- One-Dimensional Isentropic Flow

2013 ◽  
pp. 82-109
Keyword(s):  
One Dimensional ◽  
Isentropic Flow

scholarly journals On steady rotational high speed flows: the compressible Taylor–Culick profile

2006 ◽  
Vol 463 (2077) ◽  
pp. 131-162 ◽  
Author(s):  
Joseph Majdalani
Keyword(s):  
Mach Number ◽  
High Speed ◽  
Sonic Point ◽  
Rocket Motors ◽  
One Dimensional ◽  
Flow Models ◽  
Isentropic Flow ◽  
Aspect Ratios ◽  
Gas Compression ◽  
Solid Rocket

We consider the compressible flow analogue of the well-known Taylor–Culick profile. We first present the compressible Euler equations for steady, axisymmetric, isentropic flow assuming uniform injection of a calorically perfect gas in a porous chamber. We then apply the Rayleigh–Janzen expansion in powers of , where M w is the wall Mach number. We solve the ensuing equations to the order of and apply the results up to the sonic point in a nozzleless chamber. Area averaging is also performed to reconcile with one-dimensional theory. Our solution agrees with the existing theory to the extent that it faithfully captures the steepening of the Taylor–Culick profile with downstream movement. Based on the closed-form expressions that we obtain, the main flow attributes are quantified parametrically and compared to the existing incompressible and quasi-one-dimensional theories. Verification by computational fluid dynamics is also undertaken. Comparison with two turbulent flow models shows excellent agreement, particularly in retracing the streamwise evolution of the velocity. Regardless of the Mach number, we observe nearly identical trends in chambers that are rescaled by the (critical) sonic length, L s . Using a suitable transformation, we prove the attendant similarity and provide universal criteria that can be used to assess the relative importance of gas compression in solid rocket motors. Owing to sharper velocity gradients at the wall, we find that an incompressible model underestimates the skin friction along the wall and underpredicts the centreline speed by as much as 13% at the sonic point. In practice, such deviations become appreciable at high-injection rates or chamber aspect ratios.

Construction of solutions for compressible, isentropic Navier-Stokes equations in one space dimension with nonsmooth initial data

1986 ◽  
Vol 103 (3-4) ◽  
pp. 301-315 ◽  
Author(s):  
David Hoff
Keyword(s):  
Space Dimension ◽  
Stokes Equations ◽  
Initial Density ◽  
Navier Stokes ◽  
Jump Conditions ◽  
Simple Analysis ◽  
Navier Stokes Equations ◽  
One Dimensional ◽  
Isentropic Flow ◽  
The Cauchy Problem

We prove the global existence of weak solutions for the Cauchy problem for the Navier-Stokes equations for one-dimensional, isentropic flow when the initial velocity is in L2 and the initial density is in L2 ∩ BV. Solutions are obtained as limits of approximations obtained by building heuristic jump conditions into a semi-discrete difference scheme. This allows for a rather simple analysis in which pointwise control is achieved through piecewise H1 and total variation estimates.

Comparison of Micro-Pressure Wave Radiated Out of Tunnel Exit between Slab Track and Ballast Track

2011 ◽  
Vol 90-93 ◽  
pp. 2183-2187 ◽  
Author(s):  
Feng Geng ◽  
Qian Zhang
Keyword(s):  
Pressure Wave ◽  
High Speed ◽  
High Speed Train ◽  
Tunnel Length ◽  
One Dimensional ◽  
Isentropic Flow ◽  
Calculation Process ◽  
Ballast Track ◽  
Reduction Effect ◽  
The One

Based on the one-dimensional unsteady compressible non-isentropic flow theory, micro-pressure wave radiated out of tunnel exit generated by a high-speed train entering a tunnel was investigated. In calculation process, the track roadbed and tunnel length were considered. The results, which were qualitatively and quantitatively analyzed, show that the ballast track has reduction effect of micro-pressure wave in long tunnel.

Thermodynamic Model of the ASZ-62IR Radial Aircraft Engine

2018 ◽  
Vol 2018 (1) ◽  
pp. 36-48 ◽  
Author(s):  
Paweł Magryta ◽  
Konrad Pietrykowski ◽  
Michał Gęca
Keyword(s):  
Combustion Process ◽  
Calorific Value ◽  
Aircraft Engine ◽  
Stoichiometric Ratio ◽  
One Dimensional ◽  
Engine Model ◽  
Isentropic Flow ◽  
Air Stream ◽  
The One ◽  
Fuel Stream

Abstract The article presents assumptions of the one-dimensional model of the ASz-62IR aircraft engine. This model was developed in the AVL BOOST software. The ASz-62IR is a nine cylinder, aircraft engine in a radial configuration. It is produced by the Polish company WSK “PZL-Kalisz” S. A. The model is used for calculating parameters of the fuel stream and the air stream in intake system of the engine, as well as for the analyses of the combustion process and the exhaust flow to the external environment. The model is based on the equations describing the isentropic flow. The geometry of the channels and all parts of the model has been mapped on the basis of empirical measurements of the engine elements. The model assumes indirect injection where the gasoline was used as a fuel with the calorific value of 43.5 MJ/kg. The model assumes a mixture of a stoichiometric ratio of 14.5. This model is only part of the overall the ASz-62IR engine model. After the simulation tests on the full model the obtained results confirmed the correctness of the model used to create the mixture. It was found that the AVL BOOST software is good for the implementation of this type of work.

On the rotational compressible Taylor flow in injection-driven porous chambers

2008 ◽  
Vol 603 ◽  
pp. 391-411 ◽  
Author(s):  
BRIAN A. MAICKE ◽  
JOSEPH MAJDALANI
Keyword(s):  
Two Dimensional ◽  
Dimensional Approach ◽  
Dimensional Theory ◽  
Rocket Motors ◽  
One Dimensional ◽  
Flow Equations ◽  
Isentropic Flow ◽  
Experimental Approaches ◽  
Turbulent Models ◽  
Explicit Criteria

This work considers the compressible flow field established in a rectangular porous channel. Our treatment is based on a Rayleigh–Janzen perturbation applied to the inviscid steady two-dimensional isentropic flow equations. Closed-form expressions are then derived for the main properties of interest. Our analytical results are verified via numerical simulation, with laminar and turbulent models, and with available experimental data. They are also compared to existing one-dimensional theory and to a previous numerical pseudo-one-dimensional approach. Our analysis captures the steepening of the velocity profiles that has been reported in several studies using either computational or experimental approaches. Finally, explicit criteria are presented to quantify the effects of compressibility in two-dimensional injection-driven chambers such as those used to model slab rocket motors.

Streamlined Modeling of Compressible Flows

2006 ◽  
Author(s):  
Richard A. Gaggioli
Keyword(s):  
Compressible Flows ◽  
Governing Equations ◽  
One Dimensional ◽  
Specific Heats ◽  
Property Relations ◽  
Equation Solving ◽  
Isentropic Flow ◽  
Dimensional Modeling ◽  
Ideal Gases ◽  
The One

The development of the compressible flow tables by Shapiro, Hawthorne and Edelman [1-3] was a boon to the one-dimensional modeling of compressible flows - isentropic flow, Fanno flow, Rayleigh flow, normal shock. Nevertheless, the use of the tables is cumbersome. Furthermore, becoming engrossed with the mechanics of applying the tables, students and practitioners often lose sight of the fundamentals that are being applied. The present paper will illustrate the direct application of the basic one-dimensional governing equations to the modeling of compressible flows. In a straightforward fashion mass, momentum, energy and entropy balances, along with transport and property relations, are applied directly (without the use of tables or graphs) to model and to find solutions. Moreover, unlike the tables, the modeling does not need to assume ideal gases, let alone a constant ratio of specific heats. The key to this improved and easy approach, unavailable at the time the tables were developed, is the accessibility of equation solving software that includes property relations for gases and liquids. In particular, in the present work, EES (from fchart software; see fchart.com) was employed.

Sign in / Sign up

Export Citation Format

Share Document