Geometric Analysis of the Linear Expansion-Deflection Nozzle at Highly Overexpanded Flow Conditions

Abstract

The effect of nozzle geometry on the thrust efficiency of the linear expansion-deflection (ED) nozzle concept has been investigated at highly overexpanded flow conditions. A new design method for generation of the ED nozzle contour is introduced and a factorial-based approach used to determine the effect of nozzle geometry on thrust coefficient. An area ratio of 17.6 was selected to represent a core stage nozzle and eight geometric parameters compared across sixteen separate configurations. Thrust coefficient was determined numerically from a time-dependent model using dry air as the working fluid. The numerical model was verified with respect to viscous effects and dimensional grid parameters, and then validated against experimental results to quantify sources of numerical error. Results were obtained for pressure ratios ranging from 5-50 to replicate highly overexpanded conditions where flow separation would occur in an equivalent conventional nozzle. Thrust coefficient in all ED nozzle configurations relative to the conventional nozzle ranged between 105-190% at low pressures and 90-120% at high pressures. The conclusions from the factorial analysis of ED nozzle contour geometry suggested that low curve radii and high inflection angles would further improve thrust coefficient for the flow conditions tested. The results show that an improvement in thrust relative to a conventional design can be expected at highly overexpanded flow conditions through the use of an ED nozzle configuration. NomenclatureA = Area (m 2 ) R = Specific gas constant (kJkg -1 K -1 ) C = Contraction ratio r = Radius (m) C F = Thrust coefficient v = Velocity (ms -1 ) C F,% = Thrust efficiency x = Longitudinal direction (m) G t = Throat gap (m) y = Lateral direction (m) ̇ = Mass flow rate (kgs -1 ) γ = Ratio of specific heats P = Static pressure (Pa) θ = Wall angle (°) Subscripts 0 = Stagnation conditions e = Pintle contour point e a = Pintle contour point a i = Arbitrary contour point i amb = Local ambient conditions j = Arbitrary contour point j b = Pintle contour point b m = Nozzle contour point m c = Pintle contour point c n = Nozzle contour point n d = Pintle contour point d t = Throat region 1 PhD Candidate, kyll.schomberg@unsw.edu.au, Student Member AIAA.

Computational Simulation of an Altitude Adaptive Nozzle Concept

“…Theoretical and ideal pressure curves were generated using isentropic flow relations for the physical and ideal geometries respectively. All experimental results were taken from previous work [12].…”

“…The geometry utilised in all simulations was consistent with that used in a prior experiment [12]. This consisted of a fixed nozzle shroud and interchangeable flow deflectors, herein referred to as a 'pintles' to vary configurations between the CD and the ED nozzles.…”

Design of an arc-based thrust-optimized nozzle contour

“…An implicit axisymmetric pressure-based solver was selected in conjunction with second-order upwind schemes to generate all results. Although initially developed for low-speed §ows, the solver has been extended to compressible §ow conditions [10] and has modeled similar §ow ¦elds with a high degree of accuracy [11,12]. A Reynoldsaveraged approach to turbulence was used due to the quasi-steady nature of the experimental §ow conditions [9].…”

Numerical study on dynamic flow of flexible extension nozzle in rocket motors

“…At present, the height compensation nozzles widely studied include plug nozzles, expansion bias nozzles, double bell nozzles, and extension nozzles. The plug nozzle has a compact structure, continuous profile, and good height compensation ability [3], but has high requirements for cooling capacity [4][5], and the design of the nozzle structure is difficult to achieve [6]; The expansion bias nozzle has good height compensation under low altitude conditions [7], but its performance is not outstanding under high altitude conditions due to overexpansion and suction loss [8]; The dual bell shaped nozzle has a simple structure, high reliability [9], and has a certain ability to control flow separation [10][11]. However, it can only achieve height compensation under two design conditions, and the surface changes are discontinuous [12]; The traditional extension nozzle has discontinuous surface changes, fewer extension stages, and a small height compensation range [13][14].…”