DAMPER AIR FLOW LINEARIZING TUTORIAL

Transcription

1 DAMPER LINEARIZING TUTORIAL Actuator Response % Air Flow Goal is a linear change in air flow quantity per volt of signal change. Damper and Characterized Actuator Degrees Open Damper Response 90 (open) Resulting Flow with respect to control signal 1

2 Contents Introduction...3 Problem Applications...4 System Self-Correction...5 Control Loop Tuning...6 Authority Concept...6 Summary of Damper Characterization Methods...10 AMCA Figure Numbers Geometric Set-ups...10 The Danger in Over-Generalizing from Ducted to Other Geometries...12 Linearizing Actuator and Damper Combination...13 Review...14 Appendix 1 Testing Results from ASHRAE RP AMCA 5.1 Entrances...17 Louvered Entrances...18 AMCA Type 5.2 Exits...19 Louvered Exits...20 AMCA 5.3 Ducted Type Applications...20 AMCA 5.3 Ducted Type Applications...21 AMCA 5.4 Plenum Entrances...23 AMCA 5.5 Plenum Exits...24 Appendix 2 Estimating Authority...25 Appendix 3 Estimating full open damper losses

3 Damper Air Flow Response Introduction Figure 1 Problems and Design Goal Total quantity of air flow through a system. Problems TOTAL A ) Q TOTAL RA EA or OA B) Q EA or OA RA ROTATION ROTATION Design Goal C ) Q TOTAL At any given fan speed modulation of economizer dampers should allow flow quantity to remain near constant. ROTATION In modulating dampers for air flow control a number of non-linearities are possible and must be defeated to gain accuracy. The applications here concentrate on the economizer section of air handlers, but the ideas can be applied to less complex arrangements of dampers also. The goal is to present the concept of a programmable actuator and damper combination dependent on the geometry of the situation. Figure 1 shows the problems that sometimes exist and the design goal. The exact shape of any damper curve depends on these main factors: 1. Action opposed blade (OB) or parallel blade (PB). 2. Geometry Entry, ducted, plenum, etc. 3. Authority the amount of pressure loss within the damper itself compared to the subsystem in which it is installed. 3

4 4. Presence of jackshafts and/or linkages which may or may not change the rotation of the blades with respect to the actuator rotation. The full open flow is not affected by linkages or jackshafts, nor by PB or OB use. 5. The entering flow profile e.g., if near an elbow, most of the air can be moving thru the top area of the damper and flowing backwards in the bottom. 6. Free area ratio of the damper with respect to the duct or wall. This is an orifice effect where A1/A2 can have a significant effect. For small areas inside the damper, the application is similar to that of a wall. Problem Applications Figure 2 Parallel Blade Overflow EA RP RA Total Flow EAD OAD RAD Q OA & EA OA MA SA RA Damper Position In Figures 2 and 3 the common problem applications are depicted. The dampers could be matched to the system by selecting PB or OB and by adjusting the authority. In Figure 2, all PB dampers cause an increase in air flow at modulating conditions, particularly at near rotation of the dampers. A balancing damper, more duct restriction, or an orificed damper in the RA is needed to keep flows near constant during modulation. This can cause hunting of control systems, interaction with other control loops, and degradation of control and lifespan of components. In Figure 3 a different geometry is shown. All OB dampers lead to a decrease in flow at rotation. Fans may ride up their curves to a degree sufficient to cause very high pressure and other problems. A choice of PB or OB needs to be made based on geometry. While an OB damper in the RA path causes underflow, a PB causes overflow. Engineering is necessary to control the system. Controls should fine tune a mechanically balanced system. They are not suited to establishing balance itself. The worst condition on problem projects occurs when OB dampers with certain linkage or jackshaft arrangements are used. Some geometric set-ups lower the response curves too far under the linear. This starves flow at the positions. 4

5 Figure 3 OB Damper Underflow OA MA RP EA OAD RAD EAD SA RA Q Total Flow Total flow with OB dampers will be under the linear when half open in the geometric configuration above. RA OA ROTATION The solution is not so simple as simply using OB or PB in the appropriate geometry although that is a big help. The authority is also important. One cannot generalize to all cases from the drawings above. System Self-Correction The amount of pressure drop in the economizer portion is usually much lower than the rest of the system and the fan will not move far off the design operating point. This self-corrects. In other cases when the dampers or economizer system is a significant amount of the total pressure drop or more - failure to select dampers and analyze the system can lead to the problems shown in these figures. When the economizer section at damper positions is still a low (<) proportion of the fan total loss, then the effects of poorly characterized dampers are mitigated. But some severe problems can and have occurred. Trusting in system selfcorrection without analysis is wishful thinking 5

6 Control Loop Tuning Figure 4 Control Loop Tuning Q dq/ds =.25 dq/ds =2 ROTATION When dampers are not linear the control loops require a difficult if not impossible tuning process. The amount of air flow change per volt of signal change varies with non linear dampers. See Figure 4. Hunting, erratic control, energy waste, equipment wear, and comfort problems can occur. Authority Concept Within a certain range of parameters, the authority concept as defined in ASHRAE 1 can be applied to linearize the relationship between a control signal (2-10V or 4-20mA) and the velocity through a damper. Figure 5 Authority A subsystem is defined as the duct elements between two constant pressure points. ΔP across subsystem must remain constant Damper AIR FLOW C s stands for the total sum of C s of the duct elements. Authority = damper loss / subsystem loss. Authority = damper C / sum of C in subsystem. Authority = damper full open?p / damper closed?p C s ASHRAE Handbook - Fundamentals, Chapter 15, p Note the incorrect overgeneralization from the ducted to all applications. 6

7 The basic authority concept is shown in Figure 5. In Figure 5, C s symbolizes the sum of all the series loss. The authority is ΔP damper / ΔP sub-system. This is C damper / C damper + C s if the ducts are all the same area. Figure 5 is the geometric set-up used for the charts in Figures 6 and 7. Figure 6 Installed Characteristics of PB dampers in AMCA 5.3 Geometry Figure 7 Installed Characteristics of OB dampers in AMCA 5.3 Geometry Figure 6 shows typical PB response curves in the AMCA type set-up. Figure 7 shows typical OB response curves in the AMCA 5.3 type set-up. The AMCA 5.3 set-ups use long duct runs to get good flow profiles with unrealistically low pressure 2 See for information. AMCA is the Air Movement and Control Association. 7

8 drops as a result. For laboratory repeatability, good flow profiles are necessary. The authority curves do not take bad duct flow profiles into account. Examination of Figures 6 and 7 shows that a typical PB damper is linear at about 25% to 35% authority and a typical OB damper is roughly linear between and 15% authority. These charts are based on tests on old style dampers used in the 1950 s and are not highly accurate. In addition, they are ducted only and one cannot generalize to other geometries. This is a geometric application dependent issue. We cannot generalize from the ducted application to say, a plenum wall application. Figure 6 Installed Characteristics of PB damper in AMCA 5.3 Geometry Interaction of airflows is another complication as dampers are placed closer together, the interactions affect the flows for the most part, untested. The curves in Figures 6 and 7 are not as regular as shown and once thought, but they show the tendency in the damper responses in the geometry tested. If the damper is the only pressure loss in a subsystem between two constant pressure points, then it has an authority of. If it has.25 in. w.c. in a system with 1 in. w.c., then it would have 25% authority. Examination of the curves shows that if the authority is, that the PB has a shallow equal percentage curve similar to the ball or butterfly valve. If an OB damper has authority, then it has a deeper equal percentage curve similar to the Belimo characterized control valve or globe valve. Figure 8 Authority Calculation Points - Ducted Air Handling Unit Subsystems Authority = ΔP Damper ΔP Subsystem EA Damper = ΔP s Louver + Damper + Any duct elements Subsystems are indicated by dashed lines between the constant pressure points. The points EA to RP, RP to MA, and MA to OA are the pressure references for linearity of the dampers. Disregarding wind, these are constant pressure points if the system is linearized. EA RP RA The points RP and MA are constant pressure points if the dampers are linear. EAD OAD RAD RA Damper = ΔP s T RP + damper + any duct elements + T MA OA MA SA OA Damper = Δ P s Louver + Damper + duct elements + Flow Monitoring + Compression and Expansion. (Given Minimum OA may be two dampers and associated controls. 8

9 Figure 8 shows an air handling unit and the points for calculating the three dampers authorities. The ASHRAE RP1157 testing makes the damper curves in Figures 6 and 7 obsolete. The general concept of Authority is correct, but the detailed shapes of the curves are quite different in most cases. If all the dampers are near linear, then the points RP and MA become nearly constant pressure points at any given fan speed. Fan speed changes and the consequent changes in velocities do not affect the authority calculations. The values of C of each duct element are nearly constant and a change in velocity pressure is proportional across each.. Each duct element retains its ratio of losses when the total value changes. If a damper is of the subsystem drop at any given velocity, it will be nearly the same at any other. With this in mind, Figure 2 should have OB OA and EA dampers and a PB RA damper to be roughly linear. Search Figures 6 and 7 for the nearest linear curves. Figure 9 Authority Calculation Points - Equipment Room Subsystem Example LOUVERS Indicates constant pressure point for linearization of the OA Damper OAD OAD OAD Indicates constant pressure point for linearization of the RA Damper RAD AH RAD AH RAD AH Since the EA damper interacts with the fan curve, linearization is near impossible to calculate. The RAD s are open to the equipment room space. RA s are open to ceiling return. They are holes in the floor with protective bars. RA RA RELIEF FANS AIR FLOW RA damper is closest to an AMCA 5.4 configuration. OAD RAD OA damper is closest to an AMCA 5.1 configuration. 9

10 Figure 3 shows a more complex system. The full open damper with a 70-8 free area ratio has C open = about 1. The recirculation damper and each of the T s then has C =1. The authority of the damper is 33%. A PB is indicated. The EA and OA can use OB dampers since each approaches authority given the louver drop. We must be careful not to over-generalize here. The recirculation path is often convoluted due to space constraints and as its duct element pressure losses increase, an OB becomes the better choice. Knowledge of the loss coefficients of the dampers and a hydraulic analysis of the duct system must be performed to arrive at the correct sizing and selection. One should also be aware of the variation in loss coefficients in the RP and MA tees. C varies with the percent of flow from 1 to 5 in some configurations. Summary of Damper Characterization Methods There are a number of methods of maintaining constant flow. Refer to the Dampers and Air Flow Control book at (or AF Linearizing Actuator for a free copy. Material in the book details the methods that are merely listed here. The other methods are: 1. MIDPOINT LINEARIZATION 2. VAV FAN ADJUSTMENT 3. COMBINATION PARALLEL AND OPPOSED BLADE DAMPERS 4. AUTHORITY TOTALIZATION 5. MULTI-POINT COMMISSIONING AND SIGNAL CONDITIONING 6. SOFTWARE RANGE CONTROL 7. HARDWARE RANGE CONTROL 8. BLANKOFF LINEARIZATION 9. LINKAGE LINEARIZATION 10. FULLY CHARACTERIZED DAMPERS 11. MULTI STAGE DAMPER CONTROL 12. LINEARIZING ACTUATOR (Covered in this document.) AMCA Figure Numbers Geometric Set-ups The AMCA figures listed in Figure 10 are well recognized. If all other factors were the same, the geometry would cause the same damper to respond differently. For that reason, we must be able to identify the application. 1. AMCA 5.1, entrance, ducted downstream only. 2. AMCA 5.2, exit, ducted upstream only. 3. AMCA 5.3, fully ducted as shown already. 4. AMCA 5.4, wall entrance, ducted downstream only. 5. AMCA 5.5, exit, wall mounted with upstream duct. 6. Wall mounted 10

11 Figure 10 Geometric Applications with AMCA Figure numbers 5.1 Ducted Walled Any individual damper in the AH figures here could be any of the AMCA figures depending on the situation Case 6 Other geometrical effects exist which are still untested. Many applications are part one and part another AMCA Figure. Given that approximate linearization is much more accurate than none, one can average two or pick the closest. See Figure 11. Sometimes, simple logic must be applied. For example, with a face and bypass damper, one must assume that if sized correctly, the up and down stream pressures are nearly constant. If linearizing the damper, use those pressures. Figure 11 Mixed applications RA OA AMCA 5.1 Relief Wall, like a 5.3 but with a rough entering flow profile EAD Relief Chase to Outside RA fan RA AMCA 5.2 OA Half 5.4 & Half wall Half 5.4 & half 5.2 SA Indicates constant pressure point for linearization of the OA Damper Indicates constant pressure point for linearization of the RA and Relief Dampers 11

12 The Danger in Over-Generalizing from Ducted to Other Geometries The Figure 12 graph shows the ASHRAE testing results for two applications with the same OB damper. The curves deviate significantly from each other. The point of Figure 12 is that over-generalization leads to erroneous assumptions. By comparing the different responses of the same dampers in different geometric set-ups, one sees that they respond with different characteristic curves. Figure 12 Various Response Curves in Different Geometric Set-ups DAMPER Louvered Exit OB 6" B LOUVER % Max Flow A E Elbow-Damper OB B A B E F 36W X 48H 36" % Max Flow Figure 13 shows two dampers in a number of different AMCA configurations and the response curves that occur. The available pressure in each case is 1. The ASHRAE testing included louvers which had never before been tested with dampers. Note that for the most part the curves are the same until the damper is 60º to 70º open. The plenum wall has significant orifice effects which affects the flow curves. 3 3 C1 is a function of F = A2/A1 (orifice area / wall area). At.1 free area C1 will typically equal 2/F 2 = 2/.01 = 200 with respect to the duct velocity. C2 would be the coefficient with respect to the velocity pressure inside the damper; C2 = 2 in this case. The velocity pressure inside the orifice is all lost to atmosphere. 12

13 Figure 13 PB Absolute Velocities at 1" Pressure Drop Velocity A5.1 3V A5.1 AF A5.2 3V A5.2 AF A 5.3 3V A5.3 AF A5.3 AE 3V A 5.4 3V A5.4 AF A5.5 3V A5.5 AF AMCA 5.3 in Bold (open) The combined response curves and the absolute velocity are shown here. The AMCA 5.3 test set-up has C =apx..15 for an air foil. V = 4005 Pv ½. Pv = Pt/C. V = 4005 x (1/.15) 1/2 = 10,300 The AMCA 5.5 test set-up has C =apx V = 4005 Pv ½. Pv = Pt/C. V = 4005 x (1/170) 1/2 = 300. Linearizing Actuator and Damper Combination In Figure 14 the damper response is shown as an under the linear curve. The actuator is programmed to compliment the damper so that the actual flow with respect to input signal is linear. The dashed line indicates the desired linear flow. With a standard actuator, the movement would follow this line resulting in a nonlinear response between damper and flow quantity. Standard actuators are linear with respect to the control signal. The LIN actuator rotation is pre-programmed to compliment the damper. For example, a 3V signal with a 0-10V actuator would normally result in 3/10 = 3 rotation. Given 90 degrees of damper-actuator rotation this would be 27 degrees of damper rotation. However this would result in about flow in this geometry. Follow up the 27 degree open to the damper response line and read on the left y-axis % air flow. A programmed Belimo linearizing actuator sees 3V and moves to about 60 degrees open. At 60 degrees actuator rotation the damper is about 60 degrees open also. This results in about 3 flow. 13

14 To see this: Go to the x-axis Open category, go over to 27 degrees (Or just approximate to 30.) Go up to the actuator curve. Go over to the left y-axis to 6. Go back down to the x-axis. Look at 60 degree damper rotation. Read over to the y-axis to % Air Flow. It is about 3. Instead of getting flow for 3V signal, one gets 3. The goal was 3. There is significant improvement. The numbers here are approximate. While damper manufacturers may test the geometry in the lab, there are always variations in the field. However the main point is that the improvement by using linearizing actuators is significant. When some significant variation occurs due to unknowns, the actuators are field programmable to correct as necessary. Review Installed damper response curves are dependent on five main factors: 1. The type of damper opposed blade (OB) or parallel blade (PB). 14

15 2. The geometric application ducted, entrance or exit, plenum, wall mount. 3. Authority 4. Presence of jackshafts and/or linkages which may or may not change the rotation of the blades with respect to the actuator rotation. If each individual damper is linearized, then the pairs are near linear and the total flow is near linear. 5. Flow profile of the entering air 6. Free area ratio of the damper with respect to the duct or wall. The authority concept is dependent on the duct configuration. It is limited to fully ducted applications where the full open damper subsystem loss is less than of the total fan loss. AF24-LIN Belimo programmable linearizing actuator To most accurately preprogram the actuator these must be defined: 1. OB or PB. 2. Application geometry. Define the most similar AMCA Figure or case number. 3. Approximate Authority Statement of subsystem ΔP and damper ΔP for each damper is sufficient. Verbal description is not acceptable since verbal pictures are too fuzzy. A drawing is preferable. Do not apply wishful thinking. 4. Presence of Jackshafting or linkages. Standard selection criteria must still be considered static pressure, velocity at full open, size of duct, temperature limits, vertical or horizontal blades. These determine the damper model and the torque required. 15

16 Figure 15 shows how any of the exact damper geometries may be used within a system. Figure 15 LOUVER Overview AIR FLOW EA OB DUCTED EXIT WITH LOUVER RP RA OB DUCTED EXIT AMCA 5.2 EAD OB after EL disturbance AIR FLOW Any of the other AMCA Figures may apply also. RAD OA OAD Anti PB action DAMPER Close LOUVER LOUVER ENTRY Anti PB AIR FLOW DUCTED ENTRANCE AMCA 5.1 MA SA AIR FLOW ENTRANCE PLENUM AMCA

17 Appendix 1 Testing Results from ASHRAE RP1157 These are damper response curves flow vs. amount open The authority curves are all from the ASHRAE RP1157 research project. The other curves are calculated and were randomly checked for validity. Calculations were based on multiple tests whose results were averaged. Variations of about ± were commonly observed. AMCA 5.1 Entrances 5.1 PB at Varying Authorities AIR FLOW DUCTED ENTRANCE AMCA 5.1 % Maximum Flow % 5% (open) 5.1 OB at Varying Authorities DUCTED ENTRANCE AMCA 5.1 % Maximum Flow % (open) If authority were redefined for the specific application geometry, then a PB is linear enough above 15% and an OB is not linear under any circumstances. 17

18 Louvered Entrances 9 Louvered OB Entry LOUVER OB Damper DUCTED ENTRANCE w/ Louver % Maximum Flow % (open) Anti PB Louvered Entry Anti PB action DAMPER LOUVER Close LOUVER ENTRY Anti PB % Maximum Flow 6 3 5% 2.5% (open) Entry Louver with PB LOUVER PB Damper Close DUCTED ENTRY W/ LOUVER % Maximum Flow 6 3 5% 2.5% (open) 18

19 AMCA Type 5.2 Exits PB DUCTED EXIT AMCA PB Exits at Varying Authorities 9 8 % Maximum Flow % 5% 90 (open) 5.2 OB EXITS at Varying Authorities OB DUCTED EXIT AMCA 5.2 % Maximum Flow (open) 25% 5% A PB is roughly linear at 5% to authority. An OB is roughly linear at to 25% authority. In the louvered application, the damper is about authority initially, since the louver pressure loss is about nine times higher. 19

20 Louvered Exits LOUVER 1 Louver Exit OB at Varying Authorities OB DUCTED EXIT WITH LOUVER % Maximum Flow 8 6 5% 2.5% (open) LOUVER 1 PB Louver Exit at Varying Authorities Open PB DUCTED EXIT W/ LOUVER % Maximum Flow 8 6 5% 2.5% (open) LOUVER Louver Anti PB at Varying Authorities 1 Close Anti PB DUCTED EXIT W/ LOUVER % Maximum Flow 8 6 5% 2.5% (open) No authority is linear. 20

21 AMCA 5.3 Ducted Type Applications Inherent characteristic ( authority) only. Damper A is a 3V, Damper B is flanged, and Damper C is an airfoil. PB 5.3 with Duct Restriction 5.3 Type Damper-Elbow PB % Max Flow A 3V B C AF OB 5.3 with Duct Restriction Type Damper-Elbow OB % Max Flow 6 3 A 3V B C AF This and the next application are the closest to the actual AMCA Figure 5.3 in this set. There is a small amount of series loss. PB is roughly linear at 25% authority. OB is most non linear at 5% authority. 21

22 Damper A is a 3V, Damper B is flanged PB after EL disturbance Elbow-Damper PB A 3V B % Max Flow 6 OB after EL disturbance Elbow-Damper OB A 3V B % Max Flow This is an AMCA 5.3 type application, but with a disturbed entering flow profile. The authority curves are not shown so that the differences in damper type stand out. 22

23 AMCA 5.4 Plenum Entrances PB 3 AF at 3V at A = 3V A = 25% 3V A = 3V A = 5% 3V (open) V A = AF A = 3V A = 3V A = 25% 3V A = 3V A = 5% 6 3 OB (open) An authority of is roughly linear for a PB and the OB will be very roughly linear at authority. 23

24 AMCA 5.5 Plenum Exits EXIT PLENUM AMCA PLENUM WALL 6 A = A = PB 3 A = (open) OB 3 A = A = A = (open) 24

25 Appendix 2 Estimating Authority C = 2 MA C = 1 C = 1 RP C = 1 RP C = 1 A = 1/6 = 16% A = 1/3 = 33% MA C = 3 (avj) If all the ducts are the same size, the loss coefficients can be used as above. More commonly, the actual pressure losses are used as below. dp =.2" dp =.06" RP MA dp =.25" A =.06 / 51 = 12% A = 1/6 = 16% MA RP C = 2 C = 3 C = 1 A = 7% A = 7% C = 1 C = 1 C louver = 10 C louver = 10 dp = in w.g. abbreviated to MA C = 2 A = 1/5 = C = 1 C = 2 RP A = 1/11 = C = 1 7% C louver = 10 Duct sized dampers with standard elbows and louvers. A = Authority = C damper / C subsystem if areas of all ducts are equal. A = Δp damper / ΔP subsystem 25

26 If all dampers are linearized, then the points RP and MA are constant pressure points for any given fan speed. The authorities will always be the same since ALL the duct and element losses are proportional to the velocity pressure. The ratio is constant. The duct loss is rarely significant. If a high amount of the loss in a subsystem, then add to the total. Note that older ASHRAE Handbooks used the term alpha. This is not the same as authority and should not be used. Valves and all damper manufactures now use authority. Appendix 3 Estimating full open damper losses DAMPER LOSS COEFFICIENTS Full open losses are most affected by profiles. Modulated losses are less affected since the damper closes and pressure backs up. Height Width 12" 24" 36" 48" 12" " " " FAR is free area ratio, that is the open area inside the damper / area of the frame. Typical free area ratios are given above. Deduct.1 for insulated blades and industrial dampers. 26

27 The most common damper installation cases: 1. AMCA 5.1, entrance, ducted downstream only. 2. AMCA 5.2, exit, ducted upstream only. 3. AMCA 5.3, fully ducted as shown already. 4. AMCA 5.4, wall entrance, ducted downstream only. 5. AMCA 5.5, exit, wall mounted with upstream duct. 6. Wall mounted 7. Ducted but with realistic short runs of duct before and after the damper. 8. The damper can be placed at right angles to the air flow. This is complex and no data exists. It may be best to add the losses of a right elbow and the damper. Use ΔPt = C x Pv to find the loss of an individual element. Pv = (V/4000) 2 in. w.g. with V in f/s [Pv =.6V 2 in Pa with V in m/s.] AMCA Figures WALLED 5.4 Case DUCTED For multi-section dampers: Use the entire wall as the area, A1. Use the free area of the damper as A2. Then F = A2/A1. The method shown below is not absolutely precise, however it serves as a set of rules of thumb for more accurate estimation than no calculation at all. 27

28 For quick, rough calculation of open damper pressure loss, use these charts: Geometric Application, C To calculate needed F: 1. For full duct mounted applications, C 0 = Fg x [ (1/F 2 ) - 1] F = ( Fg / (C 0 + Fg) ) 2. For duct wall mounted dampers,.2 < F <.5 C 0 = Fg x (1/F 2 ) F = [ Fg / C 0 ] 3. For duct wall mounted dampers, F <.2 C 0 = Fg x (1.5/F 2 ) F = [ 1.5 * Fg / C 0 ] 4. For ducted entrances from large spaces, AMCA 5.1 C 0 = Fg x (1.4/F 2-1 ) F = ( 1.4 Fg / C 0 + Fg) 5. For ducted exits into atmosphere or large spaces, AMCA 5.2 C 0 = Fg x (1.1/F 2 ) F = [ 1.1 * Fg / C 0 ] 6. For plenum exits and entrances, AMCA 5.4 and 5.5 C 0 = Fg x (1.8/F 2 ) F = [ 1.8 * Fg / C 0 ] Fg: a. Bad Flow Profile Less than one duct diameter before damper. Fg = 1.5 b. Poor Flow Profile This is most common factor; use as default. Fg = 1 c. Good Flow Profile 5 diameters before and after the damper. Fg =.6 Note that the modulated positions are not as affected by the geometry as those near full open due to pressure build-up. The method here is complicated enough, and the 80 and 70 positions are not included. By 60 the effects are mostly diminished. 28