11 th International Conference on Pressure Surges Lisbon, Portugal, 24 – 26 October 2012 Evaluation of flow resistance in unsteady pipe flow: numerical developments and first experimental results

11 th International Conference on Pressure Surges Lisbon, Portugal, 24 – 26 October 2012 Contents  Introduction  Data Collection and Analysis  Quasi-Two Dimensional Model  Numerical Results  Conclusions and Future Work

11 th International Conference on Pressure Surges Lisbon, Portugal, 24 – 26 October 2012 INTRODUCTION

11 th International Conference on Pressure Surges Lisbon, Portugal, 24 – 26 October 2012 Classic equations of unsteady flow through closed conduits Continuity Equation INTRODUCTION Dynamic Equation Assumptions: Flow is one-dimensional and the velocity distribution is uniform over the cross section Formulas for computing the steady-state friction losses are valid for transient state conditions. Unsteady friction Steady-stade friction

11 th International Conference on Pressure Surges Lisbon, Portugal, 24 – 26 October 2012 Classic equations of unsteady flow through closed conduits INTRODUCTION Flow Assumption: Flow is one-dimensional and the velocity distribution is uniform over the cross section. Formulas for computing the steady-state friction losses are valid for transient state conditions. The flow reversal close to the pipe wall is responsable for energy dissipation that can not be described by steady state friction models. QQ=0 Viscous Forces Inertial Forces Velocity Profile – Classic ApproachReal Velocity Profile

11 th International Conference on Pressure Surges Lisbon, Portugal, 24 – 26 October 2012 Quasi two-dimensional analysis of unsteady flows INTRODUCTION Discretization of flow into a finite number of cylinders Compute momentum and continuity equations to each cylinder axial velocity Uniforme pressure at each pipe cross-section (Assumption) lateral velocity shear stress

11 th International Conference on Pressure Surges Lisbon, Portugal, 24 – 26 October 2012 DATA COLLECTION AND ANALYSIS

11 th International Conference on Pressure Surges Lisbon, Portugal, 24 – 26 October 2012 Data Collection and Analysis Experimental facility Steel pipeline with a 200 mm nominal diameter (inner diameter 200 mm) Centrifugal pump (nominal power P N = 15 kW ) Q N = 20 l/s H N = 38 m Hydropneumatic vessel Reversible pumping system Total lenght 115 m Volume = 1m 3

11 th International Conference on Pressure Surges Lisbon, Portugal, 24 – 26 October 2012 Data Collection and Analysis Data Analysis 1st Problem High electric noise with a 20 m amplitude in steady state conditions Pressure signal at three locations for Q = 5 l/s Day 3 (March 2012) 2nd Problem Presence of air in the system Filtered pressure signal at the downstream end of the pipeline (T3) in consecutives days for Q= 5l/s

11 th International Conference on Pressure Surges Lisbon, Portugal, 24 – 26 October 2012 Filtered pressure signal at the downstream end of the pipeline for different flow rates (Day 3 – March 2012) Data Collection and Analysis Data Analysis Effect due to the installation of a electric filter Effect due to the installation of air valves The calculated wave speed increased from 900 m/s (Day 3 – March 2012) to 1050 m/s (May 2012). The theoretical wave speed is 1300 m/s.

11 th International Conference on Pressure Surges Lisbon, Portugal, 24 – 26 October 2012 QUASI-TWO DIMENSIONAL MODEL

11 th International Conference on Pressure Surges Lisbon, Portugal, 24 – 26 October 2012 Quasi-Two-Dimensional Model Continuity Equation 1D Model 2D Model Mass flux Discretization of flow into a finite number of cylinders

11 th International Conference on Pressure Surges Lisbon, Portugal, 24 – 26 October 2012 Quasi-Two-Dimensional Model Momentum Equation Forces considered in the momentum equation in 2-D Model 1D Model 2D Model

11 th International Conference on Pressure Surges Lisbon, Portugal, 24 – 26 October 2012 Quasi-Two-Dimensional Model Five – Layer Viscosity Distribution Laminar Flow Turbulent Flow Numerical Solution Shear stress calculation

11 th International Conference on Pressure Surges Lisbon, Portugal, 24 – 26 October 2012 NUMERICAL RESULTS

11 th International Conference on Pressure Surges Lisbon, Portugal, 24 – 26 October 2012 Numerical Analysis of laminar flow conditions At mid-lenght of the pipelineThe downstream end of the pipeline The energy dissipation obtained with the 1D Model is approximately 0,36% of the initial pressure amplitude. On the other hand, for the same period, the Quasi - 2D Model leads to a 4.8% reduction of pressure amplitude. Energy dissipation considering the 1D Model and Quasi - 2D Model (instantaneous valve closure)

11 th International Conference on Pressure Surges Lisbon, Portugal, 24 – 26 October 2012 Numerical analysis of laminar flow conditions Radial distribution of axial velocity t = ti t = ti+0,5L/c t = ti+L/c t = ti+1,5 L/ct = ti+2 L/c Axis of the conduit

11 th International Conference on Pressure Surges Lisbon, Portugal, 24 – 26 October 2012 Q = 10,8 l/s Q = 5,5 l/s Flow (l/s) Amplitude reduction of the pressure wave (1 cycle) 1D - ModelQuasi - 2D Model 10,80,31%5,47% 5,50,18%2,58% 2,20,08%1,40% Q = 2,2 l/s Numerical Analysis of turbulent flow conditions Energy dissipation considering the 1D Model and Quasi - 2D Model (valve closure time = 0,2 s)

11 th International Conference on Pressure Surges Lisbon, Portugal, 24 – 26 October D Model versus collected data 2-D Model versus collected data The maximum pressure is reasonably described by both models. None of the numerical models describes minimum pressures and pressure wave phase and shape. Numerical analysis of turbulent flow conditions Numerical versus experimental results

11 th International Conference on Pressure Surges Lisbon, Portugal, 24 – 26 October 2012 CONCLUSIONS AND FUTURE WORK

11 th International Conference on Pressure Surges Lisbon, Portugal, 24 – 26 October 2012 Conclusions and Future Work Results have shown that Quasi – 2D Models leads to a much higher energy dissipation. The next steps in experimental facility:  Instalation of air valves along the pipeline and a electric filter in the frequency converter;  Instalation of strains gauges, hot-films and a transparant box with PIV measurements; The next steps in the numerical analysis are:  The comparasion of different turbulent flow models;  The analysis of the effect of gradually dampeded eddy viscosity distribution;  The comparison of the velocity profiles using the PIV equipment with the results obtained for different turbulent flow models;  The analysis if the real energy dissipation and the comparison with the model results.

11 th International Conference on Pressure Surges Lisbon, Portugal, 24 – 26 October 2012 Acknowledgments

11 th International Conference on Pressure Surges Lisbon, Portugal, 24 – 26 October 2012 Evaluation of flow resistance in unsteady pipe flow: numerical developments and first experimental results Pedro Leite, Dídia I. C. Covas, Helena M. Ramos Instituto Superior Técnico/Universidade Técnica de Lisboa jhj José Tentúgal Valente, Manuel Maria Pacheco Figueiredo Faculdade de Engenharia da Universidade do Porto