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A derivation of the irreversible entropy production, that is the dissipation, in two-phase flows is presented for the purpose of examining the effect of evaporative-drop modulation of flows having turbulent features.
This paper is organized as follows. In § 2, we present the DNS formulation. This formulation consists of a set of coupled conservation equations for the gas phase and the liquid phase (i.e. the drops). The coupling describing the interaction between the two phases is provided in the gas-phase conservation equations by source terms. In § 3, we analyse the DNS results; in particular, we evaluate the adopted form of the heat and mass fluxes. The gas-phase LES equations are developed in § 4 and assumptions that may simplify these equations are examined using the DNS database. Thereafter, the contribution of the source terms is examined by considering the budget of the LES equations. The final form of the LES equations are then presented, in which only the SGS fluxes and the FSTs need be modelled. A parallel perspective on the importance of the source terms is presented in § 5, wherein the irreversible entropy production (i.e. the dissipation) expression for two-phase flow with phase change is derived and evaluated for transitional DNS and the filtered flow fields. Models for the FSTs appearing in the LES equations are investigated in § 6, while several constantcoefficient SGS models are proposed and calibrated in § 7. The present study aims to create simple models so that the modelling approach can be validated by means of an SGS models are proposed and calibrated in § 7. The present study aims to create simple models so that the modelling approach can be validated by means of an a posteriori study.
When liquid is sealed at high temperature, it flashes inside the seal due to pressure drop and/or viscous heat dissipation. Two-phase seals generally exhibit more erratic behavior than their single phase counterparts. Thermal effects, which are often neglected in single phase seal analyses, play an important role in determining seal behavior under two-phase operation. It is necessary to consider the heat generation due to viscous shear, conduction into the seal rings and convection with the leakage flow. Analytical models developed work reasonably well at the two extremes - for low leakage rates when convection is neglected and for higher leakage rates when conduction is neglected. A preliminary model, known as the Film Coefficient Model, is presented which considers conduction and convection both, and allows continuous boiling over an extended region unlike the previous low-leakage rate model which neglects convection and always forces a discrete boiling interface. Another simplified, semi-analytical model, based on the assumption of isothermal conditions along the seal interafce, has been developed for low leakage rates. The Film Coefficient Model may be used for more accurate and realistic description.
A two-equation turbulence model has been developed for predicting two-phase flows. The two equations describe the conservation of turbulence kinetic energy and dissipation rate of that energy for the carrier fluid in a two-phase flow. They have been derived rigorously from the momentum equations of the carrier fluid. Closure of the time-mean equations is achieved by modeling the turbulent correlations up to third order. The new model eliminates the need to simulate in an ad hoc manner the effects of the dispersed phase on turbulence structure. Preliminary testing indicates that the model is successful in predicting the main features of a round gaseous jet laden with uniform-size solid particles.
In space applications, weight, volume and power are critical parameters. Presently liquid freon is used in the radiator planels of the Space Shuttle to dissipate heat. This requires a large amount of freon, large power for pumps, large volume and weight. Use of two-phase flow method to transfer heat can reduce them significantly. A modified commercial vapor compression refrigerator/freezer was sucessfully flown in STS-4 to study the effect of zero-gravity on the system. The duty cycle was about 5 percent higher in flight as compared to that on earth due to low flow velocity in condenser. The vapor Reynolds number at exit was about 4000 as compared to about 12,000. Efforts are underway to design a refrigerator/freezer using an oil-free compressor for Spacelab Mission 4 scheduled to fly in January 1986. A thermal system can be designed for spacecraft using the two-phase flow to transfer heat economically.
The coupling between thermal and dynamical regimes of single- and two-phase magmatic flow in dikes, due to temperature-dependent viscosity and dissipation, was investigated using finite element calculations of magma flow in dikelike channels with length-to-width ratios of 1000:1 or more. Solutions of the steady state equations governing magma flow are obtained for a variety of conditions ranging from idealized plane-parallel models to cases involving nonparallel geometry and two-phase flows. The implications of the numerical simulations for the dynamics of flow in a dike-reservoir system and the consequences of dike entrance conditions on magmatic storage are discussed. Consideration is also given to an unmixing/self-lubrication mechanism which may be important for the lubrication of silicic magmas rising to the earth's surface in mixed magma ascent scenarios, which naturally segregates magma mixtures of two components with differing viscosities to minimize the driving pressure gradient.
Transitional databases from Direct Numerical Simulation (DNS) of three-dimensional mixing layers for single-phase flows and two-phase flows with evaporation are analyzed and used to examine the typical hypothesis that the scalar dissipation Probability Distribution Function (PDF) may be modeled as a Gaussian. The databases encompass a single-component fuel and four multicomponent fuels, two initial Reynolds numbers (Re), two mass loadings for two-phase flows and two free-stream gas temperatures. Using the DNS calculated moments of the scalar-dissipation PDF, it is shown, consistent with existing experimental information on single-phase flows, that the Gaussian is a modest approximation of the DNS-extracted PDF, particularly poor in the range of the high scalar-dissipation values, which are significant for turbulent reaction rate modeling in non-premixed flows using flamelet models. With the same DNS calculated moments of the scalar-dissipation PDF and making a change of variables, a model of this PDF is proposed in the form of the (beta)-PDF which is shown to approximate much better the DNS-extracted PDF, particularly in the regime of the high scalar-dissipation values. Several types of statistical measures are calculated over the ensemble of the fourteen databases. For each statistical measure, the proposed (beta)-PDF model is shown to be much superior to the Gaussian in approximating the DNS-extracted PDF. Additionally, the agreement between the DNS-extracted PDF and the (beta)-PDF even improves when the comparison is performed for higher initial Re layers, whereas the comparison with the Gaussian is independent of the initial Re values. For two-phase flows, the comparison between the DNS-extracted PDF and the (beta)-PDF also improves with increasing free-stream gas temperature and mass loading. The higher fidelity approximation of the DNS-extracted PDF by the (beta)-PDF with increasing Re, gas temperature and mass loading bodes well for turbulent reaction rate modeling.
This report presents a study of dissipation (irreversible production of entropy) in three-dimensional, temporal mixing layers laden with evaporating liquid drops. The purpose of the study is to examine the effects of evaporating drops on the development of turbulent features in flows. Direct numerical simulations were performed to analyze transitional states of three mixing layers: one without drops, and two that included drops at different initial mass loadings. Without drops, the dissipation is essentially due to viscous effects. It was found that in the presence of drops, the largest contribution to dissipation was made by heating and evaporation of the drops, and that at large length scales, this contribution is positive (signifying that the drops reduce turbulence), while at small scales, this contribution is negative (the drops increase turbulence). The second largest contribution to dissipation was found to be associated with the chemical potential, which leads to an increase in turbulence at large scales and a decrease in turbulence at small scales. The next smaller contribution was found to be that of viscosity. The fact that viscosity effects are only third in order of magnitude in the dissipation is in sharp contrast to the situation for the mixing layer without the drops. The next smaller contribution - that of the drag and momentum of the vapor from the drops - was found to be negative at lower mass loading but to become positive at higher mass loading.
An in-house developed proprietary advanced computational fluid dynamics code called SHARP (Trademark) is a primary tool for many flow simulations and design analyses. The SHARP code is a time dependent, two dimensional (2-D) axisymmetric numerical solution technique for the compressible Navier-Stokes equations. The solution technique in SHARP uses a vectorizable implicit, second order accurate in time and space, finite volume scheme based on an upwind flux-difference splitting of a Roe-type approximated Riemann solver, Van Leer's flux vector splitting, and a fourth order artificial dissipation scheme with a preconditioning to accelerate the flow solution. Turbulence is simulated by an algebraic model, and ultimately the kappa-epsilon model. Some other capabilities of the code are 2-D two-phase Lagrangian particle tracking and cell blockages. Extensive development and testing has been conducted on the 3-D version of the code with flow, combustion, and turbulence interactions. The emphasis here is on the specific applications of SHARP in Solid Rocket Motor design. Information is given in viewgraph form.
Poor understanding of flow boiling in microgravity has recently emerged as a key obstacle to the development of many types of power generation and advanced life support systems intended for space exploration. The critical heat flux (CHF) is perhaps the most important thermal design parameter for boiling systems involving both heatflux-controlled devices and intense heat removal. Exceeding the CHF limit can lead to permanent damage, including physical burnout of the heat-dissipating device. The importance of the CHF limit creates an urgent need to develop predictive design tools to ensure both the safe and reliable operation of a two-phase thermal management system under the reduced-gravity (like that on the Moon and Mars) and microgravity environments of space. At present, very limited information is available on flow-boiling heat transfer and the CHF under these conditions.
Steady, turbulent two-phase fluid flow in a rotating annular seal with no eccentricity is analyzed. The fluid is assumed to be a homogeneous mixture of liquid and vapor in thermodynamic equilibrum. Further, the flow is assumed to be adiabatic, but the effects due to heat generation by viscous dissipation are accounted for fully. Solution of the model governing differential equations is accomplished by use of a fourth-order Runge-Kutta numerical integration scheme. The calculation of mass leakage rates under choked and unchoked conditions are discussed and the phenomenon of all-liquid choked flow is explained. Several numerical examples are presented supposing cyrogenic oxygen as the sealed fluid.
Current thermal distribution systems on large spacecraft, such as the Space Shuttle and Spacelab, use pumped fluid loops that circulate the coolant between a series of user stations and a single rejection point, involving complex plumbing and controls with a significant power penalty and limited reliability. In order to provide heat transport at near-isothermal conditions in future large spacecraft, two-phase flow systems will be implemented by taking advantage of the heat of vaporization and condensation of common working fluids at minimal expenditure of power and temperature variation. Such systems are considered for the cases of the thermal requirements of nearly 100 potential astrophysics and astronomy instruments. Data on temperature requirements, power dissipations, environmental fluxes, heat addition or rejection, and general description, are used to form conceptual designs for the thermal utility.
Transient cooling by radiation is analyzed for a cylindrical region filled with axially flowing streams of drops that are becoming solidified. This is of interest for the dissipation of waste heat from orbiting power system in space. The drops absorb, emit, and scatter radiation, and the surroundings are at a lower uniform temperature. The radiative properties are assumed gray, and the scattering is isotropic. The radiating region is a two-phase mixture that remains at the melting temperature of the drops. Its temperature uniformity maintains a high emissive power as energy is lost. This is an advantage over a sensible heat radiator in which the temperature decreases, thereby reducing the emissive power. The results provide the axial length that remains two-phase and the fraction of energy dissipated within this length in which the emissive power has not decreased because of sensible cooling. It is also shown how the radial distribution of the axial velocity of the drops can be modified to increase this energy fraction.
High-performance electronics are continuously demanding cooling of higher heat fluxes. Phase-change cooling, including pool boiling, is a useful approach to address this challenge; however, competition between liquid and vapor flows generally limit the heat fluxes that can be dissipated. A range of strategies to control these flows have been investigated previously, including capillary guides. Here a manifold structure formed from a metallic mesh is investigated to control the disposition of liquid and vapor phases above a pool fed boiling surface enhanced with porous structures. Copper mesh forms defined liquid flow paths, using capillary action to guide and distribute liquid evenly over the heated surface, along with open channels to facilitate vapor escape. The mesh provides a novel structure for liquid guidance that imposes low resistance to liquid flow while occluding a minimal area of heated surface underneath. The manifold performance is characterized in boiling fed by a pool of water above a laser-textured aluminum nitride heat dissipation surface with pin–fin structures having heights of 110 µm and spacing of 30 µm with a heated area of 5 mm x 5 mm. A maximum heat flux of 490 W/cm 2 is reached with the manifold in the pool fed configuration, representing an increase of more than 65% over the porous pin fin surface alone. The maximum stable superheat observed for the manifold of 36K is 14K higher than that for the porous surface without the manifold. The factors limiting performance of the manifold are analyzed. High superheat is attributed to partial flooding of the boiling surface as suggested by the reduction in superheat using external suction. Similar systems and structures for enhanced two-phase cooling are compared.
Large-eddy simulation (LES) is conducted of a three-dimensional temporal mixing layer whose lower stream is initially laden with liquid drops which may evaporate during the simulation. The gas-phase equations are written in an Eulerian frame for two perfect gas species (carrier gas and vapour emanating from the drops), while the liquid-phase equations are written in a Lagrangian frame. The effect of drop evaporation on the gas phase is considered through mass, species, momentum and energy source terms. The drop evolution is modelled using physical drops, or using computational drops to represent the physical drops. Simulations are performed using various LES models previously assessed on a database obtained from direct numerical simulations (DNS). These LES models are for: (i) the subgrid-scale (SGS) fluxes and (ii) the filtered source terms (FSTs) based on computational drops. The LES, which are compared to filtered-and-coarsened (FC) DNS results at the coarser LES grid, are conducted with 64 times fewer grid points than the DNS, and up to 64 times fewer computational than physical drops. It is found that both constant-coefficient and dynamic Smagorinsky SGS-flux models, though numerically stable, are overly dissipative and damp generated small-resolved-scale (SRS) turbulent structures. Although the global growth and mixing predictions of LES using Smagorinsky models are in good agreement with the FC-DNS, the spatial distributions of the drops differ significantly. In contrast, the constant-coefficient scale-similarity model and the dynamic gradient model perform well in predicting most flow features, with the latter model having the advantage of not requiring a priori calibration of the model coefficient. The ability of the dynamic models to determine the model coefficient during LES is found to be essential since the constant-coefficient gradient model, although more accurate than the Smagorinsky model, is not consistently numerically stable despite using DNS-calibrated coefficients. With accurate SGS-flux models, namely scale-similarity and dynamic gradient, the FST model allows up to a 32-fold reduction in computational drops compared to the number of physical drops, without degradation of accuracy; a 64-fold reduction leads to a slight decrease in accuracy.
In this paper we show that perturbations of the accretion flow within the central engines of some active galactic nuclei (AGNS) are likely to form shock waves in the accreting plasma. Such shocks, which may be either collisional or collisionless, can contribute to the observed high-energy temporal and spectral variability. Our rationale is the following: Observations show that the continuum emission probably originates in an optically thin, hot plasma in the AGN central engine. The flux and spectrum from this hot plasma varies significantly over light crossing timescales. Several authors have suggested that macroscopic perturbations contained within this plasma are the sources of this variability. In order to produce the observed emission the perturbations must be radiatively coupled with the optically thin hot matter and must also move with high velocities. We suggest that shocks, which can be very effective in randomizing the bulk motion of the perturbations, are responsible for this coupling. Shocks should form in the central engine, because the temperatures and magnetic fields are probably reduced below their virial values by radiative dissipation. Perturbations moving at Keplerian speeds, or strong non-linear excitations, result in supersonic and super-Alfvenic velocities leading to shock waves within the hot plasma. We show that even a perturbation smaller than the emitting region can form a shock that significantly modifies the continuum emission in an AGN, and that the spectral and temporal variability from such a shock generally resembles those of radio-quiet AGNS. As an example, the shock inducing perturbation in our model is a small main-sequence star, the capturing and eventual accretion of which are known to be a plausible process. We argue that shocks in the central engine may also provide a natural triggering mechanism for the "cold" component of Guilbert & Rees two-phase medium and an efficient mecha- nism for angular momentum transfer. Current and future missions, such as ASCA, XTE, XMM, AXAF, and ASTRO-E may determine the importance of shock-related emission from the central engines of AGNS.
Relative permeability plays an important role in the upscaling of multiphase flow in porous media from the pore scale to the Darcy scale. The entire concept of relative permeability is contingent on the existence of a representative elementary volume (REV). As we move to smaller samples to measure relative permeability, such as with digital core analysis, the concept of a classical REV has become increasingly unlikely when using the conventional approach to defining a representative volume. The “‘conventional”’ understanding of an REV is that a large enough volume must be considered such that spatial variability averages out. In digital rock methods, such as pore-scale simulations based on micro-computed tomography (CT) images, the domain size is typically 2 to 4 mm. This is approximately the length scale of a single-phase flow REV using the classic REV approach. However, the single-phase perspective does not consider the complex dynamics and fluctuations often observed in multiphase flow systems, even at centimeter-scale experiments and/or simulations. A fundamental question is, therefore, whether the domain size commonly used in digital rock simulations can provide a consistent energy budget such that the concept of relative permeability exists. Based on first principles, relative permeability accounts for the rate of energy dissipated in a stationary process. If the dynamics are fluctuating, the energy dissipated can vary but will average out over a long enough timescale. The key to determining the validity of the relative permeability is the timescale of the measurement, not the spatial scale. The conventional REV theory assumes that spatial, temporal, and ensemble averages are equivalent in an ergodic system, but it does not provide a way to test this assumption. We provide a formal way to identify the timescale where the relative permeability accurately captures energy dissipation as a way to validate relative permeability measurements and quantitatively assess their accuracy. This result will be tested for a practical SCAL test, determining how long a flow experiment needs to be run to accurately characterize the rate of energy dissipation by the flow. The outcome will be a best practice guide for the determination of relative permeability from core-scale experiments and/or digital core simulations that ensure the energy budget is fully accounted for in the relative permeability coefficient.
The main objective of this investigation is to develop a two-equation turbulence model for dilute vaporizing sprays or in general for dispersed two-phase flows including the effects of phase changes. The model that accounts for the interaction between the two phases is based on rigorously derived equations for turbulence kinetic energy (K) and its dissipation rate epsilon of the carrier phase using the momentum equation of that phase. Closure is achieved by modeling the turbulent correlations, up to third order, in the equations of the mean motion, concentration of the vapor in the carrier phase, and the kinetic energy of turbulence and its dissipation rate for the carrier phase. The governing equations are presented in both the exact and the modeled formes. The governing equations are solved numerically using a finite-difference procedure to test the presented model for the flow of a turbulent axisymmetric gaseous jet laden with either evaporating liquid droplets or solid particles. The predictions include the distribution of the mean velocity, volume fractions of the different phases, concentration of the evaporated material in the carrier phase, turbulence intensity and shear stress of the carrier phase, droplet diameter distribution, and the jet spreading rate. The predictions are in good agreement with the experimental data.