CFD Study of Ejector Nozzle Models

Ruslan Tsukanov; Sergiy Yepifanov

doi:10.2478/tar-2026-0014

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CFD Study of Ejector Nozzle Models

Transactions on Aerospace Research

Volume 2026 (2026): Issue 3 (September 2026)

By: Ruslan Tsukanov and Sergiy Yepifanov

Open Access

|Sep 2026

Figures & Tables

Ejector nozzle thrust augmentation ratio vs. α*: 1 – first solution, ideal; 2 – second solution, ideal; 3 – second solution, with nozzle underexpansion losses from 1D theory; 4 – second solution, with nozzle underexpansion losses from 2D theory.

Ejector nozzle thrust augmentation ratio vs. flight Mach number (without taking into account losses).

Computational domain (configurations 1–5).

The five meshes considered: a – 20 mm; b – 15 mm; c – 10 mm; d – 7.5 mm; e – 5 mm.

Table 1.

Values of corresponding boundary parameters.

Boundary/Parameter	Total/static pressure, Pa	Turbulence intensity, %	Mach number	Flow rate, kg/s	Total/static temperature, K
Left (Pressure-far-field)	–/101325	1.0	0.6	–	–/288.15
Top (Pressure-far-field)	–/101325	1.0	0.6	–	–/288.15
Right (Pressure outlet)	–/101325	1.0	–	–	308.89/–
AirOutlet (Mass-flow-outlet)	–	–	–	0.99	–
InletPrimary (Pressure-inlet)	209787/–	10.0	–	–	993.05/–

Table 2.

Parameter values on the corresponding meshes.

Mesh,	Integral parameter, N	Representative mesh cell size, m
1 (20 × 0.40 mm)	395.65	1.24×10⁻²
2 (15 × 0.30 mm)	396.21	1.01×10⁻²
3 (10 × 0.20 mm)	396.31	7.46×10⁻³
4 (7.5 × 0.15 mm)	394.66	5.94×10⁻³
5 (5 × 0.10 mm)	395.60	4.23×10⁻³

Table 3.

Comparative estimation of the computational results.

Parameter	Meshes 1–2–3	Meshes 2–3–4	Meshes 3–4–5
h1, m	7.46×10⁻³	5.94×10⁻³	4.23×10⁻³
h2, m	1.01×10⁻²	7.46×10⁻³	5.94×10⁻³
h3, m	1.24×10⁻²	1.01×10⁻²	7.46×10⁻³
P1, N	396.31	394.66	395.60
P2, N	396.21	396.31	394.66
P3, N	395.65	396.21	396.31
r32	1.229	1.350	1.255
r21	1.350	1.255	1.403
s	1	−1	−1
p	8.525	17.788	2.119
CR	0.192	−15.573	−0.568
	[0; 1) – monotonic convergence	(−∞; −1) – oscillating divergence	[−1; 0) – oscillating convergence
f_ex, N	396.32	394.63	396.49
e₃₂, %	0.140	0.027	0.419
e₂₁, %	0.027	0.419	0.238
GCI₃₂, %	0.036	0.000	0.848
GCI₂₁, %	0.003	0.009	0.283
	< 1% – for detailed calculations	< 1% – for detailed calculations	< 1% – for detailed calculations
AR	1.000	0.0003	1.463
	[0.95; 1.05] – optimum	(−∞; 0.95) – mesh should be improved	(1.05; ∞) – mesh should be improved
h_req	3.74×10⁻³	4.57×10⁻³	2.33×10⁻⁶

Table 4.

Differences of integral parameter calculations.

Parameter	Mesh 20 mm	Mesh 15 mm	Mesh 10 mm	Mesh 7.5 mm	Mesh 5 mm
Δ_m, %	−4.438	−4.173	−4.076	−4.605	−4.329
Δ_v, %	−17.564	−16.510	−16.232	−17.036	−16.542
Δ_p, %	25.717	24.289	23.876	24.894	24.288
Δ_{Nozzle Th}, %	−2.668	−2.488	−2.442	−2.888	−2.640
Δ_Th, %	−3.494	−3.259	−3.333	−3.737	−3.507

Pathline patterns for configurations 3 and 6 (α* = 5).

Fields of Mach number for the configurations considered (α* = 5).

Fields of Mach number for the configurations considered (α* = 4).

Fields of static pressure for the configurations considered (α* = 5).

Fields of static pressure for the configurations considered (α* = 4).

Fields of static temperature for some of the configurations considered (α* = 5).

Table 5.

Results of integral parameter calculations.

Parameter/Configuration	Secondary flow Mach number at the entrance of mixing chamber	Primary flow rate, kg/s	Entrainment ratio	Thrust, N	Augmentation ratio, φ
Alperin	0.4119	—	2.868	—	1.72
Base engine	—	1.0102	—	409.978	—
1 (α* = 5)	—	0.96537	—	395.65	—
2 (α* = 5)	—	0.96804	—	396.21	—
3 (α* = 5)	—	0.96903	—	396.31	—
4 (α* = 5)	—	0.96368	—	394.66	—
5 (α* = 5)	—	0.96647	—	395.60	—
6 (α* = 5)	—	0.97104	—	394.35	—
7 (α* = 5)	—	0.97484	—	395.92	—
8 (α* = 5)	0.32082	0.96839	2.31028	299.26	0.72994
9 (α* = 5)	—	0.61498	—	251.28	—
10 (α* = 5)	0.32750	0.97310	2.33550	301.40	0.73516
11 (α* = 5)	0.34470	0.96667	2.42548	305.87	0.74607
12 (α* = 5)	0.33997	0.96408	2.41586	305.31	0.74470
13 (α* = 5)	0.46743	0.23817	13.57310	227.01	0.55370
14 (α* = 5)	0.34294	0.96564	2.40173	304.53	0.74279
15 (α* = 5)	0.35425	0.96738	2.42944	298.82	0.72887
16 (α* = 5)	0.34583	0.94622	2.83003	365.90	0.89247
17 (α* = 5)	0.34722	0.94040	2.97538	382.91	0.93398
18 (α* = 5)	0.34472	0.93197	2.98313	383.83	0.93622
19 (α* = 5)	0.35423	0.93440	2.95817	385.23	0.93964
20 (α* = 5)	0.31634	0.92613	2.84300	381.47	0.93047
21 (α* = 5)	0.33955	0.93160	2.83899	386.71	0.94323
22 (α* = 5)	0.34451	0.92628	2.85432	386.43	0.94256
23 (α* = 5)	0.37377	0.97795	2.66855	407.85	0.99482
24 (α* = 5)	0.40219	0.98181	2.62750	405.87	0.98997
25 (α* = 5)	0.39948	0.98102	2.61869	401.61	0.97958
26 (α* = 5)	0.37102	0.97963	2.64032	410.45	1.00115
27 (α* = 5)	0.37075	0.98006	2.62426	404.57	0.98681
28 (α* = 5)	0.36716	0.98029	2.60928	402.62	0.98206
29 (α* = 5)	0.37423	0.97742	2.60485	406.13	0.99062
30 (α* = 5)	0.36818	0.97993	2.61096	402.31	0.98130
31 (α* = 5)	0.36976	0.98077	2.61755	403.16	0.98337
32 (α* = 5)	0.36390	0.97955	2.54888	378.82	0.92399
Alperin	0.379	—	2.008	—	1.62
Base engine	—	1.0102	—	409.978	—
1 (α* = 4)	0.35692	0.97862	2.04513	402.43	0.98158
2 (α* = 4)	0.35962	0.97930	2.05995	398.65	0.97238
3 (α* = 4)	0.35893	0.97805	2.06253	399.83	0.97525
4 (α* = 4)	0.35652	0.97793	2.04692	404.07	0.98559
5 (α* = 4)	0.35750	0.97854	2.04527	397.83	0.97036
6 (α* = 4)	0.35814	0.97848	2.05250	399.17	0.97363
7 (α* = 4)	0.36632	0.97972	2.03578	405.58	0.98928
8 (α* = 4)	0.36516	0.97918	2.04474	406.69	0.99198
9 (α* = 4)	0.35050	0.97629	2.06375	400.55	0.97699
10 (α* = 4)	0.35007	0.97877	2.05843	400.61	0.97715
11 (α* = 4)	0.34451	0.97490	2.03757	402.30	0.98127
12 (α* = 4)	0.35006	0.97648	2.06037	403.69	0.98467
13 (α* = 4)	0.35034	0.98014	2.04143	402.45	0.98165
14 (α* = 4)	0.35651	0.97861	2.04413	398.08	0.97097
15 (α* = 4)	0.35597	0.98016	2.03369	395.00	0.96346
16 (α* = 4)	0.35525	0.97989	2.04758	396.51	0.96716
17 (α* = 4)	0.33691	0.97977	2.04349	395.18	0.96389
18 (α* = 4)	0.38328	0.96484	2.33288	464.50	1.13298
19 (α* = 4)	0.40915	0.94874	2.63502	512.45	1.24994
20 (α* = 4)	0.09572	0.96209	0.61172	375.47	0.91584
21 (α* = 4)	0.22171	0.96876	1.35933	400.38	0.97658
22 (α* = 4)	0.58058	0.98028	2.89229	385.55	0.94040
23 (α* = 4)	0.71614	0.98227	3.14938	315.27	0.76900
24 (α* = 4)	0.70802	0.97691	3.19422	167.34	0.40818
25 (α* = 4)	0.73642	0.98236	3.17467	13.62	0.03323
26 (α* = 4)	0.35233	0.99994	1.94880	390.92	0.95351
27 (α* = 4)	0.34880	0.99459	1.98429	399.94	0.97553
28 (α* = 4)	0.37624	0.98298	2.32974	521.44	1.00290
29 (α* = 4)	0.39163	0.97016	2.59136	612.90	0.98818

Pathline patterns for the configurations considered (α* = 5).

Pathline patterns for the configurations considered (α* = 4).

Thrust augmentation ratio (φ) vs. the ratio of the common exhaust unit exit area to the mixing chamber area (*α_D*) (configurations 20, 21, 2, 22, 23, 24, 25) (α* = 4).

Thrust augmentation ratio (φ) vs. the ratio of the primary convergent-divergent nozzle exit area to its throat area (*α_Dp*) (configurations 2, 27, 26) (α* = 4).

Fields of Mach number for configurations 28, 28w, 29 and 29w (α* = 4).

Thrust augmentation ratio (φ) vs. primary nozzle pressure ratio *π_N* (the value at the point *π_N* = 4 was interpolated).

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DOI: https://doi.org/10.2478/tar-2026-0014 | Journal eISSN: 2545-2835

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Language: English

Page range: 41 - 68

Submitted on: May 10, 2026

Accepted on: Jul 21, 2026

Published on: Sep 28, 2026

Published by: ŁUKASIEWICZ RESEARCH NETWORK – INSTITUTE OF AVIATION

In partnership with: Paradigm Publishing Services

Keywords:

thrust augmenting ejector nozzle,

nozzle thrust,

grid convergence index,

CFD study,

thrust augmentation ratio,

ejector nozzle mixing chamber

Related subjects:

Engineering,

Introductions and overviews,

Materials sciences, other,

Physics,

Physics, other

© 2026 Ruslan Tsukanov, Sergiy Yepifanov, published by ŁUKASIEWICZ RESEARCH NETWORK – INSTITUTE OF AVIATION
This work is licensed under the Creative Commons Attribution 4.0 License.

Volume 2026 (2026): Issue 3 (September 2026)

CFD Study of Ejector Nozzle Models

Figures & Tables

Fig.1.

Fig. 2.

Fig. 3.

Fig. 4.

Fig. 5.

Fig. 6.

Fig. 7.

Table 1.

Table 2.

Table 3.

Table 4.

Fig. 8.

Fig. 9.

Fig. 10.

Fig. 11.

Fig. 12.

Fig. 13.

Table 5.

Fig. 14.

Fig. 15.

Fig. 16.

Fig. 17.

Fig. 18.

Fig. 19.

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