A Continuous Boiling Model for Face Seals

1990 ◽  
Vol 112 (2) ◽  
pp. 266-274 ◽  
Author(s):  
J. A. Yasuna ◽  
W. F. Hughes
Keyword(s):  
Laminar Flow ◽  
Phase Change ◽  
Thermal Convection ◽  
Experimental Verification ◽  
Numerical Solutions ◽  
Narrow Range ◽  
Anomalous Behavior ◽  
Adiabatic Flow ◽  
Low Leakage ◽  
Face Seals

Mechanical face seals with phase change have extensive engineering applications, yet little theory exists to predict dynamic and thermodynamic behavior. At present, numerical solutions exist for two operating extremes—for low leakage laminar flow where boiling is assumed to occur discretely, and for high leakage, turbulent adiabatic flow. A model is presented herein which allows for continuous boiling, and considers thermal convection effects in laminar flow. Sample calculations and results are compared to the discrete boiling model, and as leakage increases and convection effects become more important boiling may occur over a large portion of the seal face. It is shown that contrary to the discrete boiling model, there may exist a narrow range of stable or bistable operation even when saturation conditions exist near the seal inlet. Instability will invariably occur however if the seal is sufficiently perturbed. This analysis is intended to explain some of the anomalous behavior observed in typical sealing applications, and to act as a guide for experimental verification.

Phase Change in Liquid Face Seals II—Isothermal and Adiabatic Bounds With Real Fluids

1980 ◽  
Vol 102 (3) ◽  
pp. 350-357 ◽  
Author(s):  
W. F. Hughes ◽  
N. H. Chao
Keyword(s):  
Thermodynamic Properties ◽  
Phase Change ◽  
Leakage Rate ◽  
Operating Conditions ◽  
Isothermal Model ◽  
Reynolds Number Flow ◽  
Low Leakage ◽  
Real Fluid ◽  
Face Seals ◽  
Liquid Yield

Phase change effects in parallel and tapered liquid face seals are studied analytically. Both an isothermal and adiabatic model of low Reynolds number flow are considered by numerical integration of the descriptive equations for a real fluid. Real fluid thermodynamic properties are calculated for each step, using a computer program for the steam tables or thermodynamic properties of the fluid considered. Examples are presented for water. The general conclusions are: 1. For low leakage rate the isothermal model is more accurate and for high leakage rates the adiabatic model is more accurate. 2. Both parallel models, ordinarily neutrally stable with a liquid, yield the same general conclusions about stability. If the sealed fluid is near enough to saturation conditions, there will exist generally two values of the film gap, h, which yield the same separating force under a given set of operating conditions. For a given speed, face excursions about the larger value are stable, but excursions about the lower value are unstable, either growing to the larger h if displaced apart or collapsing if displaced together. 3. The transient of collapse is described by the adiabatic model which predicts a catastrophic collapse and then either failure or explosive return to a larger value of h. 4. Converging seals (ordinarily stable with a liquid at some given value of h) may become unstable, the phase change effect dominating the behavior and giving rise to collapse as described above. 5. The mass leakage rate is reduced significantly below the all liquid value when boiling occurs.

Integral Solutions of Phase Change With Internal Heat Generation

2004 ◽  
Author(s):  
Ali Siahpush ◽  
John Crepeau
Keyword(s):  
Differential Equation ◽  
Phase Change ◽  
Heat Generation ◽  
Numerical Solutions ◽  
Internal Heat ◽  
Melting Rate ◽  
Internal Heat Generation ◽  
Stefan Number ◽  
Temperature Boundary ◽  
Solid Liquid

This paper presents solutions to a one-dimensional solid-liquid phase change problem using the integral method for a semi-infinite material that generates internal heat. The analysis assumed a quadratic temperature profile and a constant temperature boundary condition on the exposed surface. We derived a differential equation for the solidification thickness as a function of the internal heat generation (IHG) and the Stefan number, which includes the temperature of the boundary. Plots of the numerical solutions for various values of the IHG and Stefan number show the time-dependant behavior of both the melting and solidification distances and rates. The IHG of the material opposes solidification and enhances melting. The differential equation shows that in steady-state, the thickness of the solidification band is inversely related to the square root of the IHG. The model also shows that the melting rate initially decreases and reaches a local minimum, then increases to an asymptotic value.

Laminar Flow over a Backward Facing Step: Numerical Solutions for a Test Problem

1984 ◽  
pp. 140-161
Author(s):  
K. A. Cliffe ◽  
I. P. Jones ◽  
J. D. Porter ◽  
C. P. Thompson ◽  
N. S. Wilkes
Keyword(s):  
Laminar Flow ◽  
Test Problem ◽  
Numerical Solutions ◽  
Backward Facing Step

Uncertainty Estimation for Numerical Solutions of Wall Bounded Turbulent Flows

2006 ◽  
Author(s):  
Francisco Elizalde-Blancas ◽  
Ismail Celik ◽  
Suryanarayana Pakalapati
Keyword(s):  
Laminar Flow ◽  
Turbulent Flows ◽  
Numerical Solutions ◽  
Turbulence Models ◽  
Grid Size ◽  
Gradient Term ◽  
True Error ◽  
Flow Solver ◽  
Solution Convergence ◽  
Manufactured Solution

In this study numerical solutions are presented for a steady state, incompressible, 2-D turbulent flow near a wall. For this specific problem a manufactured (exact) solution was provided by the organizers of the 2006 Lisbon Workshop [6]. With the help of manufactured solution, assessment of the true error and other relevant uncertainty measures are possible. The calculations were performed using the commercial flow solver FLUENT along with some user defined functions to define source terms and velocity profiles at boundaries. Though the flow regime is turbulent; the numerical solution is carried out for pseudo-laminar flow. This was done in order to avoid the errors implicit in turbulence models. The transformation from turbulent to laminar flow was done by defining a momentum source term which precludes the pressure gradient term. A detailed grid convergence analysis was performed. Using three-grid triplets the limiting values of the variables solved as the grid size tends to zero were calculated using different extrapolations. The L2 norms of the true error obtained from various extrapolations are assessed. These results exhibit solution convergence as the grid size decreases. It was also shown that cubic spline extrapolation perform the best among the methods considered.

Existence and uniqueness of a complex fractional system with delay

Open Physics ◽  
2013 ◽  
Vol 11 (10) ◽  
Author(s):  
Rabha Ibrahim ◽  
Hamid Jalab
Keyword(s):  
Time Delay ◽  
Complex Systems ◽  
Fractional Order ◽  
Thermal Convection ◽  
Existence And Uniqueness ◽  
Numerical Solutions ◽  
System With Delay ◽  
Fractional System ◽  
Liquid Flows ◽  
Liu System

AbstractChaotic complex systems are utilized to characterize thermal convection of liquid flows and emulate the physics of lasers. This paper deals with the time-delay of a complex fractional-order Liu system. We have examined its chaos, computed numerical solutions and established the existence and uniqueness of those solutions. Ultimately, we have presented some examples.

Sign in / Sign up

Export Citation Format

Share Document