ANALYSIS OF FLOW INTO SURFACE-WATER INTAKE SCREENS

FLOW INTO AN INTAKE SCREEN IN DEEP, QUIET WATER

Case 1. Flow into a point of withdrawal (see Fig. 1). Flow will be completely radial. The constant velocity surfaces will be spheres. The velocity at a given point in the field will be given by

V_i = Q/A_I = Q / (4 pi r_I ²) (EQ.1)

where V_i is velocity,

A_i is the area of a sphere radius r_i,

r_i is the distance from the point of withdrawal to the point of interest, and

Q is the volume flow rate.

From Equation 1 it is evident that velocity decreases with the square of the distance from the point of withdrawal.

Assumptions: Fluid is inviscid and the point of withdrawal is sufficiently far from fluid boundaries that end effects can be ignored.

(Comparison-first-order simulation of pipe in a lake, away from bottom and lake surfaces.)

*Current Position

Fig. 1. Diagram of Flow into a Point of Withdrawal

Case 2. Flow into a point located on a surface (see Fig. 2). Flow will be completely radial in the upper half-plane. The constant velocity surfaces will thus be hemispheric.

V_i = Q/A_I = Q / (2 pi r_I ²) (EQ.2)

where V_i is velocity,

A_i is the area of a hemisphere radius r_i,

r_i is the distance from the point of withdrawal to the point of interest, and

Q is the volume flow rate.

Again, velocity drops with the square of the distance from the point of withdrawal.

Fig. 2. Diagram of Flow into a Point Located on a Surface

Case 3. Flow into an open pipe (see Fig. 3). Flow in two dimensions is much easier to analyze and yields sufficient information to permit intuitive extension into three dimensions. This simplification eliminates the need to attack hypergeometric functions and finite-difference-type solutions. (The techniques of conformal mapping are employed.)

Fig. 3. Diagram of Flow into an Open Pipe

Consider the two-dimensional case of flow of an inviscid fluid into a channel of infinite length. Flow of an inviscid liquid in a uniform channel is shown in Figure 4, where the channel thickness is 2 pi. The velocity is uniform over the cross section and constant as a function of x.

Two-dimensional Model of Flow into an Open Pipe: Before Transformation

TWO-DIMENSIONAL MODEL OF FLOW INTO AN OPEN

PIPE AFTER TRANSFORMATION

Under the transformation w = e ^Z + Z. the conditions of Figure 4 are transformed to those of Figure 5. In Figure 4, F of fluid = +V_Ox, y = - V_Oy, and V = -Ñ F . What is desired from the model is an expression for the potential function in Figure 5 and an expression for velocities in Figure 5 in -v coordinates.

Equipotential surfaces are lines of constant x in Figure 5. Streamlines are lines of constant y. Then:

w = e ^{X + iY} + X + iY w = e ^Z + Z Z = X + iY

w = e ^X e ^iY + X + iY e ^iY = COS Y + iSIN Y

w = e ^X COS Y + i e ^X SIN Y + X + iY

w = e ^X COS Y + X + i (e ^X SIN Y + Y)

w = U + iV

U = e ^X COS Y + X V = e ^X SIN Y + Y

Figure 5, then, is a mapping of flow into a pipe in a non-flowing water body. It can be seen that even at reasonably short distances from the pipe end, the flow pattern approaches that of flow into a point of withdrawal. Further, it is apparent that the velocity near the pipe end is very high. Figure 6 displays the flow field and velocity profile around a screen of the same diameter as the pipe. Making a screen larger in diameter than the pipe to which it is attached results in an immediate reduction in the maximum velocity through the screen.

Fig. 5. Two-dimensional Model of Flow into an Open Pipe: After Transformation

Fig. 6. Long Screen Diameter Equal to Pipe Diameter

If, in fact, one could construct a spherical screen with the withdrawal pipe near the sphere center, the flow through the screen surface would then be of uniform velocity. Construction of spherical screens is expensive and very complex. There are, however, a number of practical screen shapes which approach the spherical configuration. The first is a screen large in diameter compared to the pipe and having a screen end. The velocity distribution around a screen with a screen end is shown in Figure 7.

The next step in screen design is to examine the effect of the use of a solid end plate. This is of interest because economies in screen manufacture are made possible by this type of construction. The flow pattern into a screen with a plate end is shown in Figure 8. Note that the assumption of freedom from boundary effects is no longer valid.

With careful selection of screen length Ls, screen diameter Us, and length of pipe penetration Lp, for a given pipe diameter and flow velocity, it is possible to obtain nearly uniform through-screen velocity. For the information shown in Table 1 and displayed in Figures 7 and 8 the design was based on results of a proprietary computer program developed by Johnson Division, UOP, Inc.

Fig. 7. Velocity Distribution around a Screen with Screen End

Fig. 8. Velocity Distribution around a Screen with Plate End

Table 1. Comparison of Screen Designs

To facilitate comparison of various screen designs, two parameters are generated. One, called the uniformity coefficient (CUnif), is defined by Equation 3.

Cunif = Vmax / V mln EQ 3

where Vmax is the maximum point velocity through the screen, and
Vmjn is the minimum point velocity through the screen.The second parameter, called the performance coefficient (Cperf), is defined by Equation 4.

Cperf = Vmax / Vavg EQ 4

where Vmax is defined above, and
Vavg is the selected average velocity through the screen.

A perfect screen would have performance and uniformity coefficients of 1. Table 1 is a comparison of Cunif and Cperf for the various screen designs shown in Figures 6, 7, and 8.

THE EFFECT OF STREAM FLOW

The analysis in the preceding section is confined to quiet water bodies. In this section the flowing water body is introduced. The flow field surrounding a point of withdrawal is first addressed, followed by a discussion of the behavior associated with various screen orientations.

The equation describing a uniform velocity field is:

V = V ₀ Z ^{^},

where V ₀ is the uniform stream velocity and
Z ^{^} is a unit vector in the +Z direction of withdrawal.

The equation describing the velocity field of a point of strength -Q is:

V _i = - Q R ^{^}/ 4 pi r _I ²

where r = Z ² + R ²
Q is the volume rate of withdrawal,
V is the velocity at the point of interest,
r _I is the distance from the point of withdrawal to the point of interest, and
R ^{^} is a unit vector in the. +r direction.

Then:

V _i = V ₀ Z ^{^} + (- Q) R ^{^}/ 4 pi r _I ²

If the screen were to appear invisible to the flow, then Figure 9 would represent the flow field around such a screen. This possibility will be discussed further in a subsequent section. Let us now address the flow field that would result if the screen were to behave as if it were a solid cylinder in a flow.

Fig. 9. Flow Past a Point of Withdrawal

FLOW PAST A CYLINDER IN A UNIFORM FLOW

Consider a cylinder of infinite length placed perpendicular to the current direction. Again using the techniques of conformal mapping the flow field around a cylinder can be expressed by the equation

Vcy = Vo (1 – a ² / Z² )
Vcy = Vo (1 - a ² / R² e^i2Q )
Vcy = Vo(1 - a ² / R² (cos^2Q - isin^2Q ))
Vcy = Vo(1 - a ² cos^2Q / R² - i a ² sin^2Q / R²)
Vcy = Vo(1 - a ² cos^2Q / R² ) + i Vo (a ² sin^2Q / R²
cy = Vxyc + iV ycy (EQ 5)

where a is the cylinder radius,

Z is / R e^iQ
Vo is uniform flow velocity,
Vcy is the velocity at point A,
Vxcy is the x component of the velocity at point A, and
Vycy is the y component of the velocity at point A.

Then:

Vxcy = Vo(1 - a ² cos^2Q / R² ) (EQ 6)
Vycy = Vo a ² sin^2Q / R²

This flow field is shown in Figure 10.

Fig. 10. Flow Past a Cylinder in a Uniform Flow

Examination of Equation 6 at R equal to the cylinder radius reveals an interesting effect: If the screen acts as a cylindrical obstacle to flow, then the screen cleaning current is nearly doubled in the region from 60° < ~ < 120° and 240° s ~ < 300°. Also, it is apparent that there are stagnant (no-flow) regions at ~ = 0°, 180°. The relative velocities around the upper one half cylinder on the cylinder surface are shown in Figure 11.

The actual flow pattern around any real screen will be intermediate between that shown in Figure 9 and that shown in Figure 10. The specific behavior of a given screen will depend primarily on the approach velocity and the screen open area and construction. The velocity through the screen will be of secondary importance.

Fig. 11. Velocities around a Cylinder in Uniform Flow

Fig. 12. Flow around Axis Parallel Screens

The precise interaction of the various parameters is not yet completely understood. Some preliminary information suggests that for approach velocities of 0.45 m/s (1.5 fps) or greater and 20% or less open area, the screen behaves as an obstacle to flow. Minimal boundary layer effects have been observed. Further, for approach velocities of 0.30 m/s (1.0 fps) or less and with 40% open area the screen tends to appear "invisible" to flow. This, combined with concern over large object impact, suggests an alternative screen orientation, with the screen axis parallel to the direction of flow. Figure 12 depicts the expected flow field around a pair of cylindrical screens mounted on a tee with streamlined cones attached and a continuity sheath placed over the tee. For the configuration shown in Figure 12, the velocity tangential to the screen surface is approximately equal to the approach velocity VO and there are no stagnation areas on the screen surface. For an extended discussion of these velocity effects, see Richards and Hroncich (1976).

APPLICATION OF HYDRAULIC INFORMATION
TO EXCLUSION OF BIOTA AND DEBRIS

There are two ways to protect larval forms using a totally submerged screening system. The first technique is to identify by field studies an area which is relatively free of these organisms and then locate the screening system there. Larger fish can then be protected by sizing the openings so that larger species will not be entrained and then designing the screen to have a uniform slot velocity of 0.12 m/s (0.4 fps). The second technique is to eliminate entrainment of eggs and larvae by making the screen openings smaller than the minimum body dimension of the larval form. In egg and larval protection by exclusion, screen orientation again becomes a factor. Work done by Hanson and Bason (1978) has shown that striped bass eggs tend to roll up and over screens placed perpendicular to the approach flow with minimal contact time with the screen. Field tests on the behavior of screens mounted with their axes parallel to flow have not yet been conducted. Two important hydraulic variables should be considered in the selection of screen orientation for larval protection.

1. With the flow-perpendicular orientation, contact time is minimal but the probability of contact is relatively large.

2. With the flow-parallel orientation, contact time is greater than with flowperpendicular orientation, but the probability of contact is lower.

Another observation made in the studies by Hanson and Bason is the capability of larval striped bass to display avoidance behavior. The ability of the larvae to make at least one burst in an effort to escape the screen is of great significance when one recognizes that the velocity approaching the screen as a result of pumping drops off at a rate corresponding to R ². Thus, the probability of escape is large as the larvae burst away from the screen.

As environmental concern is expressed for even smaller organisms, the screen opening size is increasingly more dependent on organism size than any other process variable. One must, however, still be concerned with how screen performance will be affected by debris, and what should be done with it. Field experience has shown that proper screen design and selection of a through-screen velocity below 0.15 m/s (0.5 fgs) precludes virtually all debris problems. This is supported by the work of Money and Tuthill (1978) who found a strong tendency for debris bypass at through-screen velocities below 0.15 m/s (0.5 fps).

In situations where a positive screen cleaning system is desired, several different backwash techniques have been developed. Among them are reverse water pumping, reverse water flows caused by air injection into the withdrawal line, and air injection into the screen section itself. The comparative efficiencies of these alternatives are not known and will be investigated in the future.

CONCLUSIONS

By proper consideration of the design variables, it is possible to obtain nearly uniform through-screen velocities. The average through-slot velocity is important in any screen system only when it is representative of the actual screen velocities. A low average velocity resulting from the addition of unproductive area is an artificial solution to the problem of sound design.

Establishing a uniform, low through-screen velocity has many advantages:

1. More efficient use of the screen and lower head loss is an immediate result.
2. The probability of entrapment of mobile aquatic organisms is substantially reduced.
3. The need for cleaning is minimized because the forces associated with debris attraction decrease with the square of the actual (not average) velocity. At low through-screen velocities (0.15 m/s [0.5 fps] or less) debris tends to go past the screen rather than cause plugging.
4. The ratio of ambient current velocity to withdrawn velocity is maximized, allowing ambient currents to more efficiently clean the screen surface.

Totally submerged power plant cooling water intakes can be designed. Appropriate consideration of the behavior of the screen itself is necessary if the design is to be efficient. If this consideration is included in the design, the result is an intake screening system which requires less maintenance, is environmentally superior, and costs less than current traveling water screen systems.

REFERENCES

Hanson, B. N., W. H. Bason, B. E. Beitz, and K. E. Charles. 1978. A practical raw water intake screen that substantially reduces the entrainment and impingement of early life stages of fish, pp. 393-407. In L. D. Jensen (Ed.), Fourth National Workshop on Entrainment and Impingement, EA Communications, Melville, N. Y.

Money and Tuthill. 1978. Personal correspondence.

Richards, R. T., and M. H. Hroncich. 1976. Perforated-pipe water intake for fish protection. J. Hydraul. Div. Proc. Am. Soc. Civ. Eng. 102:139-149.