1. Choking Pressure Ratio Guidelines for Small Critical Flow Venturis
Title
Choking Pressure Ratio Guidelines
for Small Critical Flow Venturis
and the Effects of Diffuser Geometry By
Michael S. Carter
Bradford W. Sims
Charles L. Britton
Robert J. McKee

2. Introduction
Our work addresses the maximum back pressure ratio for CFVs operating at Reynolds Numbers less than 200,000 and addresses the effects of diffuser geometry on “premature unchoking” behavior.
This applies to small CFVs with inlet pressures of 17 to 150 kPa that are common in the aircraft engine, industrial gas turbine, and automotive industries.
Previous work by Britton et. al. suggests that MPBR increases with increasing Rent and is affected by diffuser geometry that contributes to a behavior that has been called “premature unchoking”.

3. Test Program
55 CFVs, fabricated in accordance with ISO 9300, were tested
33 CFVs with throat diameters of 0.8 mm, 1.6mm, and 3.2 mm were fabricated with a variety of diffuser geometries
22 CFVs with throat diameters ranging from 0.4 mm to 12.7 mm were fabricated with an “optimized geometry” diffuser
Testing was conducted with an automated system

4. Test Results
Results are presented as the % difference from the average choked Cd' value vs. back pressure ratio
A 0.05% change in Cd' was used as the criterion for unchoking.
Decreased Rent results in a lower MBPR and increased DPI severity
This behavior is expected and has been demonstrated in previous studies

5. Test Results
- Increase in MBPR for lower diffuser half angles.

6. Test Findings - Significant trend in diffuser design
A small increase in MBPR is observed with the increased length
The DPI effect is reduced as the diffuser length is increased
This behavior was observed for all CFV throat sizes that displayed DPI
- Suggests increasing the diffuser length to over 10d

7. Background and Explanation
High MBPRs can be achieved with CFVs without effecting Cd‘
Pressure recovery in the diffuser allows MBPR to be higher than the critical pressure ratio of the gas for many geometry and inlet pressure conditions
Previous publications have addressed MBPR for small nozzles and low Rent
Carron and Britton observed an unexpected drop in Cd‘ from pressure ratios of 0.3 to They found that this drop in Cd‘ was less severe at higher inlet pressures and with small diffuser half angles
Nakao and Takamoto tested CFVs with short diffusers and very low Rent . They showed that MBPR was a function of Rent for CFVs with or without DPI
The National Institute of Metrology in China found a correlation between MBPR and Rent but they only tested a single CFV diffuser geometry
Mickan, Kramer, and Li developed a correlation between MBPR, Rent , a form of the Hagen number, and an area ratio dependent pressure term. This correlation does not address the occurrence of DPI.

8. Ideal Diffuser Behavior
This figure represents the ideal behavior of a CFV with an area ratio of
There are several possible paths for flow velocity and pressure within the diffuser.
A likely situation is that a normal shock occurs shortly after the throat and then a further pressure recovery takes place in the remainder of the diffuser. (Pt. B)
- A key question regarding the drop in Cd' at low pressure ratios, in the range of to 0.6 is what occurs in the diffuser when the expansion is nearly full. (Pt. D)

9. The lowest pressure ratio that can be achieved with a subsonic exit velocity is 0.3 with a normal shock at the exit of the diffuser as shown at Point D
To reach an exit pressure ratio of 0.3 the diffuser becomes fully expanded at Point E, where the Mach number is over The exit Mach number at Point D is approximately 0.48 where the lowest apparent MBPR occurs.
- To reach a BPR of 0.45 at Point C, the flow would expand to a Mach number of 2.5, experience a normal shock to a Mach number of 0.51 and pressure ratio at Point C is approximately 0.41 where DPI is can at times be seen.

10. For this CFV where pressure ratio is between 0. 3 and 0
For this CFV where pressure ratio is between 0.3 and 0.45 is where DPI occurs.
The diffuser can sustain expansion to high Mach numbers with an inlet pressure of 300 kPa but as the inlet pressure is reduced the diffuser no longer behaves as expected and its performance in the high Mach number region breaks down.
With low inlet pressures and highly expanded flow prior to a normal shock, the pressure is very low and there is little momentum or energy in the flow stream.
Perhaps a separation, an oblique shock, or some other loss mechanisms takes place and the diffuser is no longer able to recover pressure.
It can be expected that when the diffuser performance breaks down or inverts, less pressure recovery occurs, conditions in the diffuser change and the Cd' is reduced.

11. The highest pressure shown is the upstream CFV throat pressure and shows that flow at the standard CFV is steady and constant throughout this test.
The middle pressure is the inlet pressure at the CFV being tested and shows an increase at precisely the pressure ratios at which the Cd' drops due to DPI.
Mass flow in this test is constant and the same when the BPR is 0.7 or 0.4.
The tested CFV is not “unchoked” at the 0.4 BPR condition but the diffuser is not able to sustain an expansion to high Mach No. with an efficient recovery, thus throat and inlet pressure increase and mass flow is maintained with a lower Cd'.

12. - The 55 CFVs that were tested were categorized in 15 geometrically similar groups without regard to the throat size.
A qualitative rating based on number of DPI events in each group was assigned with 0 if no DPI events occurred and 3 if every CFV in the group experienced DPI events.
Result show almost no correlation between half angle and the DPI rating but a notable correlation between diffuser length and DPI rating shown above.

13. For area ratio, the general trend is that the highest DPI event rating occurred for area ratios between 2 and just over 4, moderate ratings for area ratio above 4 to over 6, and CFVs area ratios near 10 or higher experienced no DPI events.
A correlation does appear between the subjective DPI Rating and CFV diffuser length.
- The current test results suggest if CFVs were constructed with very long diffusers of more than 14 diameters then DPI events in the range of CFV sizes and Rent tested could be avoided.

14. Rent cutoff of 12,000.
Intermediate throat diameter CFVs were constructed and tested to verify the curve fit.
Agreement with ISO 9300 extrapolated down to Rent = 100,000.
Equation can be applied to common gases except helium and hydrogen.
Unchoking tests are still recommended for very small CFVs

15. Conclusions
“Premature unchoking” is a result of a loss of pressure recovery in the diffuser and better described as “Diffuser Performance Inversion,” DPI.
DPI is affected by Rent, by half angle, and is strongly influenced by diffuser length.
For optimized geometry CFVs, MPBR is predictable as a function of Rent to values of 12,000 as given by the equation presented here.
The presented equation conforms to an extrapolation of the ISO 9300 MPBR equation down to Rent of 100,000.
The presented equation predicts the MBPR that should be used for the optimized geometry CFVs down to Rent of 12,000.
DPI is more likely to occur when
A low BPR is required.
A small size CFV and / or a low inlet pressure are used.
Low pressure and high mach number is necessary along the diffuser path.
Diffuser half angle is large or diffuser length is short.

16. Future work
Further investigations towards understanding what takes place in a diffuser when DPI occurs and determining the controlling parameters for DPI
Studying the operation of CFVs on even lower pressure ambient temperature air down to inlet stagnation pressures as low as 17 kPa
Develop MBPR predictions and DPI avoidance parameters for a range of other gases with different isentropic exponents
Study the effects of other geometry CFVs, including longer diffusers and diffusers with backward facing steps.

17. End
Questions ?

18. Effect of Diffuser Removal on Unchoking Performance18