On the compressible Hart-McClure mean flow motion in simulated rocket motors

Brian Allen Maicke, Tony Saad, Joseph Majdalani

Research output: Contribution to conferencePaper

3 Citations (Scopus)

Abstract

We consider the compressible flow analogue of the solution known colloquially as the Hart-McClure profile. This potential motion is used to describe the mean flow in the original energy-based combustion instability framework. In this study, we employ the axisymmetric compressible form of the potential equation for steady, inviscid, irrotational flow assuming uniform injection of a calorically perfect gas in a porous, right-cylindrical chamber. This equation is expanded to order M w 4 using a Rayleigh-Janzen sequence in powers of M w 2, where M w is the wall Mach number. At leading order, we readily recover the original Hart-McClure profile and, at M w 2, a closed-form representation of the compressible correction. By way of confirmation, the same solution is re-constructed using a novel application of the vorticity-stream function technique. In view of the favorable convergence properties of the Rayleigh-Janzen expansion, the resulting approximation can be relied upon from the headwall down to the sonic point and slightly beyond in a long porous tube or nozzleless chamber. Based on the simple closed-form expressions that prescribe this motion, the principal flow attributes are quantified parametrically and compared to existing incompressible and one-dimensional theories. In this effort, the local Mach number and pressure are calculated and shown to provide an improved formulation when gauged against one-dimensional theory. Our results are also compared to the two-dimensional axisymmetric solution obtained by Majdalani (Majdalani, J., "On Steady Rotational High Speed Flows: The Compressible Taylor-Culick Profile," Proceedings of the Royal Society of London, Series A, Vol. 463, No. 2077, 2007, pp. 131-162). After rescaling the axial coordinate by the critical length Ls, a parametrically-free form is obtained that is essentially independent of the Mach number. This behavior is verified analytically, thus confirming Majdalani's universal similarity with respect to the critical distance. A secondary verification by computational fluid dynamics is also undertaken. When compared to existing rotational models, the compressible Hart-McClure plug-flow requires, as it should, a slightly longer distance to reach the speed of sound at the centerline. At that point, however, the entire cross-section is fully choked.

Original languageEnglish (US)
StatePublished - Dec 1 2010
Event46th AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit - Nashville, TN, United States
Duration: Jul 25 2010Jul 28 2010

Other

Other46th AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit
CountryUnited States
CityNashville, TN
Period7/25/107/28/10

Fingerprint

Rocket engines
Mach number
Compressible flow
Acoustic wave velocity
Vorticity
Computational fluid dynamics
Gases

All Science Journal Classification (ASJC) codes

  • Aerospace Engineering
  • Control and Systems Engineering

Cite this

Maicke, B. A., Saad, T., & Majdalani, J. (2010). On the compressible Hart-McClure mean flow motion in simulated rocket motors. Paper presented at 46th AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit, Nashville, TN, United States.
Maicke, Brian Allen ; Saad, Tony ; Majdalani, Joseph. / On the compressible Hart-McClure mean flow motion in simulated rocket motors. Paper presented at 46th AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit, Nashville, TN, United States.
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Maicke, BA, Saad, T & Majdalani, J 2010, 'On the compressible Hart-McClure mean flow motion in simulated rocket motors' Paper presented at 46th AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit, Nashville, TN, United States, 7/25/10 - 7/28/10, .

On the compressible Hart-McClure mean flow motion in simulated rocket motors. / Maicke, Brian Allen; Saad, Tony; Majdalani, Joseph.

2010. Paper presented at 46th AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit, Nashville, TN, United States.

Research output: Contribution to conferencePaper

TY - CONF

T1 - On the compressible Hart-McClure mean flow motion in simulated rocket motors

AU - Maicke, Brian Allen

AU - Saad, Tony

AU - Majdalani, Joseph

PY - 2010/12/1

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N2 - We consider the compressible flow analogue of the solution known colloquially as the Hart-McClure profile. This potential motion is used to describe the mean flow in the original energy-based combustion instability framework. In this study, we employ the axisymmetric compressible form of the potential equation for steady, inviscid, irrotational flow assuming uniform injection of a calorically perfect gas in a porous, right-cylindrical chamber. This equation is expanded to order M w 4 using a Rayleigh-Janzen sequence in powers of M w 2, where M w is the wall Mach number. At leading order, we readily recover the original Hart-McClure profile and, at M w 2, a closed-form representation of the compressible correction. By way of confirmation, the same solution is re-constructed using a novel application of the vorticity-stream function technique. In view of the favorable convergence properties of the Rayleigh-Janzen expansion, the resulting approximation can be relied upon from the headwall down to the sonic point and slightly beyond in a long porous tube or nozzleless chamber. Based on the simple closed-form expressions that prescribe this motion, the principal flow attributes are quantified parametrically and compared to existing incompressible and one-dimensional theories. In this effort, the local Mach number and pressure are calculated and shown to provide an improved formulation when gauged against one-dimensional theory. Our results are also compared to the two-dimensional axisymmetric solution obtained by Majdalani (Majdalani, J., "On Steady Rotational High Speed Flows: The Compressible Taylor-Culick Profile," Proceedings of the Royal Society of London, Series A, Vol. 463, No. 2077, 2007, pp. 131-162). After rescaling the axial coordinate by the critical length Ls, a parametrically-free form is obtained that is essentially independent of the Mach number. This behavior is verified analytically, thus confirming Majdalani's universal similarity with respect to the critical distance. A secondary verification by computational fluid dynamics is also undertaken. When compared to existing rotational models, the compressible Hart-McClure plug-flow requires, as it should, a slightly longer distance to reach the speed of sound at the centerline. At that point, however, the entire cross-section is fully choked.

AB - We consider the compressible flow analogue of the solution known colloquially as the Hart-McClure profile. This potential motion is used to describe the mean flow in the original energy-based combustion instability framework. In this study, we employ the axisymmetric compressible form of the potential equation for steady, inviscid, irrotational flow assuming uniform injection of a calorically perfect gas in a porous, right-cylindrical chamber. This equation is expanded to order M w 4 using a Rayleigh-Janzen sequence in powers of M w 2, where M w is the wall Mach number. At leading order, we readily recover the original Hart-McClure profile and, at M w 2, a closed-form representation of the compressible correction. By way of confirmation, the same solution is re-constructed using a novel application of the vorticity-stream function technique. In view of the favorable convergence properties of the Rayleigh-Janzen expansion, the resulting approximation can be relied upon from the headwall down to the sonic point and slightly beyond in a long porous tube or nozzleless chamber. Based on the simple closed-form expressions that prescribe this motion, the principal flow attributes are quantified parametrically and compared to existing incompressible and one-dimensional theories. In this effort, the local Mach number and pressure are calculated and shown to provide an improved formulation when gauged against one-dimensional theory. Our results are also compared to the two-dimensional axisymmetric solution obtained by Majdalani (Majdalani, J., "On Steady Rotational High Speed Flows: The Compressible Taylor-Culick Profile," Proceedings of the Royal Society of London, Series A, Vol. 463, No. 2077, 2007, pp. 131-162). After rescaling the axial coordinate by the critical length Ls, a parametrically-free form is obtained that is essentially independent of the Mach number. This behavior is verified analytically, thus confirming Majdalani's universal similarity with respect to the critical distance. A secondary verification by computational fluid dynamics is also undertaken. When compared to existing rotational models, the compressible Hart-McClure plug-flow requires, as it should, a slightly longer distance to reach the speed of sound at the centerline. At that point, however, the entire cross-section is fully choked.

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Maicke BA, Saad T, Majdalani J. On the compressible Hart-McClure mean flow motion in simulated rocket motors. 2010. Paper presented at 46th AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit, Nashville, TN, United States.