Chemical and Petroleum Engineering, Vol. 31, Nos. 9-10, 1995

NEW PROCEDURE FOR CALCULAT ION AND SELECT ION

OF CONTROL VALVES

V. G. Patrikeev, E. G. Pinaeva, and Yu. I. Taras'ev UDC 621.646.001.24

All of the known methods for calculating and selecting control valves (CVs) are based on the use of a flow rate coefficient which, according to Industry Standard OST 26-07-2012-79 and State Standard GOST 23866-87, is termed the "throughput capacity" K v (in m3/h). On the one hand, this parameter links the flow rate and pressure loss in a CV (we call these "information variables"); on the other hand, the parameter depends on the geometry of the flow section of the CV and the flow conditions (if the inlet and outlet fittings have equal areas). Since K v is easy to determine independently in two different systems of variables, i.e., in a geometric system by means of experiment and in an information system by means of calculation, this parameter should be regarded as a generalized characteristic of CVs [1]:

Qm 5-04sn (1)

~/Ap9 - Kv - "J{a (Rest) '

where Qm is the mass flow rate of the medium through the CV, tonnes/h; Ap is the pressure loss in the CV, kgf/cm2; P is the density of the working medium, g/cm3; s n is the nominal area of the passage, cm2; ~n(Rest) is the coefficient of resistance under conditions corresponding to those of the test-stand evaluations; Ost = 1 g/cm3; Aps t = 1 kgf/cm 2 (according to the definition of Kv); Re = Rest; 5.04 is a factor that takes into account the dimensions of the quantities appearing in Eq. (1).

Even though K v has certain advantages, it also has definite disadvantages: it is dependent on the flow regime of the working medium, and there is no way to account for the difference in kinetic energy of the flow in valves with different diameters of the inlet and outlet fittings.

These shortcomings have been eliminated in a CV calculation method developed by the Moscow State Academy of Chemical Machinery Construction and TsKBA [Central Design Office for Valve and Fitting Construction] (St. Petersburg); this method is based on describing the flow of an incompressible fluid in local resistances, including CVs, by means of an energy conservation equation with generalized parameters, in the form [1, 2]

Cq(l) Q2 m + qCt( l)Q m - Ap9 = 0, (2)

where Cq(D is the quadratic modulus, m-4; C/(/) is the Viscosity modulus, m-3; r/is the coefficient of dynamic viscosity under the working conditions, Pa.sec; Qm is the mass flow rate of the medium through the CV with a fixed l relative to the course of the adjusting control (AC), kg/sec; p is the density of the medium under the working conditions, kg/m 3.

Let us consider what is represented by the parameters Cq and C l. It was established by means of an experiment designed for this specific purpose that a CV can be considered as an

essentially perfect local resistance ha which the dissipation of flow energy proceeds under the condition that the losses due to forces of viscosity and inertia are accumulated additively.

In this case, the dissipation in the CV is described by the equation [3]

2Lal~ {y(Re) = ~,t,, + - - (3)

Re '

Translated from Khimicheskoe i Neftyanoe Mashinostroenie, No. t0, pp. 8-11, October, 1995.

0009-2355/95/0910-0539 $12.50 9 Plenum Publishing Corporation 539

where (n(Re) is the coefficient of resistance with a fixed Reynolds number Re; (m is the coefficient of resistance in the field of turbulent self-similarity; Lath is the Lagrange number.

The Lagrange number is found experimentally in the regime of laminar self-similarity, the boundary of which, depending on the type of flow section of the CV or any other local resistance, varies from 30 to 2000; the Reynolds number is defined by the expression

4Q m Re=

nDN~ '

where DN is the diameter of the nominal passage (this designation is accepted in the technical documentation for control valves). The maximum error of Eq. (3) is no greater than 20%.

For any local resistance (LR), from the Bernoulli equation (plus the condition of continuity) for an incompressible fluid, we have

Ct A.~pp Qm ~ ( Re ) (4)

where the correction for nonquadraticity (or correction for "viscosity") has the form

/~. (Re) + (s,,/s2) 2 - (s . /s l ) 2 v(Re) q ~.+(s/:2) 2- (s /sp 2 '

(here, s 1 and s 2 are the respective cross-sectional areas of the inlet and outlet fittings of the CV, in m2); C t = 2a~n/

x/~t n + (Sn/S2) 2 - (Sn/Sl) 2 is the turbulence modulus, m z. In the region of turbulent self-similarity (subscript t), from Eq. (4) we obtain, with ~b(Re) = 1, the following

expression:

Q tat ,,f2s n

qrZp, o ~ ~, + (s /~2)2_ (s/s1)2' (5)

where Qmt is the mass flow rate in the region of turbulent self-similarity; Apt is the pressure drop in the region of turbulent self-similarity.

From Eqs. (5) and (1) it follows that the turbulence modulus is a generalized constant of the LR, reflecting the manifestation of forces of inertia in the flow (~tn) and the difference between kinetic energies at the boundaries of the LR.

From Eq. (4), together with Eq. (3) for the LR, we obtain Eq. (2) for the conservation of energy of an incompressible viscous fluid with generalized constants, where the quadratic modulus is given by the expression

~.t,, + (s . / s2 ) 2 _ ( s , , / s l ) 2 = = C-2 (6)

C~ 2s 2 , , /1

and the viscosity modulus by the equation

1 (APl kp., Q ml) Lat,, ~t[Q-~ Q. -Q-~ = C , - DNs

The quadratic modulus reflects the same processes as the turbulence modulus; the viscosity modulus reflects the manifestation of forces of viscosity, and is also a generalized constant.

A significant advantage of the quadratic modulus over the turbulence modulus is the additivity of the series connection model with the quadratic modulus, i.e.,

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It

Cqc = ~ Cqi ;

n

Ct: e = ~ Cti ,

(7)

where Cqc and Ctc are the moduli of a hydraulic chain consisting of n LRs connected in series; Cqi and Cli are moduli of the i-th LR entering into the hydraulic chain.

The turbulence modulus of a hydraulic chain Ctc consisting of n LRs is related to the turbulence modulus of the i-th LR C a by a nonlinear relationship that follows from Eq. (6).

Considering Eq. (8), we find

C-t~ ~-" Z tf~tt2.

The relation between the throughput capacity and the indicated moduli is obtained from Eq. (2). In view of the definition of the throughput capacity K v (m3/h) that is given in standardization documents, as well as the dimensions of all the parameters 01st = 0.001 Parsec; Ost = 1000 kg/m3; APs t = 1.01325-105 Pa), we can write

3600-2CqK2~ + 1 9 10 -6. 3600-1ClKv - 101,325 = 0.

If we neglect the second term in Eq. (8), we obtain

(8)

Cg = 1,313" 109/K2v

or, when Eq. (6) is taken into account,

Ct = 2,76.10-SKo.

Neglect of the second term in Eq. (8) is equivalent to the statement that ~b(Rest ) = 1 and that the flow regime in performing test-stand evaluations to determine the throughput capacity is the regime of turbulent self-similarity; this statement is not always justified.

According to experimental data, the maximum error in calculating the throughput by the use of Eq. (2) is no greater than 10%. For single-seat and two-seat control valves and butterfly gate valves, experimental data were obtained in [4] over a range of variation of Reynolds number from 0.1 to 106. Analysis of these data provides grounds for recommending a universal formula relating the viscosity characteristic of a CV Ct(/) to its quadratic characteristic Cq(/):

In Cr(/) = a + b In DN + c In Cg(l),

where a, b, and c are constants for a given type of CV [5].

Thus, for LRs and CVs handling the flow of an incompressible liquid, two constants, C t (or Cq) and C l, are sufficient for a complete characterization of the design with respect to energy dissipation; the flow equation then takes on the form of (2). Hence, we must take as the basic characteristics of a CV not the flow rate coefficient (throughput capacity) Kv, but rather the turbulence modulus Ct, the quadratic modulus Cq, and the viscosity modulus C I. These are the specific characteristics that must be standardized and listed in technical standardization documents for the end-item and also in catalogs (with a statement of the procedure used to calculate the CV).

The use of an energy conservation equation with generalized constants (2) makes it possible to perform calculations for the flow of liquids and gases that behave as incompressible fluids in all elements of the hydraulic system (HS) other than the CV (in the flow of gases), and to take nonquadraticity of flow into account in all elements of the HS.

For the flow of gases, the procedure is based on a universal two-parameter equation that is generally accepted by leading firms:

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0.613pj Cyg (l) sin 1,63 Af~p Q " - K, RT -e-; 4Z '

where R is the specific gas constant; K 1 is the compressibility of the gas; Cfg is the gas characteristic of the CV; Pl is the CV inlet pressure; T is the temperature.

The maximum error of the universal equation, on the basis of experimental data, is no greater than 12%. The gas characteristic of the CV, Cfg(/), may be calculated on the basis of certificate data on the CV [for foreign CVs, Cfv(/)]

k 2 k-I

(here, k is the adiabatic exponent of the gas), or the gas characteristic may be determined by experimentally justified methods (the maximum error in calculations of the gas characteristic of CVs is no greater than 10%).

Currently in the process of approval is the final edition of the State Standard of the Russian Federation "Procedure for Calculation and Selection of Control Valves."

Development of this standard was aimed at establishing a procedure for calculating and selecting the type, size, and throughput characteristic of CVs, with due regard for the structural features of the HS when the CV is connected in series or in parallel. The HS is understood to be that section of a technological system in which the flow rate at the inlet to the controlled object is formed, i.e., the flow rate acting on the controlled object in a local automatic control system. The application of CVs in accordance with the procedure that has been developed will offer a means for maximizing the term of efficient and safe operation of not only the HS, but also the CV itself.

The GOST standard covers CVs of different types [single-seat unloaded and loaded (or cell type) and two-seat valves, ball valves, and disk gate valves] that are used in HSs transporting single-phase media, over a range of flow regimes from laminar to fully developed cavitation in the case of an incompressible liquid, and up to critical flow regimes in the case of a

compressible fluid (gas). Here, the following factors are considered: the mode of installation of the CV in the HS (series or parallel); various

types of pressure sources (centrifugal pump, receiver, positive-displacement pump); all resistances of the hydraulic circuits

included in the HS; and the properties of the substances being transported (working media). The new GOST standard regulates the parameters and conditions that are to be used in selecting the CV type, these

parameters and conditions being necessary for optimal functioning of the CV in a specific production line. The CV that is selected is checked for the existence of cavitation regimes: gas cavitation (producing intense acoustic noise) and vapor cavitation

(limiting the flow rate of the working medium in the HS). This standard recommends the following measures for protection against cavitation: installation of the CV in the initial

section of the HS; installation of an orifice or a packet of orifices following the CV; installation of a series of two CVs. For all of the versions of cavitation protection, the standard includes a procedure for calculating the diameter of the

nominal passage of the supplementary CV and the diameter of the orifice opening. For critical flow regimes of a gas in a CV, the same protection methods are recommended as in the case of cavitation

regimes, and appropriate methods of calculation are proposed. In the new GOST standard, many of the procedural errors in the existing technical standardization documents have been

corrected. For example, in those earlier documents, the correction for "viscosity" with a fully open position of the AC had been presumed to coincide with the correction for "viscosity" at maximum flow rate, when the plunger of the CV is in the fully open position (/max)" The pressure drop in the CV at maximum flow rate was compared to the maximum allowable cavitation- free pressure drop with a fully open AC. Furthermore, no account was taken of nonlinearity of the performance curve of the pressure source in the HS. There was no matching of the equations of energy conservation and continuity in tee fittings.

In developing the GOST standard, the following premises were accepted: Do not change the hydraulic parameters and characteristics of the CV indicated in the technical standardization

documents, even though studies performed in the Russian Federation over the past 30 years clearly indicate the advisability

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and effectiveness of certifying CVs on the basis of the quadratic modulus, viscosity modulus, design characteristic, acoustic

coefficients and cavitation coefficients, and the gas characteristic. Discontinue the use of averaged values of the parameters and characteristics of CVs, changing over to calculation of

individual properties of CVs in accordance with procedures that are theoretically and experimentally justified. In view of the wide use of CVs manufactured in other countries, provide the capability for performing calculations on

the basis of the parameters included in CV certification data by the leading foreign firms. Select a form of calculations of the flow rate characteristic such that the possibility of using different structures of the

HS will be taken into account. In developing the GOST software, extensive use has been made of the results from experimental studies performed

by TsKVA [Central Design Office for Valves and Fittings], the Scientific-Production Association Neftekhimavtomatika (Moscow), MGAKhM [Moscow State Academy of Chemical Machinery Construction] (Moscow), Scientific-Production Association Promavtomatika (Kirovakan), VIIAM [All-Russian Scientific-Research Institute of Valves and Fittings] (Moscow),

and several foreign firms. Currently under development is a dialog system of CV design and selection (SAPR RA), using a personal computer,

with an original, unique variational method. Thus, a dialog system SAVRA for CV calculation and selection, without accounting for the HS in which the CV is

installed, has been implemented at TsKBA in a personal computer of the IBM PC AT class. The SAVRA software is a databank (DB) containing the parameters of the CVs in regular production of the plants or in the stage of final development of technical documentation, as well as the CV hydraulic characteristics, commercial data, and so on (a total of 51 characteristics). The DB can be expanded at the request of the purchaser.

The SAVRA system is being extended to a control valve DN = 15-500, operating on single-phase Newtonian media in the range of flow regimes of an incompressible fluid from laminar to fully developed cavitation, and in all flow regimes of

a compressible fluid (gas). The set of programs of the SAVRA system is designed to accomplish the following tasks: 1. CV calculation and selection with predetermined parameters of the industrial process, namely the inlet pressure,

pressure drop, and corresponding mass flow rate of the working medium at the inlet to the object of regulation. 2. Checking for the start of cavitation. 3. Checking for the absence of acoustic noise. 4. Calculation of coordinates of plunger profile for control valves with a standard element base, in accordance with

the assigned throughput characteristic. 5. Operation of the DB of the CV in the dialog mode, and accomplishing the transfer from the CV DB to the

application programs. 6. Preparation and printing of output documentation formulated in the standard manner, to include both input and

calculated data. An outstanding feature of the SAVRA system is the possibility of creating CV arrangements (eight versions) such that

reliable operation is guaranteed, without encountering any cavitation or critical regimes. This is achieved by series connection or the use of two standard-size CVs; other alternatives include the use of a CV with one or several orifices.

REFERENCES

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2. 3.

4.

5.

V. G. Patrikeev and Yu. S. Serbulov, Special Actuators in the Chemical Industry [in Russian], VGU, Voronezh (1982). RD RTM 26-07-256-84, "Calculation and selection of control valves." A. D. Al'tshul', L. S. Zhivotovskii, and L. P. Ivanov, Hydraulics and Aerodynamics [in Russian], Stroiizdat, Moscow (1987). R. E. Veziryan, "Investigation of the design characteristics of throttling control elements," Candidate's Dissertation, Tashkent (1979). V. G. Patrikeev, V. V. Vasenin, and R. E. Beziryan, "Features of calculation of control valve up to the region of cavitation resistance," Khim. Neft. Mashinostr., No. 8, 15-16 (1991).

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