5 homogeneous equilibrium model

Used for two phase flows incorporating uniform velocity of both phases

1. Homogeneous Equilibrium Model By: Yadav Gaurav N M.Tech Thermal Sciences Project Guide: Dr. S. Jayraj

2. Introduction The components are intimately mixed. Thus entire hydrodynamics is explained by suitable average properties. Saying that two phases move as pseudo fluid is that both the phases must have same velocity. If velocity is different they manifest their individual characteristics.

3. Thus the HFM does not incorporate the concept of relative velocity. Thus if phase velocity are different there will be slip resulting in relative velocity. So to accomodate this , Drift Flux Model is used. There is attainment of thermodynamic equilibrium between the two phases.

4. This means that: u1 = u2 = j α = β = Q2/(Q1+Q2) because no slip. Thus α becomes a measurable input parameter. Applicable to: Dispersed Bubbly Flow, Annular Flow, Droplet Flow. Not applicable to: Flows through orifice or short nozzle, non adiabatic flows with changes in x, particles of solid propellant burnt in nozzles of rocket engine , counter current vertical flows.

5. Continuity Equation for HEM For single phase flows: For two phase flows: This occurs because total mass flow rate remains constant for single and two phase flows.

6. Momentum Equation for HEM For two phase flows: Wall shear stress is a function of friction factor which is a function of Reynolds no.

7. Now Reynolds No: Viscosity is a function of composition. μ TP ǂ μ 1 or μ 2 Thus and

8. Energy Balance Equation for HEM

9. The expression for pressure gradient evaluating each term of the momentum theorem becomes: More or less all terms are known except f TP So we can express f TP in terms of known quantities for two phase flows.

10. The above equation is derived under the following circumstances: Taper: dA / dz appears. Frictional pressure gradient. Gravitational pressure gradient. Quality change due to heat. Estimation of f TP is done by different Rheological models or using correlations

11. My work in HEM Relating rate of heat addition per unit length to the heat flux, Substituting this in the energy equation and since total mass flow rate is constant and neglecting KE and PE,

12. We know that: If considering the pressure changes as small then h 1 and h 12 are const. Thus