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Unformatted text preview: ENU 4134 – (Deriving/Driving Towards) 1D Transport D. Schubring September 18, 2009 Modeling of TwoPhase Flow I Averaging, averaged parameters (2) I Transport equations (2) I Homogeneous equilibrium model (1+) I Separated flow model(s) (1+) I Choked (critical) flow (1+) Approaches to the Transport Equations T&K attack the problem this way: I Develop mixture equations in 1D (Section 55), for mass, momentum, & energy I Develop integral transport equations in 3D (Section 56), for mass, momentum, & energy I Use of integral 3D transport equations in volume Δ zA z to produce 1D equations (Section 57), for mass, momentum & energy Approaches to the Transport Equations (2) We’ll proceed this way in the next two days: I Develop integral transport equations in 3D, including definition of jump conditions I Use of integral 3D transport equations in volume Δ zA z to produce 1D equations I Use 1D equations to produce mixture equations (for momentum and mass – take energy equation from book without proof) I Mass, momentum, energy in turn – all the way through the calculations Your Responsbility You should know the general balance equation and (generally) how one might obtain an integral balance for mass, momentum, and energy. You should know what a jump condition is and what it is used for. Your knowledge in this area is within the scope of Exams. Your Responsbility You should know the general balance equation and (generally) how one might obtain an integral balance for mass, momentum, and energy. You should know what a jump condition is and what it is used for. Your knowledge in this area is within the scope of Exams. You should also know how to take the integral balance to a 1D differential balance, but that’s something you learned in a math class and will not be tested on Exams here. Your Responsbility You should know the general balance equation and (generally) how one might obtain an integral balance for mass, momentum, and energy. You should know what a jump condition is and what it is used for. Your knowledge in this area is within the scope of Exams. You should also know how to take the integral balance to a 1D differential balance, but that’s something you learned in a math class and will not be tested on Exams here. The final equations in 1D are shown in Table 53 in T&K. (THE MIXTURE MOMENTUM EQUATION IS INCORRECT. Use Equation 5140 instead.) You are responsible for knowing the terms in the all of these equations. Your knowledge in this area is within the scope of Exams. General Balance Equation For any quantity X in a volume: dX dt = ˙ X in ˙ X out + ˙ X generation ˙ X dissipation (1) General Balance Equation For any quantity X in a volume: dX dt = ˙ X in ˙ X out + ˙ X generation ˙ X dissipation (1) For mass/momentum/energy, ˙ X in ˙ X out is referred to as the convection (or advection) term....
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 Spring '11
 Schubring
 Force, Mass, Trigraph, Fundamental physics concepts, vk, vk −

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