Numerical study of boundary layer transition in flowing film evaporation on horizontal elliptical cylinder

A numerical study of the onset of longitudinal transition between turbulent and laminar regimes during the evaporation of a water film is presented. These water film streams along a horizontal elliptical tube under the simultaneous effects of gravity, pressure gradients, caused by the vapor flow and curvature, and viscous forces. At the interface of water vapor, the shear stress is supposed to be negligible. Outside the boundary layer, the vapor phase velocity is obtained from potential flow. In the analysis Von Karmans turbulence model is used and the inertia and convection terms are retained. Transfers equations are discretised by using the implicit Keller method. The effects of an initial liquid flow rate per unit of length, Froude number, temperature difference between the wall and the liquid–vapor interface and ellipticity on the transition position have been evaluated. The transition criterion has been given in term of the critical film Reynolds number (Re)_C.     

Oscillating heat pipe simulation considering dryout phenomena

In heat transport devices such as oscillating heat pipe (OHP), dryout phenomena is very important and avoided in order to give the optimum performance. However, from the previous studies (including our studies), the dryout phenomena in OHP and its mechanism are still unclear. In our studies of OHP (Senjaya and Inoue in Appl Thermal Eng 60:251–255, 2013; Int J Heat Mass Transfer 60:816–824, 2013; Int J Heat Mass Transfer 60:825–835, 2013), we introduced the importance and roles of liquid film in the operating principle of OHP. In our previous simulation, the thickness of liquid film was assumed to be uniform along a vapor plug. Then, dryout never occurred because there was the liquid transfer from the liquid film in the cooling section to that in the heating section. In this research, the liquid film is not treated uniformly but it is meshed similarly with the vapor plugs and liquid slugs. All governing equations are also solved in each control volume of liquid film. The simulation results show that dryout occurs in the simulation without bubble generation and growth. Dryout is started in the middle of vapor plug, because the liquid supply from the left and right liquid slugs cannot reach until the liquid film in the middle of vapor plug, and propagates to the left and right sides of a vapor plug. By inserting the bubble generation and growth phenomena, dryout does not occur because the wall of heating section is always wetted during the bubble growth and the thickness of liquid film is almost constant. The effects of meshing size of liquid film and wall temperature of heating section are also investigated. The results show that the smaller meshing size, the smaller liquid transfer rate and the faster of dryout propagation. In the OHP with higher wall temperature of heating section, dryout and its propagation also occur faster.     

Flow characteristics of spray impingement in PFI injection systems

The present paper addresses an experimental study of the dynamic exchanges between the impact of an intermittent spray and the liquid film formed over the target, based on detailed phase Doppler anemometry (PDA) measurements of droplet size, velocity and volume flux in the vicinity of the impact. The flow configuration is that of a pulsed injector spraying gasoline onto a flat disc to simulate the port fuel injection (PFI) of an internal combustion engine operating at cold-start conditions. The measurements evidence that the outcome of impact cannot be accurately predicted based on the characteristics of the free spray, but requires precise knowledge of the flow structure, induced by the target. The implications for spray–wall interaction modelling are then discussed based on the application of conservation equations to the mass, momentum and energy exchanged between the impinging droplets and the liquid film. The results show that the liquid film starts to form in the vicinity of the stagnation region at early stages of injection and a non-negligible proportion of droplets impinging at outer regions splash after interaction with the film. Film disruption is mainly driven by the intermittent axial momentum of impinging droplets, which enhances the vertical oscillations. The radial momentum imparted to the liquid film at the stagnation region is fed back onto secondary droplets emerging later during the injection cycle at outwards locations, where momentum of impacting droplets is much smaller. As a consequence, although the number of splashed droplets is enhanced by normal momentum, their size and ejection velocity depends more on the radial spread induced onto the liquid film and, hence, on the radial momentum at impact. The analysis further shows that existing spray–wall interaction models can be improved if the dynamic exchanges between the impacting spray and the liquid film are accounted.     

Modelling and simulation of sprays in laminar flames

In the present paper we model and numerically simulate steady, laminar, premixed spray flames. The gasphase is described in Eulerian form by the equations governing the conservation of overall mass, momentum, energy and species mass. The liquid phase is described in Lagrangian form by the overall continuity equation, which reduces to an equation for the droplet size, the equations of motion, the energy equation and a droplet density function transport equation. The latter is the so-called spray equation, which, at any position in the chemically reacting flowfield, describes the joint distribution of droplet size, droplet velocity and droplet temperature. Herein the spray equation is solved using a Monte Carlo method. Detailed models of the exchange of mass, momentum and energy between the gaseous and the liquid phase are taken into account. The results presented in this paper are for an octane-air flame, where small amounts of liquid octane in form of a liquid spray are added to a fresh, unburnt gaseous octane-air mixture.Presented at Euromech Colloquium 324: The Combustion of Drops, Sprays and Aerosols, 25th–27th July 1994, Marseilles, France.     

A similarity transformation for subcooled mixed convection film boiling in a porous medium

The classical two-phase boundary layer concept was adopted to analyse the problem of combined free and forced convection film boiling over an impermeable wall embedded in a porous medium. The governing equations, namely, the equations of continuity, energy and Darcy's model, were written for both vapor and liquid layers, and were solved simultaneously by means of the similarity transformation. Similarity solutions are found for a vertical flat plate, a horizontal circular cylinder and a sphere. Numerical integrations were carried out for given sets of the parameters associated with the vapor superheating Sup, the liquid subcooling Sub, the vapor mass flow rate R and the ratio of the liquid Rayleigh number to Peclet number Ra _xf /Pe _xf . It is found that a significant simplification of the problem is possible by setting the liquid stream function at the interface to zero. This simplification also reveals that the solution of the problem virtually depends on only three parameters, namely, Sup, Ra _xf /Pe _xf and the lumped parameter Sub/R.     

Turbulent natural convection in a square enclosure bounded by a solid wall with localized heating

Turbulent natural convection and conduction in a square enclosure bounded by a massive wall with a localized heating is numerically studied. The bounding solid wall has a relative thermal conductivity of 10 and a relative thickness of 0.1. Losses to the surroundings are specified using a Biot number of 500. Two-dimensional equations of conservation of mass, momentum and energy, with the Boussinesq approximation and using the κ-ε model for turbulence are solved using finite difference method. Grids are generated in a nonuniform manner so that steep gradients near the wall regions are accounted for as required. Numerical solution is obtained for Ra numbers ranging from 10⁶ to 10¹³. The position of the source is also investigated. It is found that the heat transfer by convection is the highest when the heat source is located at the upper part of the cavity. The turbulent properties show also the same conclusion. Received on 4 November 1998     

MHD effect of mixed convection boundary-layer flow of Powell-Eyring fluid past nonlinear stretching surface

Sufficient conditions are found for the existence of similar solutions of the mixed convection flow of a Powell-Eyring fluid over a nonlinear stretching permeable sur- face in the presence of magnetic field. To achieve this, one parameter linear group trans- formation is applied. The governing momentum and energy equations are transformed to nonlinear ordinary differential equations by use of a similarity transformation. These equations are solved by the homotopy analysis method （HAM） to obtain the approximate solutions. The effects of magnetic field, suction, and buoyancy on the Powell-Eyring fluid flow with heat transfer inside the boundary layer are analyzed. The effects of the non- Newtonian fluid （Powell-Eyring model） parameters ε and δon the skin friction and local heat transfer coefficients for the cases of aiding and opposite flows are investigated and discussed. It is observed that the momentum boundary layer thickness increases and the thermal boundary layer thickness decreases with the increase in ε whereas the momentum boundary layer thickness decreases and thermal boundary layer thickness increases with the increase in δ for both the aiding and opposing mixed convection flows.     

Binary diffusion and heat transfer in laminar mixed convection channel flows with uniform wall heat flux: extremely thin film thickness

A detailed numerical study has been performed to investigate the combined heat and mass transfer in laminar mixed convection channel flows with uniform wall heat flux. In an initial effort the liquid film on the channel wall is assumed to be extremely thin in thickness. Major dimensionless groups governing the present problem areGr _T,Gr _Mx,Pr,Sc, φ andRe. Results are specifically presented for an air-water system under various conditions. The effects of wall heating flux, the Reynolds number and the relative humidity of the moist air in the ambient on the momentum, heat and mass transfer in the flow are investigated in great detail.     

Integral treatment of subcooled forced convection film boiling on a flat plate

Subcooled forced convection film boiling on a flat plate has been analysed by means of an integral method. Following the two phase boundary layer theory, the momentum and energy equations for both liquid and vapor layers are considered along with the compatibility conditions on the liquid-vapor interface. Subsequently, the governing equations are reduced to a set of algebraic equations which can readily be solved for given parameters. Comparison of the present solution with the Cess and Sparrow solution reveals an excellent performance of the present solution procedure. The effects of superheating, subcooling and liquid Prandtl number on the hydrodynamic and heat transfer characteristics are fully discussed. Furthermore, the asymptotic formulas are derived for the local Nusselt number and skin friction coefficient through a careful examination of the physical limiting conditions.     

Three-dimensional numerical analysis of heat and mass transfer in heat pipes

A three-dimensional finite-element numerical model is presented for simulation of the steady-state performance characteristics of heat pipes. The mass, momentum and energy conservation equations are solved for the liquid and vapor flow in the entire heat pipe domain. The calculated outer wall temperature profiles are in good agreement with the experimental data. The estimations of the liquid and vapor pressure distributions and velocity profiles are also presented and discussed. It is shown that the vapor flow field remains nearly symmetrical about the heat pipe centerline, even under a non-uniform heat load. The analytical method used to predict the heat pipe capillary limit is found to be conservative.     

Laminar natural convection in inclined enclosures bounded by a solid wall

Laminar natural convection has been studied in enclosures bounded by a solid wall with its outer boundary at constant temperature while the opposing side has a constant heat flux. Two-dimensional equations of conservation of mass, momentum and energy, with the Boussinesq approximation are solved using a finite difference method. The numerical procedure adopted is based on the SIMPLER algorithm. Various parameters were: Rayleigh number (from 10³ to 10⁶), dimensionless conductivity of bounding wall (from 1 to 10) and dimensionless wall width (from 0.15 to 0.5), aspect ratio (from 0.5 to 1) and the inclination angle (from 30^° to 180^°). The results are reduced in terms of the normalized Nusselt number as a function of the Rayleigh number, and other dimensionless parameters. The isotherms and streamlines are produced for various Rayleigh numbers and geometrical conditions. It is found that the heat transfer is an increasing function of the Rayleigh number, wall to fluid conductivity ratio, enclosure aspect ratio and a decreasing function of the wall thickness. It passes from a maximum for the inclination angle of about 80^°.     

Simultaneous heat and mass transfer inside a vertical tube in evaporating a heated falling alcohols liquid film into a stream of dry air

A numerical study of the evaporation in mixed convection of a pure alcohol liquid film: ethanol and methanol was investigated. It is a turbulent liquid film falling on the internal face of a vertical tube. A laminar flow of dry air enters the vertical tube at constant temperature in the downward direction. The wall of the tube is subjected to a constant and uniform heat flux. The model solves the coupled parabolic governing equations in both phases including turbulent liquid film together with the boundary and interfacial conditions. The systems of equations obtained by using an implicit finite difference method are solved by TDMA method. A Van Driest model is adopted to simulate the turbulent liquid film flow. The influence of the inlet liquid flow, Reynolds number in the gas flow and the wall heat flux on the intensity of heat and mass transfers are examined. A comparison between the results obtained for studied alcohols and water in the same conditions is made.     

Unsteady mixed convection on the stagnation-point flow adjacent to a vertical plate with a magnetic field

An analysis is performed to study the unsteady combined forced and free convection flow (mixed convection flow) of a viscous incompressible electrically conducting fluid in the vicinity of an axisymmetric stagnation point adjacent to a heated vertical surface. The unsteadiness in the flow and temperature fields is due to the free stream velocity, which varies arbitrarily with time. Both constant wall temperature and constant heat flux conditions are considered in this analysis. By using suitable transformations, the Navier–Stokes and energy equations with four independent variables (x, y, z, t) are reduced to a system of partial differential equations with two independent variables (, ). These transformations also uncouple the momentum and energy equations resulting in a primary axisymmetric flow, in an energy equation dependent on the primary flow and in a buoyancy-induced secondary flow dependent on both primary flow and energy. The resulting system of partial differential equations has been solved numerically by using both implicit finite-difference scheme and differential-difference method. An interesting result is that for a decelerating free stream velocity, flow reversal occurs in the primary flow after certain instant of time and the magnetic field delays or prevents the flow reversal. The surface heat transfer and the surface shear stress in the primary flow increase with the magnetic field, but the surface shear stress in the buoyancy-induced secondary flow decreases. Further the heat transfer increases with the Prandtl number, but the surface shear stress in the secondary flow decreases.     

Constant heat flux solution for mixed convection boundary layer viscoelastic fluid

The mixed convection boundary layer of a viscoelastic fluid past a circular cylinder with constant heat flux is discussed. The boundary layer equations are an order higher than those for the Newtonian (viscous) fluid and the adherence boundary conditions are insufficient to determine the solution of these equations completely. The governing non-similar partial differential equations are transformed into dimensionless forms and then solved numerically using the Keller-box method by augmenting an extra boundary condition at infinity. Numerical results obtained in the form of velocity distributions and temperature profiles are presented for a range of values of the dimensionless viscoelastic fluid parameter. It is found that for some values of the viscoelastic parameter and some negative values of the mixed convection parameter (opposing flow) the momentum boundary layer separates from the cylinder. Heating the cylinder delays separation and can, if the cylinder is warm enough, suppress the separation completely. Similar to the case of a Newtonian fluid, cooling the cylinder brings the separation point nearer to the lower stagnation point.     

Effects of chemical reaction on mixed convection flow of a polar fluid through a porous medium in the presence of internal heat generation

This paper reports a detailed numerical investigation on mixed convection flow of a polar fluid through a porous medium due to the combined effects of thermal and mass diffusion. The energy equation accounts for heat generation or absorption, while the nth order homogeneous chemical reaction between the fluid and the diffusing species is included in the mass diffusion equation. The governing equations of the linear momentum, angular momentum, energy and concentration are obtained in a non-similar form by introducing a suitable group of transformations. The final set of non-similar coupled non-linear partial differential equations is solved using an implicit finite-difference scheme in combination with quasi-linearization technique. The effects of various parameters on the velocity, angular velocity, temperature and concentration fields are investigated. Numerical results for the skin friction coefficient, wall stress of angular velocity, Nusselt number and Sherwood number are also presented.     

Two-phase flow over a surface with the formation of a liquid film by particle deposition

A consistent asymptotic theory of wall flow with film formation is constructed with reference to subsonic two-phase flow over a blunt body. The external flow problem and the film equations are solved simultaneously. This formulation of the problem supplements the investigation carried out in [4] in which particles deposited on the surface were assumed to disappear from the flow. It is shown that depending on the values of the governing parameters the flow in the film should be described either by the boundary layer equations or by the equations of creeping flow in a layer of unknown thickness. At the outer edge of the film the mass, momentum and energy fluxes found from the numerical solution of the flow problem are given. The case of isothermal film flow on the front of a sphere is investigated. The thickness of the film and the friction and heat transfer coefficients near the axis of symmetry are found for nonisothermal flows. The conditions under which the presence of a film significantly reduces the heat flow to the wall are determined. A similar formulation of the problem (but with another type of mass, momentum and energy sources at the outer edge) is encountered in problems of film condensation on a cold surface [5, 6].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 85–92, July–August, 1989.     

Numerical simulation of flow boiling for organic fluid with high saturation temperature in vertical porous coated tube

A semi-analytical model is developed for the prediction of flow boiling heat transfer inside vertical porous coated tubes. The model assumes that the forced convection and nucleate boiling coexist together in the annular flow regime. Conservations of mass, momentum, and energy are used to solve for the liquid film thickness and temperature. The heat flux due to nucleate boiling consists of those inside and outside micro-tunnels. To close the equations, a detailed analysis of various forces acting on the bubble is presented to predict its mean departure diameter. The active nucleation site density of porous layer is determined from the pool boiling correlation by introducing suppression factor. The flow boiling heat transfer coefficients of organic fluid (cumene) with high saturation temperature in a vertical flame-spraying porous coated tube are studied numerically. It is shown that the present model can predict most of the experimental values within ±20%. The numerical results also indicate that the nucleate boiling contribution to the overall heat transfer coefficient decreases from 50% to 15% with vapor quality increasing from 0.1 to 0.5.     

The effects of transpiration on the boundary layer flow and heat transfer over a vertical slender cylinder

This paper deals with a theoretical (numerical) analysis of the effects that blowing/injection and suction have on the steady mixed convection or combined forced and free convection boundary layer flows over a vertical slender cylinder with a mainstream velocity and a wall surface temperature proportional to the axial distance along the surface of the cylinder. Both cases of buoyancy forces aid and oppose the development of the boundary layer are considered. Similarity equations are derived and their solutions are dependent upon the mixed convection parameter, the non-dimensional transpiration parameter and the curvature parameter, as well as of the Prandtl number. Dual solutions for the previously studied mixed convection boundary layer flows over an impermeable surface of the cylinder are shown to exist also in the present problem for aiding and opposing flow situations.     

A Continuum Theory of Multispecies Thin Solid Film Growth by Chemical Vapor Deposition

A continuum theory for the chemical vapor deposition of thin solid films is proposed, in which a flowing, chemically reacting, gaseous mixture is coupled to the bulk of a growing thin film via the equations that govern the morphological evolution of the interface separating them. The vapor-film interface is viewed as a surface of zero thickness capable of sustaining mass and endowed with thermodynamic variables that account for its distinct structure. We consider situations in which species diffusion and heat conduction occur in all three phases (vapor, bulk and surface), with the former mechanism augmented by the convective transport of particles in the gas. Special attention is given to the chemical reactions that occur both in the vapor and on the film surface. Ours is a conceptual framework based on conservation laws for chemical species, momentum and energy, together with a separate balance of configurational forces. These balances are supplemented by an appropriate version of the second law which is used to develop suitable constitutive relations for each of the phases. In particular, we investigate the case of an elastic film, deposited on a rigid substrate and in contact with a reacting, multispecies, ideal vapor, whose surface behaves like an anisotropic, chemically reactive, multicomponent, ideal lattice gas. In addition to recovering the standard equations that describe the behavior of the gas and film phases, we derive the coupled PDE's that govern the interfacial morphological, chemical, and thermal evolution. In particular, the constitutively augmented interfacial configurational force balance provides a “kinetic relation” linking the thermodynamic “driving force” at the film surface to the growth rate. The special cases of (i) negligible interfacial species densities, and (ii) local (mechanical) equilibrium of both multi- and single-species films are investigated.     

Film boiling on a hot body moving in a fluid

We investigate the transient film boiling in the vicinity of a stagnation point on the frontal surface of a very hot blunt body which moves with a constant velocity in an incompressible viscous fluid in the presence of a vapor layer near the body surface. Within the unsteady two-phase boundary layer approximation, the equations of motion of the liquid and vapor phases are formulatedwith account of the conservation of mass, momentum, and energy on the a priori unknown phase interface. In the vicinity of the stagnation point on the body surface, the solution of the boundary layer equations is sought in the form of series in the longitudinal coordinate. For the leading terms of the series, a parabolic system of partial differential equations is obtained, which is solved numerically. The similarity parameters controlling the film boiling process are determined. On the basis of parametric numerical calculations, the dynamics of the vapor layer are investigated for the case of a plane hot body moving in water with the room pressure and temperature. In the space of governing parameters, the limits of the existence of steady and unsteady film boiling regimes are found.