Chemical Engineering 693R

Transcription

1 Chemical Engineering 693R Reactor Design and Analysis Lecture 4 Reactor Flow and Pump Sizing

2 Spiritual Thought 2

3 Rod Analysis with non-constant q 3 Now q = qq zz = qqq mmmmmm sin ππzz Steady state Know mm, T b,in Develop expressions for: T max (z) T fuel (z) T clad (z) T bulk (z) LL q mm T b,in

4 Bulk Flow 4 Energy increase in Flow: qq (zz) = mm ddd dddd If no phase change, dh = C p dt b mm ddcc pptt bb dddd = qq zz = qqq mmmmmm sin ππππ LL Solve for T b T b (z) = qqq mmmmmm mmcc pp LL ππ 1 cos ππππ LL

5 Solution 5 T b becomes new boundary condition Solve clad, gap, and fuel regions based on this Final solution of T max based upon new boundary condition This problem is reserved for HW #4

6 Flow Analysis 6 Size pumps Evaluate Erosion Flow rates for heat transfer Core sizing/dimensions Vibration analysis Core Orificing Valve/component sizing

7 Flux 7 Flux = quantity per unit area per unit time Heat flux : J/m 2 *s Mass flux: kg/m 2 *s Neutron flux: neutrons/m 2 *s Momentum flux: kg*m/s*m 2 *s = kg/ms 2 ρv = kg/m 3 * m/s = kg/m 2 *s = mass flux Then the flux of any quantity per unit mass (q) is.ρqv q = h J/m 2 *s Heat flux q=1 kg/m 2 *s Mass flux q=v kg/s*m 2 *s = kg/m*s 2 Momentum flux -ρ*q*v. n*a is the rate of quantity through surface A

8 Lagrangian/Eulerian 8 Lagrangian Eulerian Motion of system of fixed mass CONSERVATION LAWS Fluid elements move around and deform Some fixed control volume CONVENIENT FOR ENGINEERING Don t care about fluid elements Want pressure and velocity fields at a point. Pressure on a wing Drag on a car Not the pressure of a chunk of fluid as it moves along

9 Lagrangian Solution 9 Differential Analysis Solution at any point in space Produce vector/scalar fields Pressure Velocity Enthalpy CFD Common in Licensing, beyond class scope For concept reactors, use Eulerian approach

10 Eulerian Solution 10 Utilize Reynolds Transport Theorem: ddbb ssssss = dd dddd dddd ρρρρ dddd + ρρρρ vv nn dddd CCVV CCSS Recall that any property can be B sys Mass Continuity Equation Momentum Force Vector Balance Energy Mechanical Energy Balance

11 Governing Equation 11 0 = dd dddd CCVV ρρ dddd + CCSS ρρ vv nn dddd FF = dd dddd CCVV ρρmm vvdddd + CCSS ρρmm vv vv nn dddd. Combined, these give integral view of fluid dynamics, useful in reactor design

12 Mechanical Energy Equation 12 WW ss FF = mm PP ρρ + vv2 2 + gg zz Can be viewed as multiple components of energy balance for control volume: Gravity Stagnation (acceleration) Pressure difference Friction Shaft work

13 Non-circular flow regions 13 Non-circular flow Hydraulic Diameter, DD ee = 4AA PP ww, f lam = shape specific f turb ~ round tube f d P s DD ee DD ee = 4AA PP ww = 4ss2 4ss = s = 4AA = 4 PP ππ 4 DD PP ww ππππ f lam =57/Re f = CC ffff RRRR nn n = 1, laminar, n = 0.18, turbulent

14 Tube Bundle Friction 14 Lam - CC ffff = aa + bb 1 PP DD 1 + bb 2 PP 1 2 DD For edge and corners, P/D replaced by W/D Turb - RRRR DDDD = 10 4 ff ff cccc PP DD 1 - RRRR DDDD = 10 5 ff ff cccc PP DD 1 PP OR CC fftt = aa + bb bb PP DD DD Coefficients found in Tables 9.5 and 9.6 of Nuclear Systems I Add contributions from spacer grids and mixing vanes

15 Entrance Region Effects 15 Velocity profile develops here zz DD ee = 0.05RRRR (laminar) zz DD ee = (turbulent) Characterized by higher f (flow acceleration) Exists for most flow disruptions Sensors far from orifices, obstructions, etc.

16 Flow Networks 16 Pipe Networks composed of single pipes Pipes is series Constant VV, additive ΔP Type I find ΔP Type II find VV Pipes in parallel Constant ΔP, additive VV Type I Type II Type III Find D

17 Sample Problem 17 Calculate the pressure drop across a bare-rod core assembly (no spacer grids or mixing vanes) for a closed stainless steel assembly with 264 tubes in square configuration, P/D = 1.13, D = 0.34 in, L = 10 ft, mm = 100 kg/s water.

18 Single Phase Heat Transfer (I) 18 qq zz = mm ddd = mm ddcc pptt = qqqq(zz)ππππ dddd dddd Need a boundary condition: 1. Constant T wall 2. Constant q Case 1: TT bb zz = TT bb,iiii + qqqqππππππ mmcc pp q ` T b (z) mm T b,in

19 Single Phase Heat Transfer (II) 19 T wall Case 2, Constant T wall (BC is T(0) = T b,in ) mm ddcc pptt dddd = h TT wwaaaaaa TT bb ππππ T b (z) mm TT bb zz = CC 1 ee hππππ mmccpp zz + TT wwwwwwww T b,in TT bb zz = TT wwwwwwww T b,in 1ee hππππ mmccpp zz + TT wwwwwwww

20 How to find h? 20 Pick correct flow correlation. 5 questions:l Fuid? (Pr~1, Pr>1, Pr<<1) Flow Regime? Geometry of channel? BC? q or T w? Fully Developed Flow vs. Entry Flow? Nu + correlations can be found in books, online, textbook, etc.

21 Pump Curve Schematic 21

22 Pump Operation Curves 22 Piping system requires a given V and a given H. H loss is friction and minor losses, etc. Pump has a corresponding V and H. These must match, forming the operating point. This may not be the best efficiency. Select a pump so that the best efficiency point (BEP) occurs at the operating point. Generally oversize the pump a bit higher flow for given H req or Higher H avail for given flow Add a valve after pump raises H req to match H avail for given flow Somewhat wasteful, but offers control. Also may increase efficieny. (But higher efficieny may not compensate for extra work wasted in the valve (see example 14.2)