Rotational Flowfields in Porous Channels with Arbitrary Headwall Injection

Abstract

In this paper, Taylor's incompressible and rotational flow in a porous channel with surface mass addition is extended to account for arbitrary headwall injection. Our analysis considers Euler's steady-state equations from which an approximate solution is derived. The resulting mean flow representation satisfies the vanishing axial velocity condition at the blowing walls and is confirmed through comparisons with inviscid finite volume numerical simulations. For a given class of symmetric headwall injection profiles, our solutions are exact at the sidewall and along the midsection plane, where the error in the approximations vanishes identically. The case of uniform injection stands as an exception due to its discontinuity at the sidewall. All solutions become increasingly more accurate in the downstream direction. They hence enable us to approximate the bulk flowfield in both hybrid and solid rockets with variable headwall injection.

Compressible integral representation of rotational and axisymmetric rocket flow

“…Akiki and J. Majdalani the nozzleless chamber length. While the incompressible motion is relatively well understood (Taylor 1956;Culick 1966;Majdalani & Akiki 2010), recent advances have enabled us to account for the presence of arbitrary headwall injection (Majdalani & Saad 2007b;Saad & Majdalani 2009), wall regression (Majdalani, Vyas & Flandro 2002;Zhou & Majdalani 2002), grain taper (Saad, Sams & Majdalani 2006;Sams, Majdalani & Saad 2007), variable cross-section (Kurdyumov 2006), headwall singularity (Chedevergne, Casalis & Féraille 2006), viscous effects (Majdalani & Akiki 2010), and stability (Chedevergne, Casalis & Majdalani 2012). Furthermore, flow approximations exhibiting smoother or steeper profiles than the cold flow equilibrium state have been studied in connection with their energy content by Majdalani & Saad (2007a) and Saad & Majdalani (2008).…”

Internal Flows Driven by Wall-Normal Injection

“…Lastly, we note that the collection of variational solutions that admit variable headwall injection increase our repertoire of Euler-based approximations that may be used to model the incompressible motion in porous tubes. For the porous channel flow analogue, the planar solutions are presented by Saad & Majdalani (2008a;2009b). As for tapered grain configuration, the reader may consult with Saad et al (2006) or Sams et al (2007).…”

“…As we move closer to the central topic of this chapter, we consider recent work in which the Taylor-Culick solution is reconstructed for the case of solid rocket motors with headwall injection or hybrid motors with a large headwall-to-sidewall velocity ratio (Majdalani, 2007a). The corresponding problem is analyzed in both axisymmetric and planar configurations by Majdalani & Saad (2007b) and Saad & Majdalani (2009b), respectively. This will be the topic of Section 2 where the solutions for the Taylor-Culick flow with arbitrary headwall injection are derived and compared to steady state, second order accurate inviscid computations.…”

Rotational Approximation of the Taylor-Culick Profile for Rockets with Noncircular Grains

“…Greek α angle between e r and n ε radial deviation amplitude ratio relative to a Π wet perimeter 1 American Institute of Aeronautics and Astronautics generalizations are obtained by Majdalani and Saad,44 and Saad and Majdalani,45 in the context of flow through porous tubes and channels, respectively. Their work is further extended using a Lagrangian optimization technique, to identify two distinct families of solutions of the Taylor-Culick type, which exhibit increasing energy signatures (Saad and Majdalani 46 ).…”