1. 19-SEP-2012 «BE-RF-PM» Modelling of hydraulic system of CLIC prototype module type 0 Shoaib Azhar

2. 19-SEP-2012 «BE-RF-PM» 1.Introduction 2.Theoretical formulation 3.Numerical model

3. 3 19-SEP-2012 Modelling of hydraulic system of CLIC prototype module type 0 «BE-RF-PM» 1. INTRODUCTION: cooling system Demineralized water Nominal volumetric flow rate: 0.36 m 3 /h Water inlet temperature: 25 °C Water outlet temperature: ~45 °C Max. pressure allowed: 5 bar Inlet/outlet interface Water supply

4. 4 19-SEP-2012 Modelling of hydraulic system of CLIC prototype module type 0 «BE-RF-PM» TS7 TS1 TS2 TS6 TS4 1. INTRODUCTION: SAS and CL cooling system

5. 5 19-SEP-2012 Modelling of hydraulic system of CLIC prototype module type 0 «BE-RF-PM» 1. INTRODUCTION: PETS and RF network cooling system TS17 TS22 TS23 TS24 TS25 TS26

6. 6 19-SEP-2012 Modelling of hydraulic system of CLIC prototype module type 0 «BE-RF-PM» 1. INTRODUCTION: cooling scheme SAS CLs SAS CLs SAS CLs SAS CLs PETS unit WG1 WG2WG3 WG4 PUMP PRV CV2 CV7 CV3 CV4 CV5 Q1Q1 Q2Q2 Q3Q3 Q4Q4 Q5Q5 Q Q = total flow rate [m 3 /h] Q 1 ~ Q 4 = flow rate for SAS [m 3 /h] Q 5 = flow rate for PETS unit and wave guides [m 3 /h] P PRV = set pressure for PRV [Pa] CV = control valve PUMP = water pump f i = pipe distributed energy loss (L i = pipe length) K i = Pipe fitting coefficient (n i = Number of fittings) P PRV SAS = super accelerating structure CL = compact load WG = waveguide L 1, f 1 L 2, f 2 L 3, f 3 L 4, f 4 L 5, f 5 CV1 n 1, K 1 n 2, K 2 n 3, K 3 n 4, K 4 n 5, K 5

7. 19-SEP-2012 «BE-RF-PM» 1.Introduction 2.Theoretical formulation 3.Numerical model

8. 8 19-SEP-2012 Modelling of hydraulic system of CLIC prototype module type 0 «BE-RF-PM» 2. THEORETICAL FORMULATION: pressure head loss across pipe The head loss in pipe flow is mainly because of 2 reasons 1-Distributed Pressure Drop (friction head) 2-Concentrated Pressure drop (Valves & pipe fittings) H L = H f + ΣH c H L = Total Head Loss H f = Head loss due to pipe friction H c = Head loss in component/fittings L = L1+L2+L3+L4+L5+L6

9. 9 19-SEP-2012 Modelling of hydraulic system of CLIC prototype module type 0 «BE-RF-PM» 2. THEORETICAL FORMULATION: distributed pressure drop For Laminar flow (Re < 2000) : Darcy’s Equation: For Turbulent flow: Blasius Equation (smooth pipe) Moody’s Diagram Colebrook Equation Haaland Equation (Approximation) Re = Reynolds Number ε/D = Relative Roughness

10. 10 19-SEP-2012 Modelling of hydraulic system of CLIC prototype module type 0 «BE-RF-PM» 2. THEORETICAL FORMULATION: concentrated pressure drop Concentrated Loss (Minor Loss) BendsTeesValvesExpansionContraction…. Depends upon Velocity ‘v’ Fitting loss coefficient ‘K’ They may be small as compared to distributed pressure drop. But for short pipes with multiple fittings, minor losses are not minor ‘K’ depends on type and shape of fittings. In TM0 cooling system for AS lines there are more than 70 bends in 9 m span of diameter 6 mm.

11. 19-SEP-2012 «BE-RF-PM» 1.Introduction 2.Theoretical formulation 3.Numerical model

12. 12 19-SEP-2012 Modelling of hydraulic system of CLIC prototype module type 0 «BE-RF-PM» 3. NUMERICAL MODEL: calculation outline 4-Final Results Flow Rates Pressure Drops across Valves Distributed Pressure Drop Concentrated Pressure Drop 3-Calculated Values Valve OpeningReynolds NumberPipe frictional coefficient 2-Available Constants and Parameters Fluid Properties (Density, Viscosity) Valve Characteristics (kvs1~kvs7) Pipe Diameters & Lengths (D & L) Fitting’s loss coefficient (kb, ke, kt) 1-Required Inputs Regulating Pressure (PRV)Control Valve Voltages (v1~v7) Assumed Flow rates (Q1, Q2, Q3, Q4, Q5)

13. 13 19-SEP-2012 Modelling of hydraulic system of CLIC prototype module type 0 «BE-RF-PM» 3. NUMERICAL MODEL: required inputs Pressure: Pressure of the Regulating Pressure Valve Range: 4x10 5 Pa (4 bar) Max. Control Valve Voltages (v1~v7): to control the opening of the valve Range: 0 ~ 10 volts Assumed Flow rates: As it is iterative solution, so Initial assumption for flow rates of lines 1, 2, 3, 4 and 5 Q1, Q2, Q3, Q4 and Q5 in m 3 /h

14. 14 19-SEP-2012 Modelling of hydraulic system of CLIC prototype module type 0 «BE-RF-PM» 3. NUMERICAL MODEL: control valve characteristics Actual valve characteristic curve kvr=Kv/Kv s Interpolated valve characteristic curve #BURKERT REFERENCEk Vs [m 3 /h] CV1 Type 1 (2835, n. 175996) 0.12 CV2 CV3 CV4 CV5 Type 2 (2833, n. 175869) 0.04 CV7 Type 4 (2835, n. 176006) 0.45 Δp = pressure drop across control valve for a certain opening position [bar] ρ = water density [kg/dm 3 ] k Vs value: Flow rate value for water, measured at +20 °C and 1 bar pressure differential over a fully opened valve

15. 15 19-SEP-2012 Modelling of hydraulic system of CLIC prototype module type 0 «BE-RF-PM» 3. NUMERICAL MODEL: simplified set of equations ai.Qi 2 = Control Valve Pressure Drops Pfi.Qi = Distributed Pressure Losses (Frictional Losses) mi.Qi 2 = Concentrated Pressure Losses (bends, entrance/exit, tees, etc.) Qi = flow rate in m 3 /h in line ‘i’ ai = coefficient for Control Valve  (k s, v) mi = coefficient for pipe fittings  (K, v) Pfi = coefficient for friction loss  (L, D, v, Re, ρ, μ) Following set of implicit equations are solved in Mathcad to calculate flow rates

16. 16 19-SEP-2012 Modelling of hydraulic system of CLIC prototype module type 0 «BE-RF-PM» 3. NUMERICAL MODEL: results Inputs VP PRV (volts)[bar] 44.1 62.0 81.4 101.27 Results QQ 1~4 ΔP CV1~4 ΔP f1~4 ΔP c1~4 Q5Q5 ΔP CV5 ΔP f5 ΔP c5 ΔP CV7 ΔP c7 [m 3 /h] [bar] [m 3 /h][bar] 0.3110.0711.5630.1580.1880.0261.8670.0280.0182.1170.074 0.3120.0710.6650.1570.1870.0280.9610.0320.0220.9160.075 0.3150.0710.4090.1570.1870.0310.6980.0370.0260.5720.076 0.3170.0710.3520.1570.1870.0320.6400.0390.0280.4960.077 ΔP cv = Pressure Drop across control valve [bar] ΔP f = Total Distributed Pressure Drop due to pipe friction ΔP c = Total Pressure Drop in component/fittings V = control valve set voltage On the basis of the operating condition of the control valves (i.e. input voltage), the pressure to be set at PRV depends on the requested flow rate inside the cooling system. For each control valve, a desired voltage input can be considered into the simulation. The corresponding flow rates inside each branch of the circuit are calculated consequently.

17. 17 19-SEP-2012 Modelling of hydraulic system of CLIC prototype module type 0 «BE-RF-PM» 3. NUMERICAL MODEL: results Keeping the pressure at the PRV constant, the flow rate can be changed modifying the position (i.e. input voltage) of the control valves. The higher the pressure at the PRV, the higher the ∆Q for a given ∆V InputResults VP PRV QQ 1~4 ΔP CV1~4 ΔP f1~4 ΔP m1~4 Q5Q5 ΔP CV5 ΔP f5 ΔP m5 ΔP CV7 ΔP m0 (volts)[bar][m 3 /h] [bar] [m 3 /h][bar] 3 4.1 0.2190.051.6440.0850.0940.0181.8250.0150.0092.2140.037 40.3110.0711.5630.1580.1880.0261.8670.0280.0182.1170.074 50.3880.0891.4800.2310.2920.0331.9060.0420.0312.0170.116 7 1.4 0.2890.0660.4320.1360.1590.0280.6900.0310.0210.6000.065 80.3150.0710.4090.1570.1870.0310.6980.0370.0260.5720.076 90.3320.0750.3920.1710.2060.0330.7040.0420.0300.5520.085

18. 18 19-SEP-2012 Modelling of hydraulic system of CLIC prototype module type 0 «BE-RF-PM» CONCLUSIONS By giving the desired set pressure for pressure regulating valve and input voltages for each control valve, we can get the values of flow rates in different lines as well as pressure drop distribution along the path. Hence we can adjust the input parameters to get the desired flow in any line according to requirement. Parameters of safety valve and surface roughness of pipes & flow path can be included for better results in the model. From results we can observe that: o When the control valves are partially closed (4 volt), for each AS line the total pressure drop in the pipes is 20% of the pressure drop across control valve. o When the control valves are fully open (10 volt), for each AS line the total pressure drop in the pipes is almost the same as pressure drop across the control valve.