A Small Disturbance Model for Transonic Flow of Pure Steam With Condensation

2018 ◽  
Vol 141 (3) ◽  
Author(s):  
Akashdeep Singh Virk ◽  
Zvi Rusak
Keyword(s):  
Mass Fraction ◽  
Nonlinear Partial Differential Equation ◽  
Inviscid Flow ◽  
Droplet Growth ◽  
Small Disturbance ◽  
Flow Equations ◽  
Liquid Saturation ◽  
Nonequilibrium Condensation ◽  
Disturbance Model ◽  
Pure Steam

A small-disturbance model to study transonic steady condensing flow of pure steam around a thin airfoil is developed. Water vapor thermodynamics is described by the perfect gas model and its dynamics by the compressible inviscid flow equations. Classical nucleation and droplet growth theory for homogeneous and nonequilibrium condensation is used to compute the condensate mass fraction. The model is derived from an asymptotic analysis of the flow and condensation equations in terms of the proximity of upstream flow Mach number to 1, the small thickness ratio of airfoil, the small quantity of condensate, and the small angle-of-attack. The flow field may be described by a nonhomogeneous and nonlinear partial differential equation along with a set of four ordinary differential equations for calculating condensate mass fraction. The analysis provides a list of similarity parameters that describe the flow physics. A numerical scheme, which is composed of Murman and Cole's algorithm for the computation of flow parameters and Simpson's integration method for calculation of condensate mass fraction, is applied. The model is used to analyze the effects of heat release due to condensation on the aerodynamic performance of airfoils operating in steam at high temperatures and pressures near the vapor–liquid saturation dome.

Transonic flow of moist air around a thin airfoil with non-equilibrium and homogeneous condensation

2000 ◽  
Vol 403 ◽  
pp. 173-199 ◽  
Author(s):  
ZVI RUSAK ◽  
JANG-CHANG LEE
Keyword(s):  
Transonic Flow ◽  
Droplet Growth ◽  
Inviscid Fluid ◽  
Small Disturbance ◽  
Moist Air ◽  
Integration Rule ◽  
Flow Equations ◽  
Homogeneous Condensation ◽  
Thin Airfoil ◽  
Non Equilibrium

A new small-disturbance model for a steady transonic flow of moist air with non-equilibrium and homogeneous condensation around a thin airfoil is presented. The model explores the nonlinear interactions among the near-sonic speed of the flow, the small thickness ratio and angle of attack of the airfoil, and the small amount of water vapour in the air. The condensation rate is calculated according to classical nucleation and droplet growth models. The asymptotic analysis gives the similarity parameters that govern the flow problem. Also, the flow field can be described by a non-homogeneous (extended) transonic small-disturbance (TSD) equation coupled with a set of four ordinary differential equations for the calculation of the condensate (or sublimate) mass fraction. An iterative numerical scheme which combines Murman & Cole's (1971) method for the solution of the TSD equation with Simpson's integration rule for the estimation of the condensate mass production is developed. The results show good agreement with available numerical simulations using the inviscid fluid flow equations. The model is used to study the effects of humidity and of energy supply from condensation on the aerodynamic performance of airfoils.

Essential Ingredients for the Computation of Steady and Unsteady Blade Boundary Layers

1991 ◽  
Vol 113 (4) ◽  
pp. 608-616 ◽  
Author(s):  
H. M. Jang ◽  
J. A. Ekaterinaris ◽  
M. F. Platzer ◽  
T. Cebeci
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Stokes Equations ◽  
Inviscid Flow ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Transitional Region ◽  
Low Reynolds Numbers ◽  
Flow Equations ◽  
Low Reynolds

Two methods are described for calculating pressure distributions and boundary layers on blades subjected to low Reynolds numbers and ramp-type motion. The first is based on an interactive scheme in which the inviscid flow is computed by a panel method and the boundary layer flow by an inverse method that makes use of the Hilbert integral to couple the solutions of the inviscid and viscous flow equations. The second method is based on the solution of the compressible Navier–Stokes equations with an embedded grid technique that permits accurate calculation of boundary layer flows. Studies for the Eppler-387 and NACA-0012 airfoils indicate that both methods can be used to calculate the behavior of unsteady blade boundary layers at low Reynolds numbers provided that the location of transition is computed with the en method and the transitional region is modeled properly.

Compressible Boundary Layer-Inviscid Flow Interactions in Entrance Region of Internal Flows

1967 ◽  
Vol 89 (4) ◽  
pp. 281-288 ◽  
Author(s):  
V. D. Blankenship ◽  
P. M. Chung
Keyword(s):  
Boundary Layer ◽  
Shock Tube ◽  
Inviscid Flow ◽  
Perturbation Parameter ◽  
Entrance Region ◽  
Compressible Boundary Layer ◽  
Internal Flows ◽  
Flow Equations ◽  
Boundary Layer Equations ◽  
Interaction Problem

The coupling between the inviscid flow and the compressible boundary layer in the developing entrance region for internal flows is analyzed by solving the particular inviscid flow-boundary layer interaction problem. The interaction problem is solved by postulating certain series forms of solutions for the inviscid region and the boundary layer. The boundary-layer equations and inviscid-flow equations are perturbed to third order and each generated equation is solved numerically. In order to preserve the universality of each of the perturbed boundary-layer equations, the perturbation parameter is described by an integral equation which is also solved in series form. The final results describing the interaction problem are then constructed for any given conditions by forming the three series to a consistent order of magnitude. This technique of coordinate perturbation is generalized to show how it may be applied to the entrance regions of pipe flows, including mass injection or suction, and also to the laminar boundary layers in shock tube flows. It demonstrates analytically the manner in which the boundary layer and inviscid flow interact and create a streamwise pressure gradient. In particular, the interaction problem which occurs in shock tube flows is solved in detail by the use of this generalized method, as an example.

Numerical Method for Simulating Flows of Supercritical CO2 Compressor With Nonequilibrium Condensation

2016 ◽  
Author(s):  
Takashi Furusawa ◽  
Hironori Miyazawa ◽  
Satoru Yamamoto
Keyword(s):  
Numerical Method ◽  
Supercritical Co2 ◽  
Mass Fraction ◽  
Leading Edge ◽  
Pressure Variation ◽  
Supercritical Pressure ◽  
Local Region ◽  
Preconditioning Method ◽  
Condensation Model ◽  
Nonequilibrium Condensation

We recently proposed a numerical method for simulating flows of supercritical CO2 based on a preconditioning method and the thermophysical models programed in a program package for thermophysical properties of fluids (PROPATH). In this study, this method is applied to the investigation of cascade channel. Numerical results obtained by assuming supercritical pressure conditions indicate that the normal shock generated in the cascade channel deeply depends on the pressure condition. In particular, the speed of sound varying with the pressure variation at the supercritical state is a key thermophysical property which changes the flow field in the cascade channel. In addition, we also simulate those flows with nonequilibrium condensation in which the inlet pressure and temperature approaching to those of the critical point are specified. Then a nonequilibrium condensation model developed by our group is further applied to the numerical method. CO2 condensation observed in a case indicates that condensation occurs at a local region near the leading edge due to the flow expansion; the droplets soon grow at the local region and streams downward with keeping almost the same mass fraction.

The fluid mechanics of the aortic valve

1969 ◽  
Vol 35 (4) ◽  
pp. 721-735 ◽  
Author(s):  
B. J. Bellhouse ◽  
L. Talbot
Keyword(s):  
Aortic Valve ◽  
Inviscid Flow ◽  
Reversed Flow ◽  
Forward Flow ◽  
Flow Equations ◽  
Vortex Model ◽  
Closure Mechanism ◽  
Spherical Vortex ◽  
Human Aortic Valve ◽  
Trapped Vortex

The closure mechanism of the human aortic valve is investigated experimentally with a rigid-walled model placed in a pulsatile water-tunnel. It is shown that the valve is controlled by a fluid feed-back system incorporating a stagnation point at the downstream end of each sinus and a trapped vortex within it, and that threequarters of the valve's closure is accomplished during forward flow, requiring only very little reversed flow to seal it. The experiments are complemented by solutions of the inviscid-flow equations, based on a Hill spherical vortex model.

NUMERICAL ANALYSIS OF IDEALLY-EXPANDED SUPERSONIC JETS WITH NONEQUILIBRIUM HOMOGENEOUS CONDENSATION

2013 ◽  
Vol 10 (05) ◽  
pp. 1350024
Author(s):  
M. M. A. ALAM ◽  
T. SETOGUCHI ◽  
S. MATSUO
Keyword(s):  
Present Report ◽  
Flow Characteristics ◽  
Supersonic Jets ◽  
Droplet Growth ◽  
Nozzle Throat ◽  
Free Jets ◽  
Homogeneous Condensation ◽  
Wide Range ◽  
Growth Equations ◽  
Nonequilibrium Condensation

Steam or moist air is used as working gas in a wide range of engineering applications of supersonic jets. In these cases, nonequilibrium homogeneous condensation may occur at the downstream of nozzle throat. The surrounding gas will be heated by the release of latent heat of condensation, and may results a change in the flowfield. The present report will describe numerical investigations predicting the effect of nonequilibrium condensation on the flow characteristics of ideally-expanded supersonic free jets. A TVD numerical method is applied to solve RANS and droplet growth equations. The predicted results are compared with the experimental data.

THE WING-BODY AEROELASTIC ANALYSES USING THE INVERSE DESIGN METHOD

2010 ◽  
Vol 24 (13) ◽  
pp. 1479-1482
Author(s):  
SEUNG JUN LEE ◽  
DONG-KYUN IM ◽  
IN LEE ◽  
JANG-HYUK KWON
Keyword(s):  
Design Method ◽  
The Body ◽  
Inverse Design ◽  
Navier Stokes ◽  
Full Potential ◽  
Small Disturbance ◽  
Body Effect ◽  
Flow Equations ◽  
Applicable Range ◽  
Inverse Design Method

Flutter phenomenon is one of the most dangerous problems in aeroelasticity. When it occurs, the aircraft structure can fail in a few second. In recent aeroelastic research, computational fluid dynamics (CFD) techniques become important means to predict the aeroelastic unstable responses accurately. Among various flow equations like Navier-Stokes, Euler, full potential and so forth, the transonic small disturbance (TSD) theory is widely recognized as one of the most efficient theories. However, the small disturbance assumption limits the applicable range of the TSD theory to the thin wings. For a missile which usually has small aspect ratio wings, the influence of body aerodynamics on the wing surface may be significant. Thus, the flutter stability including the body effect should be verified. In this research an inverse design method is used to complement the aerodynamic deficiency derived from the fuselage. MGM (modified Garabedian-McFadden) inverse design method is used to optimize the aerodynamic field of a full aircraft model. Furthermore, the present TSD aeroelastic analyses do not require the grid regeneration process. The MGM inverse design method converges faster than other conventional aerodynamic theories. Consequently, the inverse designed aeroelastic analyses show that the flutter stability has been lowered by the body effect.

Velocity and pressure distributions in the aortic valve

1969 ◽  
Vol 37 (3) ◽  
pp. 587-600 ◽  
Author(s):  
B. J. Bellhouse
Keyword(s):  
Aortic Valve ◽  
Pressure Difference ◽  
Inviscid Flow ◽  
Jet Formation ◽  
Aortic Valves ◽  
Dimensional Solution ◽  
One Dimensional ◽  
Flow Equations ◽  
Pressure Distributions ◽  
Generation Of Vortices

The distribution of pressure in normal and stenosed aortic valves is investigated experimentally with a rigid-walled model placed in a pulsatile water-tunnel, and the experiments are complemented by a one-dimensional solution of the unsteady inviscid-flow equations. In the normal valve, convectively fed vortices are formed in the aortic sinuses; the vortices aid cusp positioning and the prevention of jet formation during valve closure. Aortic valve stenosis is shown to prevent the generation of vortices, causing the formation of a turbulent jet, with reduction of the pressure difference between the inlets (ostia) of the coronary arteries and the ventricle. This pressure difference is calculated for man resting and exercising, and for various degrees of stenosis.

Experimental Study of Film Condensation From Steam-Air Mixtures Flowing Downward Over a Horizontal Tube

1974 ◽  
Vol 96 (1) ◽  
pp. 83-88 ◽  
Author(s):  
J. W. Rauscher ◽  
A. F. Mills ◽  
V. E. Denny
Keyword(s):  
Heat Transfer ◽  
Experimental Study ◽  
Theoretical Analysis ◽  
Mass Fraction ◽  
Horizontal Tube ◽  
Forced Flow ◽  
Film Condensation ◽  
Air Mass ◽  
Average Value ◽  
Pure Steam

Experiments have been performed to study the effects of air on filmwise condensation from steam-air mixtures undergoing forced flow over a 3/4 in. OD horizontal tube. Local condensation rates at the stagnation point are reported for saturation temperatures of 100–150 deg F, bulk to wall temperature differences of 3–30 deg F, bulk air mass fraction 0–7 percent and oncoming vapor velocity 1–6 ft/sec. For pure steam the average value of q/qNu, where qNu is the Nusselt result, was 0.98 ± 0.10, which compares favorably with the value of 1.04 predicted by a theory which accounts for vapor drag. For steam-air mixtures the reduction in heat transfer was found to be in excellent agreement with the theoretical analysis of Denny and South; the average discrepancy in q/qNu was −2.7 percent, while the maximum was 7.1 percent.

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