Direct Computational Simulations for Internal Condensing Flows and Results on Attainability/Stability of Steady Solutions, Their Intrinsic Waviness, and Their Noise Sensitivity

2004 ◽  
Vol 71 (1) ◽  
pp. 69-88 ◽  
Author(s):  
A. Narain ◽  
Q. Liang ◽  
G. Yu ◽  
X. Wang
Keyword(s):  
Numerical Solutions ◽  
Resonance Condition ◽  
Vertical Channel ◽  
High Growth ◽  
Film Condensation ◽  
Noise Sensitivity ◽  
Reported Study ◽  
Condensing Flows ◽  
Steady Solutions ◽  
Internal Condensing Flows

The paper presents a new two-dimensional computational approach and results for laminar/laminar internal condensing flows. Accurate numerical solutions of the full governing equations are presented for steady and unsteady film condensation flows on a sidewall inside a vertical channel. It is found that exit conditions and noise sensitivity are important. Even for stable steady solutions obtained for nearly incompressible vapor phase flows associated with unconstrained exit conditions, the noise sensitivity to the condensing surface’s minuscule transverse vibrations is high. The structure of waves, the underlying characteristics, and the “growth/damping rates” for the disturbances are discussed. A resonance condition for high “growth rates” is proposed and its efficacy in significantly enhancing wave motion and heat transfer rates is computationally demonstrated. For the unconstrained exit cases, the results make possible a separately reported study of the effects of shear, gravity, and surface tension on noise sensitive stable solutions.

Effects of Gravity, Shear and Surface Tension in Internal Condensing Flows: Results From Direct Computational Simulations

2004 ◽  
Vol 126 (5) ◽  
pp. 676-686 ◽  
Author(s):  
Q. Liang ◽  
X. Wang ◽  
A. Narain
Keyword(s):  
Surface Tension ◽  
Normal Gravity ◽  
Numerical Solutions ◽  
Vertical Channel ◽  
Film Condensation ◽  
Vapor Flow ◽  
Zero Gravity ◽  
Pressure Drops ◽  
Condensing Flows ◽  
Internal Condensing Flows

The paper presents accurate numerical solutions of the full two-dimensional governing equations for steady and unsteady laminar/laminar internal condensing flows. The results relate to issues of better design and integration of condenser-sections in thermal management systems (looped heat pipes, etc.). The flow geometry, in normal or zero gravity, is chosen to be the inside of a channel with film condensation on one of the walls. In normal gravity, film condensation is on the bottom wall of a tilted (from vertical to horizontal) channel. It is found that it is important to know whether the exit conditions are constrained or unconstrained because nearly incompressible vapor flows occur only for exit conditions that are unconstrained. For the incompressible vapor flow situations, a method for computationally obtaining the requisite exit condition and associated stable steady/quasi-steady solutions is given here and the resulting solutions are shown to be in good agreement with some relevant experimental data for horizontal channels. These solutions are shown to be sensitive to the frequency and amplitude of the various Fourier components that represent the ever-present and minuscule transverse vibrations (standing waves) of the condensing surface. Compared to a vertical channel in normal gravity, shear driven zero gravity cases have much larger pressure drops, much slower wave speeds, much larger noise sensitive wave amplitudes that are controlled by surface tension, and narrower flow regime boundaries within which vapor flow can be considered incompressible. It is shown that significant enhancement in wave-energy and/or heat-transfer rates, if desired, are possible by designing the condensing surface noise to be in resonance with the intrinsic waves.

Effects of Gravity and Surface Tension and Interfacial-Waves and Heat-Transfer Rates in Internal Condensing Flows

2003 ◽  
Author(s):  
Q. Liang ◽  
X. Wang ◽  
A. S. Barve ◽  
A. Narain
Keyword(s):  
Heat Transfer ◽  
Surface Tension ◽  
Numerical Solutions ◽  
Film Condensation ◽  
Vapor Flow ◽  
Transfer Rates ◽  
Condensing Flows ◽  
Steady Solutions ◽  
Internal Condensing Flows ◽  
Good Agreement

The paper presents accurate numerical solutions of the full 2D governing equations for steady and unsteady laminar/laminar internal condensing flows. The chosen geometry allows for film condensation on the bottom wall of a tilted (from vertical to horizontal) channel. It is found that it is important to know whether the exit conditions are constrained or unconstrained because incompressible vapor flows occur only for exit conditions that are unconstrained. For the incompressible vapor flow situations, a method for computationally obtaining the stable steady/quasi-steady solutions is given here and the resulting solutions are shown to be in good agreement with some relevant experimental data for horizontal channels. These solutions are shown to be sensitive to the frequency-content and strength of ever-present minuscule transverse vibrations of the condensing surface. The effects of noise-sensitivity, gravity (terrestrial to zero-gravity), and surface tension on the attainability of stable steady/quasi-steady solutions, structure of superposed waves, and heat-transfer rates are discussed. It is shown that significant enhancement in wave-energy and heat-transfer rates are possible by designing the condensing surface noise to be in resonance with the intrinsic waves.

Direct Computational Simulations for Condensation Inside Tubes and Channels

2005 ◽  
Author(s):  
L. Phan ◽  
X. Wang ◽  
S. Kulkarni ◽  
A. Narain
Keyword(s):  
Numerical Solutions ◽  
Vertical Tube ◽  
Film Condensation ◽  
Vapor Flow ◽  
Steady Flows ◽  
Channel Geometry ◽  
Pressure Drops ◽  
Condensing Flows ◽  
Gravity Driven ◽  
Internal Condensing Flows

The paper presents accurate numerical solutions of the full 2D governing equations for steady and unsteady laminar/laminar internal condensing flows of pure vapor (R-113 and FC-72) inside a vertical tube and a channel. The film condensation is on the inside wall of a tube or one of the walls of a channel (the lower wall in case of a downward sloping channel). The new geometry in this paper is the cylindrical in-tube geometry with axisymmetric flows (vertical 1g or 0g flows). The new results encompass both the cylindrical and the earlier studied channel geometry. Exit condition specifications are again found to be important. The computations are able to predict whether or not a steady flow exists under a natural exit condition (selected from a range of choices available at the exit). If natural steady/quasi-steady flows exist — as is shown to be the case for gravity dominated or strong shear dominated condensate flows — the computations are able to predict both the natural exit condition and the associated condensate flow’s point of transition from stable to unstable behavior. Compared to gravity driven, shear driven cases (zero gravity or horizontal cases) tend to destabilize easier and generally have much larger pressure drops, much slower wave speeds, much larger role of surface tension, and much narrower flow regime boundaries within which the vapor flow can be modelled incompressible. It is found that only in gravity driven cases, be it vertical in-tube or inclined channel geometry, interfacial waves are able to cause a concurrent enhancement in heat transfer rates along with an enhancement in interfacial shear. Also it is found that this enhancement is significant if the condensing surface noise is in resonance with the intrinsic waves.

Free Surface Tracking and Steady/Unsteady Computational Simulations for Internal Condensing Flows

2001 ◽  
Author(s):  
A. Narain ◽  
Q. Liang ◽  
A. S. Barve
Keyword(s):  
Film Condensation ◽  
Navier Stokes ◽  
Steady Flows ◽  
Time Step ◽  
Navier Stokes Equation ◽  
Stability And Instability ◽  
Flow Mechanisms ◽  
Condensing Flows ◽  
Steady Solutions ◽  
Internal Condensing Flows

Abstract The computational investigation in this paper explores a new technique for steady and unsteady internal condensing flows in the annular/stratified regime. Simulation capabilities for both steady and unsteady interface laminar/laminar situations are presented for film condensation on the bottom wall of a small-to-moderate gap channel. The unsteady simulations employ a suitable adaptive grid and the solution of an interface tracking hyperbolic equation (of the type used in level-set or VOF methods). At each time-step, the scheme locates the interface, solves the Navier-Stokes equation in each phase, satisfies the full non-linear conditions at the phase change interface, and satisfies the necessary inlet, outlet, and wall conditions. The stability and instability of various exit condition dependent steady solutions are inferred from direct unsteady simulations and this leads to insights into the flow mechanisms that determine the eventual quasi-steady flows. For some cases it is found that waviness and heat transfer rates are enhanced significantly by the flow’s sensitivity to the frequency content of persistent noise in the inlet data.

Forced Flow of Vapor Condensing Over a Horizontal Plate (Problem of Cess and Koh): Steady and Unsteady Solutions of the Full 2D Problem

2010 ◽  
Vol 132 (10) ◽  
Author(s):  
S. Kulkarni ◽  
A. Narain ◽  
S. Mitra
Keyword(s):  
Numerical Solutions ◽  
Saturated Vapor ◽  
Threshold Value ◽  
Steady Solution ◽  
Forced Flow ◽  
Film Condensation ◽  
Horizontal Plate ◽  
Governing Equations ◽  
Long Time ◽  
Steady Solutions

Accurate steady and unsteady numerical solutions of the full 2D governing equations—which model the forced film condensation flow of saturated vapor over a semi-infinite horizontal plate (the problem of Cess and Koh)—are obtained over a range of flow parameters. The results presented here are used to better understand the limitations of the well-known similarity solutions given by Koh. It is found that steady/quasisteady filmwise solution exists only if the inlet speed is above a certain threshold value. Above this threshold speed, steady/quasisteady film condensation solutions exist and their film thickness variations are approximately the same as the similarity solution given by Koh. However, these steady solutions differ from the Koh solution regarding pressure variations and associated effects in the leading part of the plate. Besides results based on the solutions of the full steady governing equations, this paper also presents unsteady solutions that characterize the steady solutions’ attainability, stability (response to initial disturbances), and their response to ever-present minuscule noise on the condensing-surface. For this shear-driven flow, the paper finds that if the uniform vapor speed is above a threshold value, an unsteady solution that begins with any reasonable initial-guess is attracted in time to a steady solution. This long time limiting solution is the same—within computational errors—as the solution of the steady problem. The reported unsteady solutions that yield the steady solution in the long time limit also yield “attraction rates” for nonlinear stability analysis of the steady solutions. The attraction rates are found to diminish gradually with increasing distance from the leading edge and with decreasing inlet vapor speed. These steady solutions are generally found to be stable to initial disturbances on the interface as well as in any flow variable in the interior of the flow domain. The results for low vapor speeds below the threshold value indicate that the unsteady solutions exhibit nonexistence of any steady limit of filmwise flow in the aft portion of the solution. Even when a steady solution exists, the flow attainability is also shown to be difficult (because of waviness and other sensitivities) at large downstream distances.

Internal Condensing Flows Inside a Vertical Pipe: Experimental/Computational Investigations of Effects of Constrained and Natural Exit Conditions

2005 ◽  
Author(s):  
A. Narain ◽  
A. Siemionko ◽  
J. H. Kurita ◽  
T. W. Ng ◽  
N. Kim ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Power Plants ◽  
Computational Simulation ◽  
Vertical Tube ◽  
Film Condensation ◽  
Flow Loop ◽  
Transfer Rates ◽  
Application Systems ◽  
Condensing Flows ◽  
Internal Condensing Flows

The flow and heat transfer rates inside a condenser depend on the specification of inlet, wall, and exit conditions. For steady/quasi-steady internal condensing flows (that involve compressible vapor at low Mach Numbers), the vapor’s ability to change its density — and hence interfacial mass transfer rates and associated locations of the interface — allows the flow to have a rather significant dependence on exit conditions. Both experimental and direct computational simulation results presented here show that this is indeed the case for flows of pure vapor experiencing film condensation on the inside walls of a vertical tube. In applications, the totality of boundary conditions are determined not only by the condenser; but also by the flow-loop (or the system) — of which the condenser is only a part. Therefore, the results outlined here should contribute towards a better understanding of the behavior (particularly the extent to which vapor compressibility effects affect the flow regimes of operation — i.e. annular, plug/churn, etc.) and response (transients due to start-up, system instabilities, etc.) of condensers in application systems (e.g. Rankine Cycle power plants, Capillary Pumped Loops, Looped Heat Pipes, etc.). In this connection, an experimental example of a relevant system instability is presented here. In summary, the experimental results presented here, and computational results presented elsewhere, reinforce the fact that there exist multiple steady solutions (with different heat transfer rates) for different exit conditions and that there also exists a “natural” steady solution for straight vertical condensers (circular and rectangular cross-sections).

Similar Solutions for Laminar Film Condensation with Adverse Pressure Gradients

1973 ◽  
Vol 95 (2) ◽  
pp. 268-270 ◽  
Author(s):  
P. M. Beckett
Keyword(s):  
Numerical Solutions ◽  
Saturated Vapor ◽  
Film Condensation ◽  
Pressure Gradients ◽  
Two Dimensional ◽  
Laminar Film ◽  
Approximate Models ◽  
Laminar Film Condensation ◽  
Similar Solutions

Steady two-dimensional laminar film condensation is investigated when the saturated vapor has the Falkner–Skan mainstream. Numerical solutions and approximate models are discussed with reference to other published work.

scholarly journals Consistent Weighted Average Flux of Well-Balanced TVD-RK Discontinuous Galerkin Method for Shallow Water Flows

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
Thida Pongsanguansin ◽  
Montri Maleewong ◽  
Khamron Mekchay
Keyword(s):  
Shallow Water ◽  
Discontinuous Galerkin ◽  
Numerical Solutions ◽  
Order Approximation ◽  
Weighted Average ◽  
Flat Bottom ◽  
Flux Function ◽  
Dg Method ◽  
Average Flux ◽  
Steady Solutions

A well-balanced scheme with total variation diminishing Runge-Kutta discontinuous Galerkin (TVD-RK DG) method for solving shallow water equations is presented. Generally, the flux function at cell interface in the TVD-RK DG scheme is approximated by using the Harten-Lax-van Leer (HLL) method. Here, we apply the weighted average flux (WAF) which is higher order approximation instead of using the HLL in the TVD-RK DG method. The consistency property is shown. The modified well-balanced technique for flux gradient and source terms under the WAF approximations is developed. The accuracy of numerical solutions is demonstrated by simulating dam-break flows with the flat bottom. The steady solutions with shock can be captured correctly without spurious oscillations near the shock front. This presents the other flux approximations in the TVD-RK DG method for shallow water simulations.

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