INCAS BULLETIN, Volume 10, Issue 3 2018, pp. 3 14 (P) ISSN 2066 -8201, (E) ISSN 2247 -4528 [623865]

INCAS BULLETIN, Volume 10, Issue 3/ 2018, pp. 3 – 14 (P) ISSN 2066 -8201, (E) ISSN 2247 -4528
Computational Study in Centrifugal Compressor
Irina -Carmen ANDREI1, Gabriela STROE*,2
*Corresponding author
1INCAS ‒ National Institute for Aerospace Research “Elie Carafoli” ,
B-dul Iuliu Maniu 220, Bucharest 061126, Romania ,
[anonimizat], [anonimizat]
2POLITEHNICA University of Bucharest, Fa culty of Aerospace Engineering,
Gh. Polizu Street 1 -7, Sector 1, Bucharest , 011061 , Romania ,
[anonimizat]*
DOI: 10.13111/2066 -8201. 2018.10.3. 1
Received: 29 May 2018/ Accepted : 21 June 2018/ Published: September 2018
Copyright © 2018. Published by INCAS. This is an “open access” article under the CC BY -NC-ND
license (http://creativecommons.org/licenses/by -nc-nd/4.0/)
6th International Workshop on Numerical Modelling in Aerospace Sciences, NMAS 2018 ,
16 – 17 May 2018, Bucharest, Romania, (held at INCAS, B -dul Iuliu Maniu 220, sector 6)
Section 1 – Launchers propulsion technologies and simulations of rocket engines
Abstract: The active control for centrifugal compressor systems consists in using, monitoring and
managing the sensors to detect fluid disturbances, the actuators to introduce desired perturbations
and a suitable controller to determine the optimal actuator actions using the sensor information. The
object of an interesting centrifugal compressor design is to obtain the most air through a given
diameter compressor, with a minimum number of stages while maintaining high efficienci es and
aerodynamic stability over the operating range. The high efficiency of the axial compressor system
decreases dramatically when used in small high -pressure applications, especially due to the large
relative tip clearance. In addition, the high centri fugal force, dominating the pressure rise, results in a
superior operability and the short axial length of the centrifugal compressor offers rotor -dynamic
multiple advantages. These qualities allow the centrifugal compressor system to be used as the last
stage of a high -pressure compressor of an aero engine as well as turbo pump assemblies used in
liquid -propelled rocket engines.
Key Words: Aerodynamic stability, Centrifugal compressor, control system, disturbances
1. INTRODUCTION
For all applications dedicated to aviation, the centrifugal compressor system consists either
of a dual centrifugal compressor (meaning the increase in air mass flow, since the intake is
on both sides), or no more than two series of centrifugal compressors connected, due to the
potential amplification of loss of pressure inside the connector ducts.
The purpose of a centrifugal compressor system is to produce a distinct increase in static
pressure, thus effectively increasing the static enthalpy [3-4].
From the thermo -dynamical analysis stan dpoint, the compressor pressure ratio is the
most significant parameter, since it enables the calculation of the jet engine performances,
for all the engine running regimes and for the entire flight envelope, and also the design of
the centrifugal compressor .

Irina -Carmen ANDREI, Gabriela STROE 4

INCAS BULLETIN, Volume 10, Issue 3/ 2018 Centrifugal compressor rotating stall is limited to low-pressure systems and high –
pressure systems at partial speed. For the most commonly used centrifugal system
configuration in aeronautical applications , includ ing high-pressure systems , while
functioning at design speed, it has been noticed that the rotating stall has little effect on
pressure rise and flow rate, and just serves as a precursor to surge [3-4].
All types of fluid dynamic instabilities can limit the overall compressor performance s
and can alter the safe operation of the entire engine. Unsteady fluctuations, caused by
rotating stall or surge, may lead to excessive heating of the impeller blades and to a greater
compressor exit temperature. Large am plitude fluctuations can cause additional periodic
loads of the blades, which result in increased operating noise levels as well as fatigue, or
even fatal damage of the centrifugal compression system [3-4].
Due to the severity of these dangerous conditions , centrifugal compressors are
classically designed to operate well below the peak pressure rise point [3-4].
2. ANALITICAL MODELING OF CENTRIFUGAL COMPRES SOR
CONTROL
The Navier -Stokes equations describe continuum fluid flows from the first principles of
thermos -dynamics . An appropriate derivation of the Navier -Stokes equations is given in the
classic paper of Schlichting [2] where terms of the Navier -Stokes equations may be
simplified or ne glected if certain assumptions are made [5-8].
For the numerical solution of the analytical model, the v iscous effects are considered;
the computational domain surrounding the body geometry is divided into small cells.
Following the i ntegration of the Navier -Stokes equations across each computational cell , the
flow field at time level is completely solved [9-14]. The reason of this numerical algorithm is
to advance the solution to a new time level, by using a discrete time step [9-14].
𝛿𝑡∙𝑞⃗+𝛿𝑥∙𝐸⃗⃗+𝛿𝑦∙𝐹⃗+𝛿𝑧∙𝐺⃗=𝛿𝑥∙𝑅⃗⃗+𝛿𝑦∙𝑆⃗+𝛿𝑧∙𝑇⃗⃗ (1)
𝑞⃗=
[ 𝜌
𝜌𝑢
𝜌𝑣
𝜌𝑤
𝑒]
,𝐸⃗⃗=
[ 𝜌𝑢
𝜌𝑢2+𝑝
𝜌𝑢𝑣
𝜌𝑢𝑤
(𝑒+𝑝)𝑢]
,𝐹⃗=
[ 𝜌𝑣
𝜌𝑣𝑢
𝜌𝑣2+𝑝
𝜌𝑣𝑤
(𝑒+𝑝)𝑣]
,𝐺⃗=
[ 𝜌𝑣
𝜌𝑣𝑢
𝜌𝑤𝑣
𝜌𝑤2+𝑝
(𝑒+𝑝)𝑤]
(2)
𝑅⃗⃗=
[ 0
𝜏𝑥𝑥𝜏𝑥𝑦
𝜏𝑥𝑧
𝑢𝜏𝑥𝑥+𝑣𝜏𝑥𝑦+𝑤𝜏𝑥𝑧−𝑞𝑧]
,𝑆⃗=
[ 0
𝜏𝑦𝑥
𝜏𝑦𝑦
𝜏𝑦𝑧
𝑢𝜏𝑦𝑥+𝑣𝜏𝑦𝑦+𝑤𝜏𝑦𝑧−𝑞𝑧]
,
𝑇⃗⃗=
[ 0
𝜏𝑧𝑥𝜏𝑧𝑦
𝜏𝑧𝑧
𝑢𝜏𝑧𝑥+𝑣𝜏𝑧𝑦+𝑤𝜏𝑧𝑧−𝑞𝑧]
(3)
𝜏𝑖𝑗=𝜇(𝜕𝑢𝑖
𝜕𝑥𝑗+𝜕𝑢𝑗
𝜕𝑥𝑖)−2
3𝜇𝜕𝑢𝑘
𝜕𝑥𝑘𝛿𝑖𝑗, 𝑖,𝑗,𝑘=1,2,3 (4)

5 Computational Study in Centrifugal Compressor

INCAS BULLETIN, Volume 10, Issue 3/ 2018 𝑞𝑖=−𝑘𝜕𝑇
𝜕𝑥𝑖, 𝑖=1,2,3 (5)
𝑝=(𝛾−1)[𝑒−1
2𝜌(𝑢2+𝑣2+𝑤2)] (6)
𝑒=𝑐𝑣𝑇 ℎ=𝑐𝑝𝑇 (7)
𝜕
𝜕𝑡∭𝑞⃗𝑑𝑉+
𝑉∬[𝐸⃗⃗+𝐹⃗+𝐹⃗]∙𝑛⃗⃗𝑑𝑆
𝑆=∬[𝑅⃗⃗+𝑆⃗+𝑇⃗⃗]∙𝑛⃗⃗𝑑𝑆
𝑆 (8)
∬[𝐸⃗⃗+𝐹⃗+𝐺⃗]∙𝑛⃗⃗𝑑𝑆
𝑆
≈[(𝐸⃗⃗∙𝑛⃗⃗)|∆𝑆|]𝑖+1
2+[(𝐸⃗⃗∙𝑛⃗⃗)|∆𝑆|]𝑖−1
2+[(𝐹⃗∙𝑛⃗⃗)|∆𝑆|]𝑗+1
2
+[(𝐹⃗∙𝑛⃗⃗)|∆𝑆|]𝑗−1
2+[(𝐺⃗∙𝑛⃗⃗)|∆𝑆|]𝑘+1
2+[(𝐺⃗∙𝑛⃗⃗)|∆𝑆|]𝑘−1
2 (9)
(𝐸⃗⃗∙𝑛⃗⃗)|∆𝑆|≈𝐸̂
[(𝐸⃗⃗∙𝑛⃗⃗)|∆𝑆|]𝑖+1
2+[(𝐸⃗⃗∙𝑛⃗⃗)|∆𝑆|]𝑖−1
2≈𝐸̂
𝑖+1
2−𝐸̂
𝑖− 1
2 (10)
𝐸̂
𝑖+1
2=0.5{𝐸̂𝑅(𝑞⃗𝑅)+𝐸̂𝐿(𝑞⃗𝐿)}|𝑖+1/2−|𝐴̃|{𝑞⃗𝑅−𝑞⃗𝐿}|𝑖+1/2 (11)
𝑞⃗𝑅=[𝜌𝑅, 𝑢𝑅, 𝑣𝑅,𝑤𝑅,𝑝𝑅 ]𝑇 (12)
𝑞⃗𝐿=[𝜌𝐿, 𝑢𝐿, 𝑣𝐿,𝑤𝐿,𝑝𝐿 ]𝑇 (13)
𝑞⃗𝑅=𝑞⃗𝑖+1−1
6𝛷
𝑖+3
2−(𝑞⃗𝑖+2−𝑞⃗𝑖+1)−1
3𝛷
𝑖+1
2+(𝑞⃗𝑖+1−𝑞⃗𝑖) (14)
𝑞⃗𝐿=𝑞⃗𝑖+1
3𝛷
𝑖+1
2−(𝑞⃗𝑖+1−𝑞⃗𝑖)+1
6𝛷
𝑖−1
2+(𝑞⃗𝑖−𝑞⃗𝑖−1) (15)
𝛷
𝑖+1
2−=𝛷(𝑟
𝑖+1
2−),𝛷
𝑖−1
2+=𝛷(𝑟
𝑖−1
2+) (16)
𝑟
𝑖+1
2−=𝑞𝑖−𝑞𝑖−1
𝑞𝑖+1−𝑞𝑖,𝑟
𝑖−1
2+=𝑞𝑖+1−𝑞𝑖
𝑞𝑖−𝑞𝑖−1 (17)
𝛷(𝑟)=𝑚𝑎𝑥[0,min(2𝑟,1),min (𝑟,2)] (18)
𝐸̂𝑅(𝑞⃗𝑅)=
[ 𝜌𝑅𝑈𝑅
𝜌𝑅𝑈𝑅𝑢𝑅+𝑝𝑅𝑛𝑥
𝜌𝑅𝑈𝑅𝑣𝑅+𝑝𝑅𝑛𝑦
𝜌𝑅𝑈𝑅𝑤𝑅+𝑝𝑅𝑛𝑧
𝜌𝑅𝑈𝑅ℎ𝑜𝑅−𝑝𝑅𝑛𝑡]
,𝐸̂𝐿(𝑞⃗𝐿)=
[ 𝜌𝐿𝑈𝐿
𝜌𝐿𝑈𝐿𝑢𝐿+𝑝𝐿𝑛𝑥
𝜌𝐿𝑈𝐿𝑣𝐿+𝑝𝐿𝑛𝑦
𝜌𝐿𝑈𝐿𝑤𝐿+𝑝𝐿𝑛𝑧
𝜌𝐿𝑈𝐿ℎ𝑜𝐿−𝑝𝐿𝑛𝑡]
(19)

Irina -Carmen ANDREI, Gabriela STROE 6

INCAS BULLETIN, Volume 10, Issue 3/ 2018 𝑈=(𝑉⃗⃗−𝑉⃗⃗𝑔𝑟𝑖𝑑)∙𝑛⃗⃗|∆𝑆| (20)
ℎ𝑜=𝑒+𝑝
𝜌 (21)
𝑛𝑡=−(𝑉⃗⃗𝑔𝑟𝑖𝑑∙𝑛⃗⃗)|∆𝑆|
(22)
|𝐴̃|{𝑞⃗𝑅−𝑞⃗𝐿}|𝑖+1/2=∆𝑞⃗=|𝜆̃1|∆𝑞⃗+𝛿1𝑈̃∗+𝛿2𝑁̃𝑛 (23)
𝑈̃∗=
[ 𝑞̃
𝑞̃𝑢̃
𝑞̃𝑣̃
𝑞̃𝑤̃
𝑞̃ℎ̃𝑜]
,𝑁̃𝑛=
[ 0
𝑛𝑥𝑛𝑦
𝑛𝑧
𝑈̃]
(24)
𝛿1=(−|𝜆̃1|+|𝜆̃2|+|𝜆̃3|
2)∆𝑝
𝑞̃𝑎̃2+|𝜆̃2|−|𝜆̃3|
2∆𝑈
𝑎̃ (25)
𝛿2=(−|𝜆̃1|+|𝜆̃2|+|𝜆̃3|
2)𝜌̃∆𝑈+|𝜆̃2|−|𝜆̃3|
2∆𝑝
𝑎̃ (26)
𝜆̃1=𝑈̃,𝜆̃2=𝑈̃+𝑎̃,𝜆̃3=𝑈̃−𝑎̃ (27)
𝑞̃=√𝜌𝑅𝜌𝐿 (28)
𝛷̃=𝛷𝐿(1
1+√𝜌𝑅𝜌𝐿)+𝛷𝑅(√𝜌𝑅𝜌𝐿
1+√𝜌𝑅𝜌𝐿) (29)
∆𝑞̂𝑛
∆𝑡=𝐸̂𝑖+1/2𝑛+1−𝐸̂
𝑖−1
2𝑛+1+𝐹̂
𝑗+1
2𝑛+1−𝐹̂
𝑗−1
2𝑛+1+𝐺̂
𝑘+1
2𝑛+1−𝐺̂𝑘−1/2𝑛+1 (30)
∆𝑞̂𝑛=(𝑞̂𝑛+1−𝑞̂𝑛)∆𝑉 (31)
𝐸̂𝑛+1=𝐸̂𝑛+𝐴̂𝑛∆𝑞̂𝑛 (32)
𝐹̂𝑛+1=𝐹̂𝑛+𝐵̂𝑛∆𝑞̂𝑛 (33)
𝐺̂𝑛+1=𝐺̂𝑛+𝐶̂𝑛∆𝑞̂𝑛 (34)
𝐴̂𝑛=[𝜕𝐸̂
𝜕𝑞̂]𝑛
, 𝐵̂𝑛=[𝜕𝐹̂
𝜕𝑞̂]𝑛
, 𝐶̂𝑛=[𝜕𝐺̂
𝜕𝑞̂]𝑛
(35)
𝑀𝑛∆𝑞̂𝑛=−∆𝑡𝑅𝑛 (36)
𝑅𝑛=[𝐸̂𝑖+1/2𝑛−𝐸̂𝑖−1/2𝑛+𝐹̂𝑗+1/2𝑛−𝐹̂𝑗−1/2𝑛+𝐺̂𝑘+1/2𝑛−𝐺̂𝑘−1/2𝑛] (37)
𝑀𝑛≈𝑀1𝑛𝑀2𝑛𝑀3𝑛 (38)

7 Computational Study in Centrifugal Compressor

INCAS BULLETIN, Volume 10, Issue 3/ 2018 𝑀1𝑛=
[ ⋱
⋱⋱
⋱
−∆𝑡𝐴̂𝑖−1/2𝑛
⋱
⋱⋱
⋱
𝐼
⋱
⋱⋱
⋱
∆𝑡𝐴̂𝑖+1/2𝑛
⋱
⋱⋱
⋱]
(39)
𝑀1𝑛∆𝑞̂∗=−∆𝑡𝑅𝑛 (40)
𝑀2𝑛∆𝑞̂∗∗=∆𝑞𝑛 (41)
𝑀13𝑛∆𝑞̂∗=∆𝑞̂∗∗ (42)
𝐴̂𝑖𝑛=(𝑇𝛬̂𝑇−1)𝑖 (43)
−(𝑇𝛬̂𝑇−1)𝑖∆𝑞̂𝑖−1∗+𝐼∆𝑞̂𝑖∗+(𝑇𝛬̂𝑇−1)𝑖∆𝑞̂𝑖+1∗=−∆𝑡𝑅𝑛 (44)
−𝛬̂𝑖(𝑇−1∆𝑞̂𝑖−1∗)+𝐼(𝑇−1∆𝑞̂𝑖∗)+𝛬̂𝑖(𝑇−1∆𝑞̂𝑖+1∗)=−∆𝑡𝑇−1𝑅𝑛 (45)
−𝑢𝑖′𝑢𝑗′̅̅̅̅̅̅=𝑣𝑡(𝑑𝑢𝑖
𝑑𝑥𝑗+𝑑𝑢𝑗
𝑑𝑥𝑖) (46)
𝑣𝑡=𝑣̃𝑓𝑣1, 𝑓𝑣1=1−χ3
χ3+𝑐𝑣13, χ=𝑣̃
𝑣 (47)
𝑆̃=𝑆+𝑣̃
κ2𝑑2𝑓𝑣2, 𝑓𝑣2=1−χ
1+χ𝑓𝑣1 (48)
𝑓𝑤=𝑔[1+𝑐𝑤36
𝑔6+𝑐𝑤36]1/6
, 𝑔=𝑟+𝑐𝑤3(𝑟6−𝑟), 𝑟=𝑣̃
𝑆̃κ2𝑑2 (49)
𝑓𝑡1=𝑐𝑡1𝑔𝑡exp (−𝑐𝑡2𝑤𝑡2
∆𝑈2(𝑑2+𝑔𝑡2𝑑𝑡2)) (50)
𝑓𝑡2=𝑐𝑡3exp(−𝑐𝑡4χ2) (51)
𝑔𝑡=min(0.1,∆𝑈
𝑤𝑡∆𝑥𝑡) (52)
𝑝𝑛
√𝜁𝑥2+𝜁𝑦2+𝜁𝑧2=𝜌(𝜕𝜁𝑡
𝜕𝜏+𝑢𝜕𝜁𝑥
𝜕𝜏+𝑣𝜕𝜁𝑦
𝜕𝜏+𝑤𝜕𝜁𝑧
𝜕𝜏) (53)
𝜕
𝜕𝑡(2𝑎
𝛾−1−𝑢𝑛)+(𝑢−𝑎)𝜕
𝜕𝑛(2𝑎
𝛾−1−𝑢𝑛)=0 (54)
2𝑎
𝛾−1−𝑢𝑛|
𝑖=1=2𝑎
𝛾−1−𝑢𝑛|
𝑖=2 (55)
𝑎2
𝛾−1+𝑢𝑛2
2=𝑐𝑝𝑇0 (56)

Irina -Carmen ANDREI, Gabriela STROE 8

INCAS BULLETIN, Volume 10, Issue 3/ 2018 𝜕
𝜕𝑡(𝜌𝑝𝑉𝑝)=𝑚̇𝑐−𝑚̇𝑡 (57)
𝑉𝑝𝜕𝜌𝑝
𝜕𝑝𝑝𝜕𝑝𝑝
𝜕𝑡=𝑚̇𝑐−𝑚̇𝑡 (58)
𝑎𝑝2=𝜕𝑝𝑝
𝜕𝜌𝑝 (59)
𝜕𝑝𝑝
𝜕𝑡=𝑎𝑝2
𝑉𝑝(𝑚̇𝑐−𝑚̇𝑡) (60)
𝑝𝑝𝑛+1=𝑝𝑝𝑛+𝐶(𝑚̇𝑐−𝑚̇𝑡)∆𝑡 (61)

Fig. 1 – Centrifugal compressor assembly for a turbojet engine [1]
The safety margin of 10 to 20 percent is generally introduced between the surge line and
the design compres sor system operating conditions [15-17].
In the last years, due to the implementation of appropriate stall detection and stall
avoidance devices , the safety margin has been significantly reduced [18-20].
The implementation of such precuation measures enable the safe operation of the
centrifugal compressor, especially for the operating conditions: higher pressur e ratios and
smaller flow rates [18-20].
Following a large survey on this topic, the control of the centrifugal compressor
operation fall s into one of these two categorie s:
(1) passive or open -loop control, and
(2) active or closed -loop control.

9 Computational Study in Centrifugal Compressor

INCAS BULLETIN, Volume 10, Issue 3/ 2018
Fig. 2 – Active & passive control for the centrifugal compressor , intended as a part of a jet engine
Open -loop control is reached following changes induced in the centrifugal compressor
design and construction such that the performance characteristic map is modified and the
surge line is shifted to smaller flow rates [18-20]. Open -loop control method s are aimed to
moving the pressure peak to smaller mass flo w rates, even taking all risks supposed by slight
decrease in adiabatic efficiency. The active control method is used via a direct link between
the controller unit and a set of actuation devices [18-20]. Pinsley et all [21] presented a
plenum gate valve to control the flow leaving the compression system. The valve was
operated at frequencies tailored to damp out all potential disturbances that would lead to the
onset of surge. The closed -loop control in centrifugal compressor is an ongoing area of
research with advancements , which can bring significant improvements in centrifugal
compressor performance ; certain issues that are real challenges , require a proper solution and
construction, prior to be applied in closed -loop compressor control in engines [21]. The high
pressure ratio as well as the superior operability characteristics of the centrifugal compressor
make it suitable as a compressor system part of an aero engine [22]. The continuous increase
of the pressure ratios, intended as a main jet engine design parameter, as well as the increase
in air traffic and the growing number of restrictions with respect to fuel consumption in
conjunction with the environmental restrictions for emissions , require a better understanding
of the detailed aerodynamic s of the centrifugal compressor [22]. Especially in the coming
future, new aerodinamical propulsion concepts with intercooled compressors using a
centrifugal compressor as an intermediate stage between the low and the high -pressu re
compressor system will create a high and strong potential for new generations of centrifugal
compressors. The use of the centrifugal compressors as parts of the aero engines is in a
certain extent restricted by the pressure ratio, i.e. for values larger than 6, local inclusions of
supersonic flow within the impeller can occur and further develop , with the consequen t
manifest of the intense pressure losses, due to presence of shock waves . This is why
centrifugal compressors are not widely used for all aer o engines but , on the other hand , the
flow inside a centrifugal compressor is very intricate, with three -dimensional complex
intrinsic features; therefore, the level of know -how regarding the detailed aerodynamics of
this type of compressor as part of jet engines, needs an in -depth study, far much rich in
details t han the axial co mpressor [22].

Irina -Carmen ANDREI, Gabriela STROE 10

INCAS BULLETIN, Volume 10, Issue 3/ 2018 3. NUMERICAL SIMULAT ION AND CONCLUSION S
Advancements in numerical simultion methods and e xperimental studies are providing new
insights into the aerodynamics of the centrifugal compressor and are being applied to
increase the compressor’s efficiency as well as the operating range. The challenge of the
centrifugal compressor remains the design of the diffusion system.

Fig. 3 – Schematic diagram of a centrifugal compressor, highlighting the 3D computational domain for the
impeller [22]
The C omputational Fluid Dynamics CFD simulations carried on for the steady -state
represent an essential instrument in the design process of centrifugal compressors systems.
The design of centrifugal compressors involves the use of computational methods in
conjunction with experimental validation to provide precise analysis with a fast turn -around
between design iterations. The difficulty that appears when using computational methods is
the simulation turn over time, which depends heavily on the grid used, boundary conditions
applied (meaning a proper selection of types of boundary layer conditio ns and most adequate
and case tailored distribution of parameter values on the boundaries, both equally important)
and the turbulence model cho sen. Full stage unsteady numerical simulations are usually too
expensive and time consuming for the iterative des ign process , but in certain cases, requiring
high IT system performances, the full stage unsteady numerical simulations can be used for
animations and preparations for complex multidisciplinary laboratories, such as the 3D
Virtual Laboratory, enabling complex studies on this topic. Steady -state models which use a
mixing plane method to model the interface between rotating and stationary domains are
favorite due to the considerably reduced simulation time. However, the importance of
turbulence model cho sen still plays a significant role in obtaing realistic predictions of the
centrifugal compressor performance. The t urbulence models in current use, which consist in
a single equation or a set of non-linear partial differential equations , must be associate d to
the Navier -Stokes equations , in purpose to completely describe the complex features of the
flow, including the effects of viscosity and turbulence. It is very useful to integrate certain
Preparatory Tools in a CFD code, with the intent of computing ti me reducing. In case of the
centrifugal compressor, for both design process and off-design operational performance
analysis, the use of and date management from the Universal Map is compulsorily and very
important. The coordinates of the Universal map are the corrected flow (62) versus the
pressure ratio (63):

11 Computational Study in Centrifugal Compressor

INCAS BULLETIN, Volume 10, Issue 3/ 2018 𝐶𝑜𝑟𝑟𝑒𝑐𝑡𝑒𝑑 _𝑓𝑙𝑜𝑤=𝑀̇𝑎√𝑇1∗
𝑝1∗ (62)
𝑃𝑟𝑒𝑠𝑠𝑢𝑟𝑒 _𝑟𝑎𝑡𝑖𝑜=𝜋𝑐∗=𝑝2∗
𝑝1∗ (63)
𝑆𝑝𝑒𝑒𝑑𝑟𝑒𝑔𝑖𝑚𝑒=𝑛𝑏𝑎𝑟=𝑛̅=𝑛𝑜𝑓𝑓−𝑑𝑒𝑠𝑖𝑔𝑛
𝑛𝑑𝑒𝑠𝑖𝑔𝑛 (64)
As one can easily notice, the surge line is highlighted (in red contour). Speed operation
regime lines reflect the behavior of the centrifugal compressor at off -design regimes, from
idle (50%), up to cruise (95%), design (100%) and maximum (105%). The centrifugal
compressor efficiency domain ranges from 0.65 up to 0.78, the constant efficiency contours
being well represented within the Universal Map field.

Fig. 4 – Universal Map of a centrifugal compressor , where design pressure ratio = 5.9 , [23]
A useful Preparatory Tool was designed following a thorough study with regard to the
construction of the approximation functions for the constant speed regime lines. The
difficulty of such approach, is given by the fact that if the cartesian reference syst em is
considered as corrected flow versus pressure ratio, large errors on pressure ratio will be
introduced for small variation s of the corrected flow, which aspect becomes more evident
with the increase of the speed regime, e.g. over 80%. A more efficien t approach, which also
expels this inconvenient, consists in shifting the coordinates of the cartesian reference
system.

Irina -Carmen ANDREI, Gabriela STROE 12

INCAS BULLETIN, Volume 10, Issue 3/ 2018
Fig. 5 – Universal Compressor Map , expressed as
Pressure ratio and efficiency versus corrected flow
Different study cases were investigated to obtain an optimal design of the centrifugal
compressor, and further, to design the proper control system.
Numerical simulations have been performed for the turbojet engine thrust control. The
variations of the sp ecific thrust [Ns/kg] of the turbojet engine versus the speed regime (64),
for different nozzle exit areas A5 [m^2] are il lustrated in the next diagrams.

Fig. 6 .1 – Numerical simulations for turbojet engine thrust control

Fig. 6.2 – Numerical simulations for turbojet engine thrust control

13 Computational Study in Centrifugal Compressor

INCAS BULLETIN, Volume 10, Issue 3/ 2018
Fig. 6.3 – Numerical simulations for turbojet engine thrust control
The control system is designed such that to take advantage for th e time allowance and to
use slower -responding control elements, and eventually to pr ovide a temperature regulation.
Fuel flow is selected as the rotor speed limiting element , although fuel flow c an be used
for both temperature and rotor speed regulation, o n simple aero engine s.
Over -temperature condition for very short periods, required by engine acceleration or
other transients, can also be accepted.
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