Some Generalizations in One-Dimensional Constant Density Fluid Dynamics

1962 ◽  
Vol 84 (1) ◽  
pp. 44-48
Author(s):  
William G. Steltz ◽  
Robert P. Benedict
Keyword(s):  
Pressure Ratio ◽  
Isothermal Flow ◽  
Direct Application ◽  
Constant Density ◽  
Flow Function ◽  
Flow Process ◽  
One Dimensional ◽  
Flow Maps ◽  
Density Flow ◽  
Flow Processes

We present a Generalized Constant Density Flow Function, Γ, which is shown to have direct application in the treatment of many simplified, workless, one-dimensional flow processes. Those particular flow processes treated in this paper are: the familiar adiabatic flows, with or without friction, with area variations always allowed; and diabatic flows with or without friction, with area variations always allowed. Moreover, the Γ function is shown to have significance in a generalized flow process having an arbitrary combination of heat transfer, friction, and area and elevation variation. Development of the Γ function is given in some detail. Schematic isentropic, Fanno, Rayleigh, and isothermal flow maps are presented in terms of the conventional enthalpy—entropy diagram, and again in terms of the pressure ratio—Γ diagram. Numerical examples are included to illustrate the solution of typical problems through use of the Generalized Constant Density Flow Function.

A Generalized Approach to One-Dimensional Gas Dynamics

1962 ◽  
Vol 84 (1) ◽  
pp. 49-67 ◽  
Author(s):  
Robert P. Benedict ◽  
William G. Steltz
Keyword(s):  
Compressible Flow ◽  
Gas Dynamics ◽  
Large Scale ◽  
Pressure Ratio ◽  
Flow Function ◽  
Flow Process ◽  
One Dimensional ◽  
Flow Maps ◽  
Shock Process ◽  
Area Variation

We present a Generalized Compressible Flow Function (Γ) which is shown to have direct application in the treatment of many simplified one-dimensional flow processes. Those particular processes treated in this paper are: (a) the familiar adiabatic flows, with or without friction, with area variations always allowed; (b) the little-discussed diabatic flows, with or without friction, with area variations allowed under certain conditions; and (c) the discontinuous normal shock process. Moreover, the Γ function is shown to have significance in a generalized flow process having an arbitrary combination of heat transfer, friction, and area variation. Development of the Γ function is given in some detail. A large scale plot of pressure ratio (p/pt) versus Γ is given along with Generalized Compressible Flow Tables for the convenience of the user. Schematic isentropic, Fanno, Rayleigh, and isothermal flow maps are presented in terms of the conventional enthalpy-entropy diagram, and again in terms of the pressure ratio —Γ diagram. Numerical examples are included to illustrate the solution of typical problems through the use of the Generalized Compressible Flow Tables.

scholarly journals Numerical Solution and Application of Time-Space Fractional Governing Equations of One-Dimensional Unsteady Open Channel Flow Process

2016 ◽  
Author(s):  
Ali Ercan ◽  
M. Levent Kavvas
Keyword(s):  
Channel Flow ◽  
Open Channel ◽  
Open Channel Flow ◽  
Transport Processes ◽  
Governing Equations ◽  
Flow Process ◽  
One Dimensional ◽  
Time Space ◽  
Flow Processes ◽  
Saint Venant Equations

Abstract. Although fractional integration and differentiation have found many applications in various fields of science, such as physics, finance, bioengineering, continuum mechanics and hydrology, their engineering applications, especially in the field of fluid flow processes, are rather limited. In this study, a finite difference numerical approach is proposed to solve the time-space fractional governing equations of one-dimensional unsteady/non-uniform open channel flow process. By numerical simulations, results of the proposed fractional governing equations of the open channel flow process were compared with those of the standard Saint Venant equations. Numerical simulations showed that flow discharge and water depth can exhibit heavier tails in downstream locations as space and time fractional derivative powers decrease from 1. The fractional governing equations under consideration are generalizations of the well-known Saint Venant equations, which are written in the integer differentiation framework. The new governing equations in the fractional order differentiation framework have the capability of modeling nonlocal flow processes both in time and in space by taking the global correlations into consideration. Furthermore, the generalized flow process may shed light into understanding the theory of the anomalous transport processes and observed heavy tailed distributions of particle displacements in transport processes.

Filtering of Markov renewal queues, IV: Flow processes in feedback queues

1985 ◽  
Vol 17 (2) ◽  
pp. 386-407 ◽  
Author(s):  
Jeffrey J. Hunter
Keyword(s):  
Queue Length ◽  
Queueing Systems ◽  
Arrival Process ◽  
Markov Renewal Process ◽  
Renewal Processes ◽  
Flow Process ◽  
Special Cases ◽  
Flow Processes ◽  
Transition Points ◽  
The Times

This paper is a continuation of the study of a class of queueing systems where the queue-length process embedded at basic transition points, which consist of ‘arrivals’, ‘departures’ and ‘feedbacks’, is a Markov renewal process (MRP). The filtering procedure of Çinlar (1969) was used in [12] to show that the queue length process embedded separately at ‘arrivals’, ‘departures’, ‘feedbacks’, ‘inputs’ (arrivals and feedbacks), ‘outputs’ (departures and feedbacks) and ‘external’ transitions (arrivals and departures) are also MRP. In this paper expressions for the elements of each Markov renewal kernel are derived, and thence expressions for the distribution of the times between transitions, under stationary conditions, are found for each of the above flow processes. In particular, it is shown that the inter-event distributions for the arrival process and the departure process are the same, with an equivalent result holding for inputs and outputs. Further, expressions for the stationary joint distributions of successive intervals between events in each flow process are derived and interconnections, using the concept of reversed Markov renewal processes, are explored. Conditions under which any of the flow processes are renewal processes or, more particularly, Poisson processes are also investigated. Special cases including, in particular, the M/M/1/N and M/M/1 model with instantaneous Bernoulli feedback, are examined.

Altitude Effects on the Performance of Small Radial Turbomachinery: Part I — Compressor Impellers

2016 ◽  
Author(s):  
Dries Verstraete ◽  
Kjersti Lunnan
Keyword(s):  
Reynolds Number ◽  
Performance Analysis ◽  
Rotational Speed ◽  
Pressure Ratio ◽  
Unmanned Aircraft ◽  
Good Match ◽  
One Dimensional ◽  
Design Changes ◽  
Current Article ◽  
The Impact

Small unmanned aircraft are currently limited to flight ceilings below 20,000 ft due to the lack of an appropriate propulsion system. One of the most critical technological hurdles for an increased flight ceiling of small platforms is the impact of reduced Reynolds number conditions at altitude on the performance of small radial turbomachinery. The current article investigates the influence of Reynolds number on the efficiency and pressure ratio of two small centrifugal compressor impellers using a one-dimensional meanline performance analysis code. The results show that the efficiency and pressure ratio of the 60 mm baseline compressor at the design rotational speed drops with 6–9% from sea-level to 70,000 ft. The impact on the smaller 20 mm compressor is slightly more pronounced and amounts to 6–10%. Off-design changes at low rotational speeds are significantly higher and can amount to up to 15%. Whereas existing correlations show a good match for the efficiency drop at the design rotational speed, they fail to predict efficiency changes with rotational speed. A modified version is therefore proposed.

Invariants of weak equivalence in primitive matrices

2000 ◽  
Vol 20 (2) ◽  
pp. 611-626 ◽  
Author(s):  
RICHARD SWANSON ◽  
HANS VOLKMER
Keyword(s):  
Inverse Limit ◽  
Direct Application ◽  
Topological Classification ◽  
Weak Equivalence ◽  
Transition Matrices ◽  
Inverse Limit Spaces ◽  
Positive Dimension ◽  
One Dimensional ◽  
Dimension Group

Weak equivalence of primitive matrices is a known invariant arising naturally from the study of inverse limit spaces. Several new invariants for weak equivalence are described. It is proved that a positive dimension group isomorphism is a complete invariant for weak equivalence. For the transition matrices corresponding to periodic kneading sequences, the discriminant is proved to be an invariant when the characteristic polynomial is irreducible. The results have direct application to the topological classification of one-dimensional inverse limit spaces.

Mathematical Analysis for Off-Design Performance of Cryogenic Turboexpander

2011 ◽  
Vol 133 (3) ◽  
Author(s):  
Subrata K. Ghosh ◽  
R. K. Sahoo ◽  
Sunil K. Sarangi
Keyword(s):  
Pressure Ratio ◽  
Expansion Ratio ◽  
Flow Conditions ◽  
Flow Properties ◽  
Dimensional Solution ◽  
One Dimensional ◽  
Design Performance ◽  
Fluid Properties ◽  
The Mean ◽  
Inlet Conditions

A study has been conducted to determine the off-design performance of cryogenic turboexpander. A theoretical model to predict the losses in the components of the turboexpander along the fluid flow path has been developed. The model uses a one-dimensional solution of flow conditions through the turbine along the mean streamline. In this analysis, the changes of fluid and flow properties between different components of turboexpander have been considered. Overall, turbine geometry, pressure ratio, and mass flow rate are input information. The output includes performance and velocity diagram parameters for any number of given speeds over a range of turbine pressure ratio. The procedure allows any arbitrary combination of fluid species, inlet conditions, and expansion ratio since the fluid properties are properly taken care of in the relevant equations. The computational process is illustrated with an example.

Flow Aerodynamics Modeling of an MHD Swirl Combustor: Calculations and Experimental Verification

1982 ◽  
Vol 104 (3) ◽  
pp. 385-391 ◽  
Author(s):  
A. K. Gupta ◽  
J. M. Bee´r ◽  
J. F. Louis ◽  
A. A. Busnaina ◽  
D. G. Lilley
Keyword(s):  
Computer Code ◽  
Staggered Grid ◽  
Constant Density ◽  
Swirl Combustor ◽  
Second Stage ◽  
Density Flow ◽  
Swirl Velocity ◽  
Theoretical Predictions ◽  
Seed Distribution ◽  
Shaped Nozzle

This paper describes a computer code for calculating the flow dynamics of constant density flow in the second stage trumpet shaped nozzle section of a two stage MHD swirl combustor for application to a disk generator. The primitive pressure-velocity variable, finite difference computer code has been developed to allow the computation of inert nonreacting turbulent swirling flows in an axisymmetric MHD model swirl combustor. The method and program involve a staggered grid system for axial and radial velocities, and a line relaxation technique for efficient solution of the equations. Turbulence simulation is by way of a two-equation κ-ε model. The code produces as output the flowfield map of the nondimensional stream function, axial, and swirl velocity. Good argeement was obtained between the theoretical predictions and the qualitative experimental results. The best seed injector location for uniform seed distribution at combustor exit is with injector located centrally on the combustor axis at entrance to the second stage combustor.

Transient Fluid Flow in Porous Media: Inertia-Dominated to Viscous-Dominated Transition

1981 ◽  
Vol 103 (2) ◽  
pp. 339-343 ◽  
Author(s):  
R. H. Nilson
Keyword(s):  
Transition Period ◽  
Separation Of Variables ◽  
Pressure Ratio ◽  
Solution Procedure ◽  
Infinite Medium ◽  
Flow In Porous Media ◽  
One Dimensional ◽  
Forchheimer’S Equation ◽  
Gas Compression ◽  
Self Similar

A one-dimensional isothermal flow is induced by a step change in the pressure at the boundary of a semi-infinite medium. The early flow is inertia-dominated, in accordance with Ergun’s equation, and is self-similar in the variable x/t3. The late flow is viscous-dominated, in accordance with Darcy’s law, and is self-similar in the variable x/t. Comprehensive numerical results are presented for both of these asymptotic regimes and also for the intermediate transition period which is governed by Forchheimer’s equation. The only explicit parameter is the pressure ratio, N, which is varied from N → ∞ (strong gas-compression), through N → 1 (constant compressibility liquid), to N → 0 (strong gas-rarefaction). The solution procedure is based on a generalized separation-of-variables approach which should also be useful in other problems which possess self-similar asymptotic solutions both at early times and at late times.

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