TRANSIENTS IN MACHINERY HYDRAULICS

Yu.V. Kolevatov

Deputy Director of Siberian Research Institute of Aviation (SibNIA),

Polzunova Str, 21, Novosibirsk, 630051, Russia

Tel.: (383-2) 79-70-89, Fax: (383-2) 18-70-13, 

A.A. Moroz

Head of Pilot Plant,

Polzunova Str, 21, Novosibirsk, 630051, Russia

Tel.: (383-2) 79-54-25, Fax: (383-2) 22-07-01, E-mail: moroz@mail.cis.ru, 

V.I. Sabel’nikov

Leading Researcher of SibNIA, 

V.V. Tarasevich

Associate Prof. of Novosibirsk State University of Architecture and Civil Engineering

NGASU, Leningradskaya Str, 113, Novosibirsk, 630008, Russia

Tel.: (383-2) 669411, Fax (383-2) 161107, E-mail: tvv@iis.nsk.su.

 Abstract: The mathematical model of a problem, including the specification of the hydrodrive topology, the description of liquid flows in pipes and of the equipment functioning in non-steady modes is given. Considered computational technique is used for computation of the working fluid supply system for test stand. The effect of such protective measures as safety valve and air dome is researched. The comparison the using of variable-capacity pump with fixed-capacity pump is fulfilled. The influence of the adjusted pressure and capacity of relief valve on intensity of transient is investigated. The dependencies illustrating the air volume value influence on pressure in system are presented. It is ascertain that the capacity of relief valve is the key parameter, which influences on the maximum pressure in the system. The mathematical models and computational methods provide a reliable toolkit for modeling of various regular and irregular situations in such complex structure as hydraulic drivers that enables elaborating the modes of its safe operation. 

Keywords: machinery hydraulics, piping system, fittings, transient, mathematical model, numerical simulation results

1    Introduction

The hydraulic drives realized the power support for various machinery and equipment, in particular, for test stand. The hydraulic drive has a number of advantages (reliability and stability in operation, the large initial effort, opportunity to receive any required working characteristics, etc.) in comparison with the electric drive (other widespread drive). The hydrodrive is a typical example of complex pressure piping system, which structure contains: (1) the high pressure pipe network, supplying the high pressure; (2) low pressure pipe network, on which the discharge liquid is being gathered and delivered to pumps again; (3) one or several pump stations supplying a working liquid to system; (4) safety valves and regulating ones for maintenance of required modes of operation and protection of system from overloads; (4) actuating devices; (5) busting pump (or pumps); (6) air domes and other fittings. The displacement pumps are usually used in the hydraulic drives. Strictly speaking, the specificity of the hydrodrive is being manifested through the actuators.

It is necessary to know calculate the system parameters under various modes of behavior (both optimum situations and emergencies) for accurate design and operation of hydraulic drives. Mathematical modeling is a most effective way of solving this problem.

2    MATHEMATICAL FORMULATION OF PROBLEM

2.1    Domain of definition

The considered pipe network is being described by directed graph G. Each arc of G corresponds to the pipe of network, and each vertex of G corresponds to the node of network. Let arcs of G are numerated from 1 to S, and vertexes (tops) be numerated from 1 to J. Superscript j will mark the quantities, relating to the top with number j, and subscript i will mark the quantities relating to the pipe with number i. The each arc i have the «length» L_i corresponding to the length of pipe i. The arc orientation defines the positive direction of x-axes along each arc, where 0≤x≤L_i. Thus, such graph can be considered as the generalization of x-axis [1].

2.2    Governing equations

The liquid flow in each pipe i (i=1，…，S) is described by the known equations of the water hammer [2, 3]:

,                    (1)

where p=p(t,x) is pressure; Q=Q(t,x) is liquid discharge; r is the density of liquid, a is the velocity of water hammer wave, w is cross-section area of pipe, g is acceleration of gravity, z=z(x) is pipe ordinate, l is hydraulic friction coefficient [3].

2.3    Boundary condition

The equations describing the functioning of system nodes will serve as the boundary conditions for equations (1). Let's denote the pressure and the discharge at the extremity of i-th pipe nearest j-th node as  and , correspondingly. Let  is the vector of all intrinsic parameters of node j, vectors  and  are formed by the components  and  correspondingly. Then boundary condition for each node j will be described by the next relationships in general form:

,   where j=1,…,J                     (2)

The specific realization of boundary conditions (2) for hydraulic pump (pump station), hydraulic engine (hydromotors), boost pump, pipe junction, various kind of local resistances (valve, filter, etc) and air dome were considered in details in authors' paper [ 4].

2.4    Initial data

The initial flow parameters must be specified for the each pipe and node of system (if it is necessary):

  ,   ,  where i=1,…,S; j=1,…J        (3)

Usually the stationary solution of systems (1) – (2) is used as initial data (3).

Thus the problem is reduced to the solving of the initial-boundary problem (1) – (3) for the system of hyperbolic equations (1) defined on the graph [1].

3    METHOD OF CALCULATION

3.1    Explicit-implicit scheme of running calculation

The rectangular grid with the x-axis step h_i = L_i/N_i (i=1,…,S) and time step t  is considered, where the integer N_i > 0 . The scheme with the changeable time step t has shown the most efficiency for calculations of unsteady process in pipe system. This scheme can flexibly accommodate to the peculiarities of the pipe system and the unsteady process.

,  where n=1,…,N_i

, where n=N_i–1,…,0

Here k is time step index; n is x-axis step index; r_i = c_it/h_i is Courant number; s_i=min(1,r_i);  and  are Riemann invariants; and .

3.2    Calculation under conditions of Inexact or/and incomplete data

The modeling of work of a hydrodrive is frequently complicated by absence of the initial information necessary for calculation realization, especially under the dynamic modes. Many initial parameters are possible to be evaluated only approximately. Thus, rather typical the situation is, when the account should be executed under conditions of incompleteness or/and uncertainty of the initial information. Two approaches are applied to overcoming this uncertainty: 1) additional imitations of separate parts of system with the purpose of specification of initial parameters on the indirect data or estimation of their influence on process as a whole; 2) applications of modern information technologies, which allow to work with an inexact and/or an incomplete information. The first approach was realized by the authors in the form of "mathematical test stand" technique [5]. The other approach was developed by the authors with help of such integrated intellectual software as NeMo+ and Semp-TAO systems [6].

4    SOME RESULTS OF CALCULATION

4.1    Comparison with experiment

The full-scale experiment on hydrodrive was performed for check of adequacy of a calculation technique. Water hammer in the hydraulic system was produced by closing the high-speed stopcock on a pumping main therefore the violent non-stationary process arose in all a pressure pipelines, which caused the operation of valves, change of modes of operations of pumps etc. Comparison the results of account with the experimental data have confirmed acceptable accuracy and reliability of used techniques of account (see [4]).

4.2    Transients in hydraulic drive of test stand

Developed technique is used for computation of working fluid supply system for test stand, simplified scheme of which is shown in Fig 1. The working fluid is delivered from oil-pressure pumping station (OPPS) to consumer C (test stand) by pumping main with overall length of 286 m. The maximum circulation 3 m³/sec is considered as the design circulation.

OPPS represents the group of 9 axial-piston pumps connected in parallel, which deliver the oil into system through high-pressure filter bank. Each pump is provided with safety valve with passage diameter dp = 32 adjusted for the pressure pt= 32 MPa. The valve pressure dumping occurs when the pressure rises up to pt. The unloading valves attach also to the consumer to prevent possible pressure boosts. The effect of such protective measures as safety valve and air dome is researched by numerical experiments.

The effect of the adjusted pressure and capacity of relief valve on intensity of transient is investigated. The graphs showing the effect of the adjusting pressure of relief valve on pressures in pipe system are represented in Fig.2. One can see from these diagrams that the adjusting pressure exerts not great influence on maximum pressure in system. But the increasing of the transient's intensity is to be observed in a whole when the operating level of relief valve will increase.

The dependencies illustrating the air volume value influence on pressure in system are presented in Fig.3. One can see from Fig.3 that the air volume increasing diminishes the transient oscillation frequency unambiguously but dumps the amplitude weakly. Some drop of amplitude with magnitude about 2 MPa is possible, but this fact has no the nature of regularity because the amplitude increasing with air volume increasing can be observed also. This is connected with resonance condition seemingly.

The system is found the most responsive to safety valve capacity. The graphs of the pressure under various capacity values are presented in Fig.4. One can see from Fig.4 that the relief valve loses its safety quality and not prevent the system against high pressure in the presence of inadequate valve capacity (see curves 1 and 2 in Fig.4).

The comparison the case of variable-capacity pump (curve a) with fixed-capacity pump (curve b) is presented in Fig.4. One can see from results of calculations that both variable-capacity pump and fixed-capacity pump give the same maximum pressure in the system (the first pressure peak). But the variable-capacity pump has greater amplitude of following oscillations. It is caused by that the control of such pump operating not keep pace with pressure oscillations and responds to them with some lag. The system «swinging» and pressure amplitude increasing occur in result.

5    CONCLUSION

As a whole, it is possible to infer by results of calculations that "richness" of the control and protective equipment not always reduces in a warranted protection against high pressures. Mentioned above examples demonstrate, that more simple case (fixed-capacity pumps, absence of an air domes, etc) appears by more reliable. A key moment of a protection of a hydraulic system against high pressures is the capacity of relief valves, which should be chosen with a reserve, since the relief valves lose the protective role due to poor capacity.

The above-mentioned mathematical models and methods of computation provide reliable toolkit for modeling of various regular and irregular situations on such complex structure as a hydraulic drives and other machinery hydraulics. This enables to elaborate the modes of its safe operation.

References

[1]    Voevodin,  A.F. and Shugrin, S.M. The numerical methods of calculating of one-dimensional systems.- Novosibirsk, Nauka, 1981. (In Russian).

[2]    Zukowsky,  N.E. About the water hammer in water-supply pipelines // Proc. 4th Russian water-supply congress. - Moscow, Russia, 1899. (See also: N.E.Zukowsky,  About the water hammer in water-supply pipelines. - Moscow-Leningrad, OGIZ, 1948, vol.2.) (In Russian).

[3]    Streeter,  V.L. and Wylie, E.B. Hydraulic transients. New York, McGraw-Hill, 1968.

[4]    Atavin,  A.A., Vasiliev, O.F., Moroz, A.A. and Tarasevich, V.V. Transients in the Hidrodrive of Ship Elevator. Advances in Hydro-Science and –Engineering, // Proceedings of the IV International Conference on Hydro-Science and –Engineering, Seoul, Republic of Korea, September 26-29, 2000, Abstract, vol. IV, p. 233, paper on CD-ROM.

[5]    Shero nosova, T.Yu. and Tarasevich, V.V. The Simulation of Transients in Hydro-Automatic Systems under Flow Control. Water Industry Systems: Modelling and Optimization Applications (Eds. D.Savic, G.Walters), vol.1, Research Studies Press ltd., Baldock, Hertfordshire, England, 1999. p.425-436.

[6]    Taras evich, V.V. and Zagorulko, G.B. Computation of Flow Distribution in a Pipe Network With the Help of NeMo+ System.  Water Industry Systems: modelling and optimization applications (Eds. D.Savic, G.Walters), vol.2, Research Studies Press ltd., Baldock, Hertfordshire, England, 1999. p.53-64.

Fig. 1    Schema of hydraulic drive of test stand

Fig. 2    The influence of the valve actuation pressure on system pressure.
Here curve 1 corresponds to р_t = 22 MPa; curve 2 corresponds to  р_t = 25 MPa; curve 3 corresponds to  р_t = 30 MPa.

Fig. 3    The influence of air dome on system pressure.
Here: 1 is without the air dome; 2 is for the air dome with the volume of 0,05 m³; 3 is for the air dome with the volume of 0,1 m³; 4 is for the case of two air domes by 0,1 m³ volumes.

Fig. 4    Pressure at consumer.
(a) – variable-capacity pump; (b) – fixed-capacity pump; 1 – the capacity of relief valve is halved (with comparison to case (b); 2 – the capacity is diminished by factor of 5.