# Non-linear dynamics of a two phase flow system in an evaporator: The effects of (i) a time varying pressure drop (ii) an axially varying heat flux

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### Cites background from "Non-linear dynamics of a two phase ..."

...As explained in Equation (4), ΔPf, ΔPg, ΔPa, ΔPl, in Figure 12, are frictional, gravitational, acceleration, and form pressure drop, respectively....

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...The additional acceleration a is a vector composition of translational acceleration and rotational acceleration, which is shown as Equation (21). a=at +ω× ω× rð Þ+ β× r+2ω×u ð21Þ where the vector terms can be decomposed into the components along three axes (x, y, z), as shown in Equation (22). a= atx aty atz 2 64 3 75+ ωx ωy ωz 2 64 3 75× ωx ωy ωz 2 64 3 75× rx ry rz 2 64 3 75 0 B@ 1 CA+ βx βy βz 2 64 3 75× rx ry rz 2 64 3 75 + 2 ωx ωy ωz 2 64 3 75× ux uy uz 2 64 3 75 ð22Þ According to Equation (21), the additional force on the fluid Fa can be expressed in Fa =F t +Fce +F ta +Fco = −ρ at +ω× ω× rð Þð + β× r+ 2ω×uÞ ð23Þ where Ft is the translational inertial term, Fce is the centrifugal term, Fta is the tangential term, and Fco is the Coriolis term....

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...For the onedimensional analysis along the channel, Equation (27) can be reduced to the form used in Ma et al.23 With the additional acceleration on fluid, dPadd can be derived by Equation (28) in which k is the unit vector of flow direction....

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...The expression to formulate the void fraction in Chexal et al18 is given as Equation (5). α= β C0 + Vgj=j ð5Þ Combining the vapor volumetric fraction in Equation (6), the void fraction in Equation (5) could be transformed into Equation (7). β= 1 1+ 1−xð Þ=xð Þ+ ρg=ρl ð6Þ α= 1 C0 1+ 1−xð Þ=x ρg=ρl + Vgjρg=xG ð7Þ The expression of drift velocity for calculation of void fraction is given as: Vgj =1:41 ρl−ρg σg ρ2l 2 4 3 5 1=4 C1C2C3C4 ð8Þ The parameters Ci are given in detail in Chexal et al. 18 Its validity is verified for .01 ≤ α ≤ .95, 0.01 ≤ G ≤ 2100 kg/m2/s1, and 0.1 ≤ P ≤ 14.5 MPa under nonadiabatic conditions....

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...Nsub =Npch−Xe vfg vfs ð31Þ For a given subcooling condition, after the threshold heating power triggering instability in the system is obtained in experiment or calculation, the corresponding heating power Q, flow rate w and other physical properties are substituted into Equations (29) and (30) to calculate Npch and Nsub....

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### "Non-linear dynamics of a two phase ..." refers methods in this paper

...The attractor is reconstructed using the time delay embedding method described in Grassberger and Procacia (1983), Leibert and Schuster (1991)....

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...The attractor is reconstructed using the time delay embedding method described in Grassberger and Procacia (1983), Leibert and Schuster (1991). We now discuss how the method can be used to characterise the dynamic behaviour of the system using velocity time series data....

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...The attractor is reconstructed using the time delay embedding method described in Grassberger and Procacia (1983), Leibert and Schuster (1991). We now discuss how the method can be used to characterise the dynamic behaviour of the system using velocity time series data. It also enables us to determine the minimum number of variables required to describe the system completely. The reconstructed attractor is obtained from the following steps 1. The time series 6in(t) is generated by simulations. The time interval of integration is 0.005 (in dimensionless time units). This time series is viewed as experimental data obtained by sampling the inlet velocity at the above time period. The system can be characterised quantitatively if we can determine the embedding dimension d and delay time Td. Optimum values of these variables is essential for the successful computation of the attractor dimension g. 2. The time delay Td is estimated in terms of the sampling time using the method of Leibert and Schuster (1991). A sample of 5000 points (after the initial transients have died down) was used to determine the delay time....

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### "Non-linear dynamics of a two phase ..." refers methods in this paper

...The attractor is reconstructed using the time delay embedding method described in Grassberger and Procacia (1983), Leibert and Schuster (1991)....

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...The time delay Td is estimated in terms of the sampling time using the method of Leibert and Schuster (1991)....

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...This is called the upwind difference scheme (Ozicik (1994))....

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149 citations

### "Non-linear dynamics of a two phase ..." refers background in this paper

...Saha et al. (1976) studied experimentally the effect of various parameters like inlet sub-cooling, inlet restriction, exit restriction on the stability of the system to DWO....

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