Develop a finite volume framework to solve for pressure and velocity along the flow direction in...

 

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Develop a finite volume framework to solve for pressure and velocity along the flow direction in a Venturimeter as depicted in the figure. Staggered grid is used to discretize as shown. Assumptions: i) The physics is treated as a 1D flow problem. ii) Viscous forces are ignored. iii) Body forces such as gravity is ignored. iv) Flow is incompressible. inlet A₁ Po t P2 1₂ 0.35 P3 P4 P5 a. Inlet pressure b. outlet velocity 0.2 iv) Inlet velocity is u₁ = 10 m/s v) Outlet pressure is P11 = 0 Pa (gauge) 146 P6 P7 P8 1 0.5 Po outlet Given: i) Inlet area, A₁ = 2500 mm²; throat area, At = 1000 mm²; outlet area, A₂ = 2500 mm². ii) Length of nozzle, throat and diffuser sections are 1₁ = 0.35 m, l₂ = 0.2 m, l3 = 0.5 m iii) Density of the fluid is p = 1000 kg/m³ 12 1. Finite volume formulation for SIMPLE algorithm. a. Continuity equation (p-node) (explain for one internal-node) b. Momentum equation (u-node) (explain for one internal-node) 2. How would you apply boundary conditions? a. Inlet b. outlet 3. Assuming all unknowns to have initial guess as 0, setup up SIMPLE interations. Solve until avg L₂ (p') <10 and avg L₂ (u') < 10-6. (You may use TDMA, GS-SOR, or any other solver developed in earlier assignment) 4. Post-processing: calculate the following. [20 points] [10 points] [20 points] [10 points] Develop a finite volume framework to solve for pressure and velocity along the flow direction in a Venturimeter as depicted in the figure. Staggered grid is used to discretize as shown. Assumptions: i) The physics is treated as a 1D flow problem. ii) Viscous forces are ignored. iii) Body forces such as gravity is ignored. iv) Flow is incompressible. inlet A₁ Po t P2 1₂ 0.35 P3 P4 P5 a. Inlet pressure b. outlet velocity 0.2 iv) Inlet velocity is u₁ = 10 m/s v) Outlet pressure is P11 = 0 Pa (gauge) 146 P6 P7 P8 1 0.5 Po outlet Given: i) Inlet area, A₁ = 2500 mm²; throat area, At = 1000 mm²; outlet area, A₂ = 2500 mm². ii) Length of nozzle, throat and diffuser sections are 1₁ = 0.35 m, l₂ = 0.2 m, l3 = 0.5 m iii) Density of the fluid is p = 1000 kg/m³ 12 1. Finite volume formulation for SIMPLE algorithm. a. Continuity equation (p-node) (explain for one internal-node) b. Momentum equation (u-node) (explain for one internal-node) 2. How would you apply boundary conditions? a. Inlet b. outlet 3. Assuming all unknowns to have initial guess as 0, setup up SIMPLE interations. Solve until avg L₂ (p') <10 and avg L₂ (u') < 10-6. (You may use TDMA, GS-SOR, or any other solver developed in earlier assignment) 4. Post-processing: calculate the following. [20 points] [10 points] [20 points] [10 points]

Answer rating: 100% (QA)

Answer 1 Continuity Equation PNode The continuity equation states that the change in mass of the fluid per unit volume is equal to the rate of change ... View the full answer