by E. S. DeHaven, The D o w Chemical Co.
I EQUIPMENT
AND
A
F E A T U R E
W O R K B O O K
DESIGN
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Control Valve Design . . . For Viscous Pseudoplastic Fluids Very few standard control valves have suitable characteristics for process control w h e n used w i t h viscous fluids, particularly w h e n these fluids are pseudoplastics
OTANDARD types of control valves— V-port, beveled disk, and throttle plug—have been used in control service where fluid passing through the valve is in turbulent flow. Application in these cases is successful because primary interest in such valve designs is to provide a variable area opening. This area is the parameter of primary significance in determining flow rate at any given available pressure drop through the valve. Such is not the case with viscous flow. Here, the matter of primary significance is not so much the crosssectional area of the opening, but is a matter of :
• clearance between walls of the passage through which the fluid must flow • nature of perimeter formed by such walls when viewed in the direction of fluid flow • length through which the fluid flows during its confinement between the walls Design of control valves used in viscous flow should adhere to prin-
Figure 1. Pressure d r o p is taken from the liquid as it moves through the annular passage b e t w e e n plug a n d seat
I/EC
ES
downward
ORKBOOK FEATUitBS
°3A
Ε
Ε
Ξ
EQUIPMENT A N D DESIGN
1.0
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A Workbook
Feature
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200
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= 5.36
X = 5.36
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Figure 2. As the fourth step in the design procedure, the plug profile (left) and the pressure d r o p (right) a r e established as a function of the clearance between plug and seat
ciples different from those involved in turbulent flow.
The Valves T w o new valve designs are pro posed for application to control of flow of viscous fluids. O n e , a char acterized plug-in-seat design, is .es pecially suited to the scmilogarithmic characteristic. T h e other, a stepped-sliding-stem type, has essen tially linear characteristics. Principal feature of the plug-inscat valve (Figure 1) is that the seat is somewhat deeper t h a n the seat in a conventional plug throttle valve. T h e plug is also longer. T h e depth of the seat is just equal to the length of the valve stem travel a n d the characterized portion of the plug is twice as long as the valve stem travel. Pressure d r o p is taken along the entire a n n u l a r channel between the plug and the seat, since this area is active in causing pressure d r o p to the fluid. This is in contrast to the conventional throttle plug design, where the primary pressure loss is attributed to the plane of m i n i m u m cross-section area available for flow. T h e control element in the slidingstem valve (Figure 5) is a rod which is stepped. T h e lower active portion is of smaller diameter than the u p p e r portion. W h e n the valve is closed, this rod rests in a corresponding 64 A
cavity consisting of a bore of the smaller d i a m e t e r a n d a counterbore of the larger diameter. As the rod is lifted, fluid flows a r o u n d the smaller diameter portion of the rod. This valve is inherently linear, ex cept for a small region during the initial opening of the valve. The valve is not suited for conditions where shutoff is required but serves a useful purpose where linear valves can be used. It is particularly a d a p t e d to areas where rather dif ficult materials of construction must be used. T h e design procedure is
4000 Ομ. 5.36
X 1 Ts
ft. Ibf
2000
1000
-40
-.30
-.20
-JO
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Figure 4 . As the fifth step in the d e sign procedure, segments of Figure 3 are integrated to give the total valve pressure d r o p as it varies with section of the plug profile used
INDUSTRIAL AND ENGINEERING CHEMISTRY
1.0
inch
Figure 3. The graphs of Figure 2 a r e combined to give the local pressure d r o p as a function of the location along the plug
simple; it is almost completely de scribed by E q u a t i o n 8.
Design Procedure for Plug V a l v e
First step; set down basic working Equations 3 a n d 4. Equation 4 is a n e x a m p l e of a m a t h e m a t i c a l de scription of assumed desired c h a r a c teristics of a valve with respect to flow. T h e constants are established on the basis of 50-fold rangeability, a n d the characteristic calls for a semilogarithmic response. T h e 50-fold rangeability implies, at constant available pressure d r o p , a 50-fold range in flow at constant viscosity, a 50-fold range in viscosity at constant flow rate, or from the equations, a 50-fold range in the product of flow rate a n d viscosity. Viscosity for pseudoplastic fluids is zero shear viscosity. Second step; establish the d i a m eter of bore of the seat. T o dp this, consider the highest product of vis cosity a n d flow rate to be encoun tered. F r o m some preconceived notion of the size of pipeline to be used to convey the fluid, establish the valve stem travel likely to be available in a standard motor valve. This establishes the length of passage for pressure d r o p . By trial calcu lations, using a n average clearance, Y, a n d using AP/H for dP/dL, com pute b, the channel width, which is
determined by the bore, as a function of trial values of the clearance, Y [b = TT(D — Y)]. It is easy to recog nize a reasonable and practical com bination of Y and b. Third step; express Equations 3 and 4 in terms of the established bore of the seat and in terms of the estab lished product of flow rate and vis cosity (Equations 5 and 6). From these latter two equations, it appears that there are four variables, ζ)μ„, Ρ, L, and h. However, there are implicitly two other equations not yet mentioned. They are contained in the knowledge that the total pres sure drop must be the established value for valve design, and that the total length of channel for pressure drop must be equal to H. There fore, a solution for the valve profile which will yield the desired char acteristic flow must be found. Imagine a location, Llyp (Figure 1), such that, during the entire valve stem travel, clearance, F tyP , is repre sentative to the extent that the pres sure drop and flow, at each valve stem position, h, are equal to those calculated on the basis of constant clearance over length H. For the purposes of the calculation, a typical clearance is located always at the same plane across the valve. With this stipulation, referring to Equa tion 5, convert dP/dL to — AP/AL AP is simply the established pressure drop and AL is equal to H. Then, by assuming trial values of F, yp compute values of Q/u„, and proceed to Equation 6 to compute correspond ing values of h. Thus lift as a func tion of the typical clearance is ob tained (Figure 2, left). This de fines the initial assumption as to the plug profile. (The values on all the graphs are for a valve designed for maximum ()μ0 = 575 g.p.m.poise, with C = 5 X 10-« ft.Vlbf2, with a seat 1 inch in diameter by 0.6 inch deep, with 50-fold flow range, semilogarithmic characteris tics, and ΔΡ = 1 5 p.s.i.) Fourth step; determine Liyi>, to locate the beginning and end of the profile. This can be done (Equation 5) by computing Y as a function of Y(dP)/(dL), and thus dP/dL as a function of Y (Figure 2, right), for the condition of minimum established ()μ„, a quantity already computed on the basis of h = 0. The "initial as sumption as to plug profile" can be expressed graphically by translation
>' Lift
to Open
Plunger shown in half open position
3)
\ 0
Plunger
Packing Gland
4 ) Valve Body -ζβ)
Bottom Ring
Figure 5. In the stepped-sliding-stem valve the fluid flows between the bore and the smaller diameter stem
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Figure 6. The length of path for fluid flow in the steppedsliding-stem valve is taken from a cross section through the open portion of the valve
(by relabeling in parentheses) of co ordinates (Figure 2, left). With the flow rate at its minimum, h = 0, and dP/dL may be plotted as a function of L' — L tvp using these two graphs (Figure 3). Fifth step; use Equation 7 for the total pressure drop, which may be obtained by integration of trial segments of Figure 3, the segments
being in magnitude equal to H, along the abscissa. The results are shown on Figure 4. From the es tablished value of AP, the established valve pressure drop, read from this figure the value of L' — Z,tyP· This value is actually — Z,typ—that is, the coordinates have been translated so that U = zero when AP is the estab lished value, and when (2μ0 is at its VOL. 5 1 , NO. 7
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JULY 1959
65 A
Il WÈ K H
EQUIPMENT A N D
DESIGN
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A Workbook Feature
Here are the equations from which design of the valves w a s developed: log,,, q
Shear rate, Newtonian άμ _ τ dy μ
(1)
Shear rate, pseudoplastic, as used in example du dy
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