Research Papers: Techniques and Procedures

Inhomogeneous Multifluid Model for Prediction of Nonequilibrium Phase Transition and Droplet Dynamics

[+] Author and Article Information
A. G. Gerber

Department of Mechanical Engineering, University of New Brunswick, Fredericton, NB, E3B5A3, Canadaagerber@unb.ca

J. Fluids Eng 130(3), 031402 (Mar 11, 2008) (11 pages) doi:10.1115/1.2844580 History: Received February 13, 2007; Revised December 05, 2007; Published March 11, 2008

A pressure based Eulerian multifluid model for application to phase transition with droplet dynamics in transonic high-speed flows is described. It is implemented using an element-based finite-volume method, which is implicit in time and solves mass and momentum conservation across all phases via a coupled algebraic multigrid approach. The model emphasizes treatment of the condensed phases, with their respective velocity and thermal fields, in inertial nonequilibrium and metastable gas flow conditions. The droplet energy state is treated either in algebraic form or through transport equations depending on appropriate physical assumptions. Due to the complexity of the two-phase phenomena, the model is presented and validated by exploring phase transition and droplet dynamics in a turbine cascade geometry. The influence of droplet inertia on localized homogeneous nucleation is examined.

Copyright © 2008 by American Society of Mechanical Engineers
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Figure 1

Homogeneous phase transition at (a) part-load, (b) design, and (c) overload conditions presented in Ref. 6 where nmax=log(Jmax). The cross-hatched regions represent the approximate ranges of nmax:nmax−1 for the inner and nmax−1:nmax−9 for the outer. A topological representation of the multifluid model phases is given in (d). Each condensed phase is introduced into the flow using a source specific approach.

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Figure 2

Depiction of droplet (Td) and continuous phase (Tc) temperatures (Tc), for either evaporation or condensation, versus radius emanating from the droplet center. Conditions for (a) a small droplet model nominally in the range 2rd⩽1μm, and (b) a large droplet model in the nominal range 2rd>1μm. Note that for case (a), droplet temperature Td is treated algebraically as a function of rd, as described for energy (2) in Table 1.

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Figure 3

Element-based finite-volume discretization of the spatial domain. Solid lines define element boundaries, and dashed lines divide elements into sectors. Solution unknowns are colocated at the nodal points (●), and surface fluxes are evaluated at integration points (○). Control volumes are constructed as unions of element sectors (shaded region).

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Figure 4

Cascade blade geometry taken from Ref. 16 along with mesh. The inset (bottom left) gives the topology of the solution phases with P1 as the continuous phase, P2 as droplets formed within the domain by homogeneous nucleation, and P3 as a phase containing larger droplets formed upstream of the inlet.

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Figure 5

Case W1 (16) results with (a) mass fraction of phase P3 highlighting deviation of droplets from equilibrium trajectory, (b) supercooling level with the Wilson line indicated, (c) location and strength of nucleation front, and (d) location of formation of phase P2 mass fraction

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Figure 6

Comparison of predicted suction side (Ss) oblique shock and condensation front (Sc) locations, as given in (a), with schlieren photographs given in (b) for case W1 in Ref. 16

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Figure 7

Predicted blade static pressure profiles for case W1 (16)

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Figure 8

Predicted droplet size distributions for case W1 (16)

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Figure 9

Change in phase transition location with (a) P3 droplet size 0.5μm and (b) 5μm. As shown in (c), the suction side static pressure rise moves upstream with increasing P3 inlet size.

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Figure 10

Dispersed phase (P3) droplet trajectory for inlet diameters of (a) 0.5μm, (b) 2μm, and (c) 5μm. Note that the 1μm case is already given in Fig. 5.

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Figure 11

Influence of dispersed phase energy equation treatment on exit temperature/mass fraction/size predictions for the case of P3 inlet diameters of (a) 5μm and (b) 1μm. Solid lines are obtained with energy 1, and dashed lines with an algebraic treatment energy 2, as shown in Table 1.

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Figure 12

Predicted efficiency using the present Eulerian multifluid model (CFD-MF) and the Eulerian–Lagrangian (CFD-LA) approach reported in Ref. 16. Two test sets (W and L) are considered from Ref. 16.




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