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.

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.

An approach to generalized one-dimensional self-similar elasticity

2012 ◽  
Vol 61 ◽  
pp. 103-111 ◽  
Author(s):  
Thomas M. Michelitsch ◽  
Gérard A. Maugin ◽  
Mujibur Rahman ◽  
Shahram Derogar ◽  
Andrzej F. Nowakowski ◽  
...  
Keyword(s):  
One Dimensional ◽  
Self Similar

Shock–like structure of phase-change flow in porous media

1981 ◽  
Vol 104 ◽  
pp. 467-482 ◽  
Author(s):  
L. A. Romero ◽  
R. H. Nilson
Keyword(s):  
Porous Media ◽  
Phase Change ◽  
Single Phase ◽  
Flow In Porous Media ◽  
Two Phase ◽  
Flows In Porous Media ◽  
Dissipative Effects ◽  
Condensing Flows ◽  
Self Similar ◽  
Phase Change Flows

Shock-like features of phase-change flows in porous media are explained, based on the generalized Darcy model. The flow field consists of two-phase zones of parabolic/hyperbolic type as well as adjacent or imbedded single-phase zones of either parabolic (superheated, compressible vapour) or elliptic (subcooled, incompressible liquid) type. Within the two-phase zones or at the two-phase/single-phase interfaces, there may be steep gradients in saturation and temperature approaching shock-like behaviour when the dissipative effects of capillarity and heat-conduction are negligible. Illustrative of these shocked, multizone flow-structures are the transient condensing flows in porous media, for which a self-similar, shock-preserving (Rankine–Hugoniot) analysis is presented.

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.

scholarly journals Gas-Driven Fracture Propagation

1981 ◽  
Vol 48 (4) ◽  
pp. 757-762 ◽  
Author(s):  
R. H. Nilson
Keyword(s):  
Gas Flow ◽  
Oil And Gas ◽  
Elementary Function ◽  
Separation Of Variables ◽  
Pressure Ratio ◽  
Leading Edge ◽  
Late Time ◽  
Shooting Methods ◽  
Uniform Compression ◽  
Penetration Length

A one-dimensional gas-flow drives a wedge-shaped fracture into a linearly elastic, impermeable half space which is in uniform compression, σ∞, at infinity. Under a constant driving pressure, p0, the fracture/flow system accelerates through a sequence of three self-similar asymptotic regimes (laminar, turbulent, inviscid) in which the fracture grows like an elementary function of time (exponential, near-unity power, and linear, respectively). In each regime, the transport equations are reducible under a separation-of-variables transformation. The integro-differential equations which describe the viscous flows are solved by iterative shooting methods, using expansion techniques to accomodate a zero-pressure singularity at the leading edge of the flow. These numerical results are complemented by an asymptotic analysis for large pressure ratio (N = p0/σ∞ → ∞) which exploits the disparity between the fracture length and penetration length of the flow. Since the seepage losses to a surrounding porous medium are shown to be negligable in the late-time long-fracture limit, the results have application to geologic problems such as: containment evaluation of underground nuclear tests, stimulation of oil and gas wells, and permeability enhancement prior to in situ combustion processes.

One-Dimensional Transient Heat Conduction in Composite Living Perfuse Tissue

2013 ◽  
Vol 135 (7) ◽  
Author(s):  
S. M. Becker
Keyword(s):  
Heat Conduction ◽  
Initial Conditions ◽  
Separation Of Variables ◽  
Composite Layer ◽  
Circulatory System ◽  
Transient Heat Conduction ◽  
Bioheat Equation ◽  
Perfusion Rate ◽  
One Dimensional ◽  
Perfuse Tissue

Modeling the conduction of heat in living tissue requires the consideration of sudden spatial discontinuities in property values as well as the presence of the body's circulatory system. This paper presents a description of the separation of variables method that results in a remarkably simple solution of transient heat conduction in a perfuse composite slab for which at least one of the layers experiences a zero perfusion rate. The method uses the natural analytic approach and formats the description so that the constants of integration of each composite layer are expressed in terms of those of the previous layer's eigenfunctions. This allows the solution to be “built” in a very systematic and sequential manner. The method is presented in the context of the Pennes bioheat equation for which the solution is developed for a system composed of any number of N layers with arbitrary initial conditions.

Sign in / Sign up

Export Citation Format

Share Document