proptools.nonsimple_comp_flow module

Non-simple compressible flow.

Calculate quasi-1D compressible flow properties with varying area, friction, and heat addition. “One-dimensional compressible flows of calorically perfect gases in which only a single driving potential is present are called simple flows” [1]. This module implements a numerical solution for non-simple flows, i.e. flows with multiple driving potentials.

References

[1] L. Pekker, “One-Dimensional Compressible Flow in Variable Area Duct with Heat Addition,”
Air Force Research Laboratory, Edwards, CA, Rep. AFRL-RZ-ED-JA-2010-303, 2010. Online: http://www.dtic.mil/dtic/tr/fulltext/u2/a524450.pdf.
[2] A. Bandyopadhyay and A. Majumdar, “Modeling of Compressible Flow with Friction and Heat
Transfer using the Generalized Fluid System Simulation Program (GFSSP),” Thermal Fluid Analysis Workshop, Cleveland, OH, 2007. Online: https://tfaws.nasa.gov/TFAWS07/Proceedings/TFAWS07-1016.pdf
[3] J. D. Anderson, Modern Compressible Flow with Historical Perspective, 2nd ed.
New York, NY: McGraw-Hill, 1990.

Matt Vernacchia proptools 2016 Oct 3

proptools.nonsimple_comp_flow.differential(x, state, mdot, c_p, gamma, f_f, f_q, f_A)

Differential equation for Mach number in non-simple duct flow.

Note: This method will not be accurate (and may divide by zero) for flows which contain a region at Mach 1, e.g. a choked convergent-divergent nozzle.

Parameters:
  • state (2-vector) – Stagnation temperature [units: kelvin], Mach number [units: none].
  • x (scalar) – Distance from the duct inlet [units: meter].
  • mdot (scalar) – The mass flow through the duct [units: kilogram second**-1].
  • c_p (scalar) – Fluid heat capacity at constant pressure [units: joule kilogram**-1 kelvin**-1].
  • gamma (scalar) – Fluid ratio of specific heats [units: none].
  • f_f (function mapping scalar->scalar) – The Fanning friction factor as a function of distance from the inlet [units: none].
  • f_q (function mapping scalar->scalar) – The heat transfer into the fluid per unit wall area as a function of distance from the inlet [units: joule meter**-2].
  • f_A (function mapping scalar->scalar) – The duct area as a function of distance from the inlet [units: meter**2].
Returns:

d state / dx
proptools.nonsimple_comp_flow.main()
proptools.nonsimple_comp_flow.solve_nonsimple(x, M_in, T_o_in, mdot, c_p, gamma, f_f, f_q, f_A)

Solve a non-simple flow case

Parameters:
  • state (2-vector) – Stagnation temperature [units: kelvin], Mach number [units: none].
  • x (array) – Distances from the duct inlet at which to return solution [units: meter].
  • T_o_in (scalar) – Inlet stagnation temperature [units: kelvin].
  • M_in (scalar) – Inlet Mach number [units: none].
  • mdot (scalar) – The mass flow through the duct [units: kilogram second**-1].
  • c_p (scalar) – Fluid heat capacity at constant pressure [units: joule kilogram**-1 kelvin**-1].
  • gamma (scalar) – Fluid ratio of specific heats [units: none].
  • f_f (function mapping scalar->scalar) – The Fanning friction factor as a function of distance from the inlet [units: none].
  • f_q (function mapping scalar->scalar) – The heat transfer into the fluid per unit wall area as a function of distance from the inlet [units: joule meter**-2].
  • f_A (function mapping scalar->scalar) – The duct area as a function of distance from the inlet [units: meter**2].
Returns:

The stagnation temperature at each station in x [units: none]. M (array of length len(x)): The Mach number at each station in x [units: none]. choked (boolean): True if the flow chokes at M=1 in the duct. M and T_o for x past the

choke point will be nan. Choking can cause shocks or upstream effects which this model does not capture; therefore results for choked scenarios may not be accurate.
Return type:

T_o (array of length len(x))