Numerical Investigations of Hydraulic Transients in Pipelines having Centrifugal Pumps

Transcription

1 International Journal of Applied Engineering Research ISSN Volue 13, Nuber 8 (2018) pp Research India Publications. Nuerical Investigations of Hydraulic Transients in Pipelines having Centrifugal Pups Riyad Jassi Tilefih Al- Furat Al- Awsat Technical University, Najaf Technologies Institute, Iraq. Abstract: This paper focus on the different between the diagnostic results of hydraulic grade line syste. Basic fluid equations solved either, in the tie doain, using classical ethod of characteristics (MOC) and copare the results with aplace transforations ethod and Fourier transforations ethod. aplace transfor solution approach overcoes this difficulty accordingly, the results for the pipeline syste having varying deand showed that the aplace transforation sense to wave pressure occur due to suddenly increase in flow rate either than Fourier transforations ethod. By applying these ethod on assued network having suddenly change in flowrate. Keywords: Hydraulic Transients. INTRODUCTION The transients of hydraulic is tie varying syste. The flow in the pipe transients is defined by set of hyperbolic calculations consequent aer the preservation of ass and Newton s law in the otion [1, 2, 3, 10, 11, 12], and Matheatically the ethod of characteristics (MOC) is used for the calculations and other nuerical ethods [3,4,5,6] with reasonable success. Theoretical analysis (Characteristic Equations) Generally, the spatial variation is fewer iportant in defining the perforance than the tie-varying, two independent partial differential equations [7]...(1) (2) ȴ is a constant and naed a agrange ultiplier...(3) Regrouping ters,. (4) The partial equations are changed by two pair of ordinary differential equations as shown..(5)...(6) 5999

2 International Journal of Applied Engineering Research ISSN Volue 13, Nuber 8 (2018) pp Research India Publications. Finite Difference The equations (5) and (6) have new representation.(7)..(8) The ter (tp - 0) is replaced with ( t) then the new for gives And (9) (10) Figure 1. The characteristic grid for a single pipe Figure 2: Disturbance propagation in the s-t plane Nuerical Process The (H) value and (V) value which placed in the ends of pipe are founded by boundary conditions. The equations are developed to calculate (H) and (V) at the inside. Solving (9) and (10) to get (11) 6000

3 International Journal of Applied Engineering Research ISSN Volue 13, Nuber 8 (2018) pp Research India Publications. The Pipeline with varying deand discharge For this case the pipeline can be represented and divided by the intakes gives a new deand discharge with very sall neighborhood (2ε) as explained in Figure (3) [3] Figure 4 shows the block diagra of surge phenoenon. Figure 3: A pipeline with varying discharge Figure 4: Block diagra of transient flow analysis in pipeline systes HYDRAUIC APPICATIONS Figure 5 explain one of the ost case used to study to analysis the syste, the pipeline odel contains six pipes, the characteristics of this syste is shown in table (1). The six nodes data about are shown in table (2), the pup is cobined into a net and situated at one of 3 reservoirs. The analyzing take up the deand release is rapidly increased fro (50 gp) to (790 gp) unpaid pup on pipe six revive to operate at (20 sec.) and the transient occur down the pup, the wave speed is about /s also the friction factor (0.02) for all pipes, [7]. 6001

4 International Journal of Applied Engineering Research ISSN Volue 13, Nuber 8 (2018) pp Research India Publications. Pipe No. Nodes Fro to Figure 5: Pipeline syste Table 1: Pipeline data ength Dia. In. f Q gp Vel. Ft/s H Figure 5: Pressure head downstrea the pup in pipe six. Node Deand gp Table 2: Nodes data El. Head Pressure Psi. HG El CONCUSIONS In the analysis and observations of the ethod used in this paper, which depend on aplace transfor ethod for accurate sensing the pressure wave when suddenly change in the puping rate network systes. Figure. (5) obviously exposed the wave pressure accurse in pipe nuber six in the proposed work aer change in the rate of flow. The aplace provides the pressure better than others ethods. Sae results are got when applying the odel on pipe nuber two. Figure 6: Pressure head downstrea the pup in pipe two. REFERENCES [1] Allievi,. "Theory of water haer", Translated by E. E. Halos. Riccardo Garroni, Roe, [2] Zielke, W.."Frequency-dependent friction in transient pipe flow."journal of Basic Engineering. ASME, 90, , [3] X. Wang, M. F. abert and A. R. Sipson, "Analysis of a Transient in a Pipeline with eak Using aplace Transfors", 14th Australian Fluid Mechanics Conference [4] Rich, G. R. "Water haer analysis by the aplace- Mellin transforation" Transactions of ASE, 67, , [5] Chaudhry, M. H."Applied Hydraulic Transients", Van Nostrand Reinhold Copany, New York, [6] Wood, F. M."Application of Heaviside's operational calculus to the solution of probles in water haer" Transaction of ASME, 59, , [7] Bruce E. arock, Roland W. Jeppson, Gary Z. Watters." Hydraulic of Pipeline Systes,"

5 International Journal of Applied Engineering Research ISSN Volue 13, Nuber 8 (2018) pp Research India Publications. [8] Vardy, A. E., and Hwang, K-.." A characteristics odel of transient friction in pipes" Journal of Hydraulic Research, IAHR, 29(5), , [9] Brunone, B., Golia, U. M., and Greco, M. " Modeling of fast transients by nuerical ethods" International eeting on hydraulic transients with Colu Separation, IAHR, Valencia, Spain, , [11] Gülich, Johann Friedrich (2010). Centrifugal Pups (2nd ed.). ISBN [12] Moniz, Paresh Girdhar, Octo (2004). Retrieved 3 April [10] R. K. Bansal (2005). A textbook of fluid echanics and hydraulic achines, Firewall Media. p ISBN NOMENCATURE Sybol Quantity SI Unit English Diension A Cross section area of pipe A n Fourier coefficients A P Polynoial constants a Wave celerity /s /s /t a IC (x * ) and b IC (x*) Piecewise continuous functions C d A Effective intake area D Pipe diaeter F i= C da a/ A 2Gh o Intake paraeter f Friction factor g Gravitational acceleration /s 2 /s 2 /t 2 H Transient head H 0 Steady state head H 1 Reference head in a pipe H o Steady state head at the intake h p Pup head ȴ Scale factor P Pressure Pa Ib/ 2 M -1 t -2 Q o Steady state flow rate 3 /s 3 /s 3 t -1 R= fq o/2daa Resistance ter s Space t * = t / (/a) tie x * = x/ distance V Average velocity /s /s t -1 x * = x / intake function ρ Mass density Kg/ 3 Ib/ 3 M -3 λ agrange ultiplier sub scribt) P Node value for finite deference sub scribt) e e value for finite deference sub scribt) Ri : Right value for finite deference δ(x * - x ) * Dirac delta function ε sall neighborhood 6003