Accurately measuring fluid flow in systems of moving gas or air has always been a difficult task to achieve.
The most common approach to measuring fluid flow entails first determining the differential pressure within a system, often referred to as differential velocity pressure since the pressure differential referred to is the difference between the static and total pressure within the moving fluid system. After determining differential velocity pressure of the moving fluid system, it follows that the velocity and flow volume can be determined mathematically.
As a practical matter though, the real problem in measuring fluid flow in a duct is that the velocity profile across the duct or conduit is almost always nonuniform and not predictable. This is especially true about the sides and corners of ducts or conduits.
To accurately measure flow, one method known entails traversing the cross sectional area of the duct with a differential pressure pitot device and to take multiple readings at numerous positions across the duct. These multiple readings are then appropriately averaged and the velocity of the fluid flow can be determined therefrom. This approach, however, is more of a laboratory method of determining fluid flow, and does not lend itself to an in-line commercial or industrial instrument.
There are commercially available primary devices that are known today for measuring air flow. For example, see the disclosures found in U.S. Pat. Nos. 3,981,193; 4,036,054; and 3,785,206. These primary devices include an array of static and total pressure pitots arranged in a duct so as to yield an average flow across the cross sectional area of the duct. For the most part, such primary devices are not very accurate. Although they use an averaging approach, the velocity profile about the sides and corners of the duct is nonuniform and consequently substantial error is likely to be introduced, resulting in inaccurate flow measurement.
The present invention entails a nozzle pitot averaging primary that is designed to give a more accurate and precise fluid flow measurement than commercial and industrial air flow primary devices known today. More particularly, the nozzle pitot averaging primary of the present invention tends to overcome problems of known primary devices by producing a more predictable velocity profile, especially about the outer side and corner regions of the moving fluid system. In fact, the nozzle pitot averaging primary of the present invention tends to yield a predictable velocity profile across substantially the entire cross sectional area of the nozzle portion of the primary. This enables an array of static and total pressure pitots to be arranged in such a way as to more accurately and precisely average the velocity of the fluid flow within the system.
In addition, in the development of the nozzle pitot averaging primary device of the present invention, certain physical relationship between the nozzle, the array of pitots and the size of the main duct or conduit were discovered that are deemed important design considerations. For example, in a cylindrical type design, the ratio of the diameter of the pitot array to the inside or throat diameter of the nozzle seems to be important in averaging and measuring velocity in the fluid stream. Moreover, the ratio of the inside or throat diameter of the nozzle to the diameter of the main duct seems also to be important. These factors and how they are utilized in a particular design is explored in more detail subsequently herein.
It is, therefore, an object of the present invention to provide a more accurate averaging pitot primary device that has the capability to accurately measure fluid flow within a moving fluid system.
A further object of the present invention resides in the provision of an averaging pitot primary that positively acts on the moving fluid so as to produce a more predictable velocity profile, which results in the ability to more accurately and precisely measure fluid flow within the system of moving fluid.
It is a further object of the present invention to provide an averaging pitot primary of the character referred to above that includes means for constricting the flow of fluid therethrough in such a manner as to produce a predictable velocity profile of the fluid passing therethrough, and an array of averaging static and total pressure pitot disposed about the constricted area so as to measure differential velocity pressure in this region.
Another object of the present invention resides in the provision of an averaging pitot primary of the character referred to above that utilizes a nozzle type flow constricting means to produce a generally predictable velocity profile.
Still a further object of the present invention is to provide an averaging nozzle pitot primary that provides a relatively sharp wall boundary for aiding in the shaping of a predictable velocity profile and which overcomes the problems of known primary device of the prior art where the velocity profile about the sides and corners are very erratic and unpredictable.
Another object of the present invention is to provide a nozzle pitot primary of the character referred to above that establishes certain design criteria for the relationship between the nozzle and pitot array, and between the nozzle and the main duct carrying the fluid to be measured.
Another object of the present invention resides in the provision of an averaging pitot primary device of the nozzle or constricting type, wherein the array of pitots is strategically placed with respect to the nozzle such that the primary device is relatively insensitive to Reynolds Number.
Other objects and advantages of the present invention will become apparent from a study of the following description and the accompanying drawings which are merely illustrative of the present invention.
FIG. 1 is a side elevational view of the nozzle averaging primary of the present invention.
FIG. 2 is a cross sectional view of the nozzle primary taken through the lines 2--2 in FIG. 1.
FIG. 3 is a diagrammatic cross sectional view of the nozzle pitot illustrating the Gamma and Beta ratios discussed in the present disclosure.
FIG. 4 is a graph based on laboratory data used for determining C1, as discussed in the present disclosure, for a Beta ratio of 0.707.
With further reference to the drawings, the nozzle averaging pitot primary of the present invention is shown therein in the form of a spool assembly, indicated generally by the numeral 12, and operatively interconnected within a main duct or conduit 10 carrying or channeling the fluid flow to be measured.
Spool assembly 12 includes two cylindrical sections 14 and 16, with each section including two flanged end portions 18. Disposed upstream and within spool section 14 is a flow straightening device 20 that is preferably of a honeycomb cross sectional area and which can be typically constructed of aluminum or stainless steel. This flow straightening device acts to straighten the flow prior to the flow reaching the nozzle pitot primary to be discussed subsequently herein.
Interposed within the spool assembly 12 and particularly connected between cylindrical sections 14 and 16, there is provided flow constricted means in the form of a nozzle. The nozzle includes a flange portion 22 that extends between the flange end portions 18 of the two respective cylindrical sections 14 and 16, and is held therebetween by a series of bolts 21 that extend through the nozzle flange 22 and on through openings provided within the respective flanged end portions 18. It should be noted that a gasket is preferably imposed between each side of the nozzle flange 22 and the respective flanged ends of sections 14 and 16.
As seen in the drawings, the nozzle includes a main wall section 24 that extends from an inlet end 26 of the nozzle to an outlet end 28. Because of the nature of the nozzle, it is appreciated that the diameter of the same becomes progressively smaller from the inlet end 26 thereof to the outlet end 28, with the inside diameter of the nozzle being referred to as the throat diameter and in the present design the diameter of the outlet end 28.
Associated with the nozzle is an array of averaging pitots shown in an assembly form and indicated generally by the numeral 30. This averaging pitot assembly 30 includes a series of alternately spaced static and total pressure pitots 32 and 34 respectively. It is seen that pitots 32 and 34 are arranged in a circular fashion generally co-axial with the axis of the nozzle and arranged in a pattern whose diameter of the array is smaller than the inside or throat diameter of the nozzle.
In conventional fashion, the averaging pitot array assembly 30 includes a series of static pitots 32 that are aligned such that their longitudinal axis extends generally parallel with the axis of the nozzle and cylindrical sections 14 and 16. Likewise, the total pressure pitots 34 are also disposed so as to extend in general parallel relationship with the axis of the nozzle and cylindrical sections 14 and 16. It is appreciated that the static pitots 32 include an opening about the side of the forwardmost tip, with the openings being oriented in a plane generally parallel to the direction of flow of fluid within the main duct 10 and through the spool assembly 12. Also in conventional fashion, the total pressure pitots 34 include tip openings that face or extend transverse to the general direction of fluid flow.
Extending from the averaging pitot assembly 30 is a high pressure outlet tube 38 that is communicatively connected with the total pressure pitots 34 and which is adapted to direct a total pressure signal therefrom. A low pressure tube 36 is communicatively connected with the static pitots 32 and is adapted to direct a low or static pressure signal from the array of averaging static pitots.
As appreciated in the art, by connecting the high and low pressure tubes 38 and 36 of the averaging pitot assembly 30 with a differential pressure transmitter, such as the Brandt Model 21DPT2000, a differential pressure signal can be derived by effectively subtracting the static pressure from the total pressure. In effect this gives what is often referred to as a differential velocity pressure which is related to the square of the velocity. This, of course, enables the velocity or flow within main conduit 10 to be determined mathematically.
In order to minimize head loss and to generally improve the profile, a bullet shaped protrusion 40 is provided about the center of the pitot array and faces upstream as seen in FIG. 2.
It is appreciated that the nozzle would include a central axis that would extend axially through the nozzle parallel to the direction of flow of fluid through the nozzle and through the bullet shaped protrusion 40 associated with the pitot array as shown in FIG. 2.
Through a series of tests, it was discovered that a number of physical relationships within the nozzle pitot averaging primary is significant.
First, in a cylindrical or circular design, for example, the ratio of the diameter of the pitot array to the throat or inside diameter of the nozzle was found to be important. This is referred to as the Gamma ratio (see FIG. 3) and is considered significant even in cases where the nozzle and/or main duct are not circular or cylindrical.
In the design of the nozzle pitot averaging primary of the present invention, it was deemed desirable that the same be relatively insensitive to Reynolds Number. Through a series of tests for a six-inch nozzle pitot averaging primary for example, an appropriate Gamma ratio was found to be 0.633. At this particular Gamma ratio, Reynolds Number had relatively little effect on the performance of the nozzle pitot averaging primary for Reynolds Numbers exceeding 100,000. Thus based on this test and other such tests it was found that the Gamma ratio for the nozzle pitot averaging primary of the present invention should be approximately 0.633.
In addition it was found that the ratio of the throat or inside diameter of the nozzle to the diameter of the main duct carrying the fluid was another significant relationship. This is defined as the Beta ratio. Based on a series of tests, it was discovered and found that an appropriate Beta ratio for designs of the type disclosed herein was 0.707.
Finally due to the nature of the nozzle pitot averaging primary of the present invention, a correction coefficient C must be determined and provided in order that the effective area, AE, can be calculated in order to accurately determine flow.
In tests conducted by Applicant, it was determined that this correction coefficient would depend and relate to three factors. First, the correction coefficient would depend upon C1, the velocity profile passing through the nozzle and the Beta ratio. Next the area reduction in the plane of the pitot tubes will be a second factor, C2, that will contribute to the overall correction coefficient. Lastly a Gamma ratio correction, C3, will be determined since the position of the array of pitots with respect to the nozzle can influence flow measurement.
Consequently the final correction coefficient C can be said to be a product of all three of these factors; i.e., C=C1 ×C2 ×C3. Through laboratory tests, these individual correction factors can be determined and from them the final overall correction coefficient C can be determined.
The following is an example for determining the correction coefficient C for a nozzle having a throat diameter of 22 inches, a Gamma ratio of 0.640, a Beta ratio of 0.707 and eight 1/8 inch pitot probes. As pointed out above, the total or final correction coefficient C will be the product of C1 (correction due to Beta ratio and profile shape), C2 (due to the area reduction of the pitot probes) and C3 (correction relating to the Gamma ratio factor).
First, with respect to C1, one is referred to FIG. 4. C1 is a constant due to profile and is plotted against Reynolds Number. This determination can be accomplished through laboratory tests and as seen from the graph, for a Beta ratio of 0.707, C1 is determined to be 1.0479. C2 =(A-Ap)÷A
A=area of nozzle
Ap =area of pitots A (nozzle)=222 ×π÷576=2.6398 ft.2 Ap =(1.1252 ×π)÷576×8=0.00068 ft.2 C2 =2.6398-0.00068÷2.6398=0.99974
An equation was derived for C3 and this is as follows: C3 =(0.25) (0.640)+0.841675=1.0017
C3 is correct only for a Beta ratio of 0.707 and for high Reynolds Numbers. The worst error that the Gamma ratio contributes is where the Reynolds Number is low and for this reason the Gamma ratio should be held as close to 0.633 as possible. Thus C can be calculated as follows: C=C1 ×C2 ×C3 C=1.0479×0.99974×1.0017=1.0404
Now the effective area (AE) for the nozzle can be calculated as follows: AE =AC=2.6398×1.0404=2.77 ft.2
From the foregoing, it is appreciated that the nozzle pitot averaging primary of the present invention is designed to enable one to accurately and precisely measure fluid flow in a moving air or gas system. In contrast to flow primaries of the prior art, the present nozzle pitot primary positively acts on the moving fluid system in such a manner as to actually aid in shaping the velocity profile such that the same is relatively uniform and predictable. This enables the pitot array to be strategically placed with respect to the nozzle and the resulting velocity profile so as to give a more precise flow measurement. In addition, the increased velocity through the nozzle inherently enhances accuracy. As pointed out above, various conventional mathematical approaches can be utilized to correct for flow and span discrepancies introduced by the nozzle type design.
The present invention, of course, may be carried out in other specific ways than those herein set forth without departing from the spirit and essential characteristics of the invention. The present embodiments are, therefore, to be considered in all respects as illustrative and not restrictive, and all changes coming within the meaning and equivalency range of the appended claims are intended to be embraced therein.