axial gaps downstream of subsequent turbine stages are found to agree reasonably well. It is also shown that the obtained numerical solution gives considerable improvement over the solution based on the thermally and calorically perfect gas model.

Experimental study on the characteristics of axisymmetric cavity actuated supersonic flow

2016 ◽  
Vol 231 (14) ◽  
pp. 2570-2577
Author(s):  
S Jeyakumar ◽  
Shan M Assis ◽  
K Jayaraman
Keyword(s):  
Supersonic Flow ◽  
Pressure Loss ◽  
Static Pressure ◽  
Effective Means ◽  
Supersonic Nozzle ◽  
Stagnation Pressure ◽  
Complex Flow ◽  
Wall Angle ◽  
Blow Down ◽  
Axisymmetric Cavity

The effective means of air fuel mixing and flame holding can be achieved by incorporating cavity in supersonic combustor. Understanding the complex flow field of cavity flow is essential for the design of supersonic combustor. An attempt is made to understand the characteristics of supersonic flow past axisymmetric cavity, and a series of nonreacting experiments are carried out in a blow-down type supersonic flow facility. The facility consists of a supersonic nozzle, issues a flow Mach number of 1.80 into a circular cross sectional supersonic combustor in which axisymmetric cavity is placed. Cavity of two consecutive aft wall angles is the key parameter for the study. The performance of the cavity is investigated based on the static pressure measurement, momentum flux distribution at the exit plane of the combustor, and the stagnation pressure loss of the flow. Wall static pressure distribution revealed that pressure increases with decrease in the secondary aft wall angle below 45° due to stronger recompression of shear layers. Moreover, decreasing primary aft wall angle provides a uniform mixing profile along with decrease in stagnation pressure loss across the combustor.

Effect of finite width cavity in axisymmetric supersonic flow field

2016 ◽  
Vol 232 (1) ◽  
pp. 180-184 ◽  
Author(s):  
S Jeyakumar ◽  
K Jayaraman
Keyword(s):  
Supersonic Flow ◽  
Flow Field ◽  
Test Section ◽  
Pressure Loss ◽  
Supersonic Nozzle ◽  
Stagnation Pressure ◽  
Test Facility ◽  
Main Stream ◽  
Finite Width ◽  
Constant Length

In this research, the effect of finite width cavities in supersonic flow field is experimentally investigated. The test facility consists of a supersonic nozzle, which provides flow Mach number of 1.9. A circular cross-sectional test section is fastened at the exit of the nozzle. Cavities are incorporated in the test section at a distance of 20 mm from the inlet. Cavities of constant length and width, and varying depth are used for the study. Entrainment of flow in the main stream is observed immediate downstream of the cavity aft edge due to three dimensional effect. As the depth of the cavity is increased, residence time of the fluid as well as the mixing characteristics are enhanced and stagnation pressure loss also increased. Twin cavities are also arranged symmetrically, which further leads to an improvement in mixing with marginal rise in stagnation pressure loss.

Effect of Axisymmetric Aft Wall Angle Cavity in Supersonic Flow Field

2018 ◽  
Vol 35 (1) ◽  
pp. 29-34 ◽  
Author(s):  
S. Jeyakumar ◽  
Shan M. Assis ◽  
K. Jayaraman
Keyword(s):  
Supersonic Flow ◽  
Flow Field ◽  
Supersonic Nozzle ◽  
Stagnation Pressure ◽  
Wall Angle ◽  
Blow Down ◽  
Cross Sectional ◽  
Axisymmetric Cavity ◽  
Scramjet Combustors ◽  
Stable Flow

AbstractCavity plays a significant role in scramjet combustors to enhance mixing and flame holding of supersonic streams. In this study, the characteristics of axisymmetric cavity with varying aft wall angles in a non-reacting supersonic flow field are experimentally investigated. The experiments are conducted in a blow-down type supersonic flow facility. The facility consists of a supersonic nozzle followed by a circular cross sectional duct. The axisymmetric cavity is incorporated inside the duct. Cavity aft wall is inclined with two consecutive angles. The performance of the aft wall cavities are compared with rectangular cavity. Decreasing aft wall angle reduces the cavity drag due to the stable flow field which is vital for flame holding in supersonic combustor. Uniform mixing and gradual decrease in stagnation pressure loss can be achieved by decreasing the cavity aft wall angle.

scholarly journals A new design method for high conditions applied to minimum length nozzles

2021 ◽  
Vol 33 ◽  
pp. 134-151
Author(s):  
Mohamed Roudane ◽  
Merouane Salhi ◽  
Ahmed Boucherit
Keyword(s):  
Initial Conditions ◽  
Design Method ◽  
Molecular Size ◽  
State Equation ◽  
Minimum Length ◽  
Real Gas ◽  
The Real ◽  
Finite Differences Method ◽  
Linear Differential ◽  
The One

This present work focused on new nozzles design method, based on the characteristics method, which is a technique method to reduce a partial differential equation to linear differential equations along which the solution can be integrated from initial conditions. The latter is developed under the real gas theory, because when the both pressure and temperature of a gas increases, the specific heat and their ratio do not remain constant anymore and start to vary with the gas parameters. The gas doesn’t stay perfect, and it becomes a real gas. The presented equations of the characteristics remain valid whatever area or field of study. With the assumptions that Berthelot’s state equation accounts for molecular size and intermolecular force effects, expressions are developed for analyzing the supersonic flow for thermally and calorically imperfect gas. The resolution has been made by the finite differences method using the corrector predictor algorithm. As result, the developed mathematical model used to design 2D minimum length nozzles under effect of the stagnation parameters of fluid flow. A comparison for air with the perfect gas PG and high temperature HT models on the one hand and our results by the real gas theory on the other of nozzles are made. An important gain of length and weight can rise up to 40% and 20% respectively. It is in this context that Minimum Length Nozzle (MLN) nozzles for aerospace engines based on real gas theory were developed to achieve maximum thrust with the smallest possible nozzle weight (minimum length).

One-dimensional adiabatic flow of equilibrium gas–particle mixtures in long vertical ducts with friction

1989 ◽  
Vol 203 ◽  
pp. 251-272 ◽  
Author(s):  
Guido Buresti ◽  
Claudio Casarosa
Keyword(s):  
Equilibrium Mixture ◽  
Adiabatic Heating ◽  
Explosive Eruptions ◽  
Perfect Gas ◽  
Typical Application ◽  
One Dimensional ◽  
Adiabatic Flow ◽  
Flow Parameters ◽  
Constant Area ◽  
Inlet Conditions

The equations of the steady, adiabatic, one-dimensional flow of an equilibrium mixture of a perfect gas and incompressible particles, in constant-area ducts with friction, are derived taking into account the effects of gravity and of the finite volume of the particles. As is the case for a pure gas, the mixture is shown to be subject to the phenomenon of choking, and the possibility of an adiabatic heating of the mixture in a subsonic expansion is also theoretically predicted for certain flow inlet conditions. The model may be used to approximately describe the conditions existing in portions of volcanic conduits during the Plinian phases of explosive eruptions. Some results of the numerical integration of the equations for a typical application of this type are briefly discussed, thus showing the potential of the model for carrying out rapid analyses of the influence of the main geometrical and flow parameters describing the problem. A non-volcanological application is also analysed to illustrate the possibility of the adiabatic heating of the mixture.

Uncertainty quantification of real gas models in CO2 supersonic flow

2021 ◽  
pp. 101479
Author(s):  
Wenna Raissa dos Santos Cruz ◽  
Fabio Pereira dos Santos ◽  
Ricardo de Andrade Medronho
Keyword(s):  
Supersonic Flow ◽  
Uncertainty Quantification ◽  
Real Gas

Aerodynamic Similarity Principles and Scaling Laws for Windmilling Fans

2018 ◽  
Author(s):  
Dilip Prasad
Keyword(s):  
Rotational Speed ◽  
Pressure Loss ◽  
Scaling Laws ◽  
Dynamic Pressure ◽  
Stagnation Pressure ◽  
Design Parameters ◽  
Similarity Parameter ◽  
Wide Range ◽  
Simulation Results ◽  
Good Agreement

Windmilling requirements for aircraft engines often define propulsion and airframe design parameters. The present study is focused is on two key quantities of interest during windmill operation: fan rotational speed and stage losses. A model for the rotor exit flow is developed, that serves to bring out a similarity parameter for the fan rotational speed. Furthermore, the model shows that the spanwise flow profiles are independent of the throughflow, being determined solely by the configuration geometry. Interrogation of previous numerical simulations verifies the self-similar nature of the flow. The analysis also demonstrates that the vane inlet dynamic pressure is the appropriate scale for the stagnation pressure loss across the rotor and splitter. Examination of the simulation results for the stator reveals that the flow blockage resulting from the severely negative incidence that occurs at windmill remains constant across a wide range of mass flow rates. For a given throughflow rate, the velocity scale is then shown to be that associated with the unblocked vane exit area, leading naturally to the definition of a dynamic pressure scale for the stator stagnation pressure loss. The proposed scaling procedures for the component losses are applied to the flow configuration of Prasad and Lord (2010). Comparison of simulation results for the rotor-splitter and stator losses determined using these procedures indicates very good agreement. Analogous to the loss scaling, a procedure based on the fan speed similarity parameter is developed to determine the windmill rotational speed and is also found to be in good agreement with engine data. Thus, despite their simplicity, the methods developed here possess sufficient fidelity to be employed in design prediction models for aircraft propulsion systems.

Sign in / Sign up

Export Citation Format

Share Document