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Group-based multiple pipe routing method for aero-engine focusing on parallel layout

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Abstract

External pipe routing for aero-engine in limited three-dimensional space is a typical nondeterministic polynomial hard problem, where the parallel layout of pipes plays an important role in improving the utilization of layout space, facilitating pipe assembly, and maintenance. This paper presents an automatic multiple pipe routing method for aero-engine that focuses on parallel layout. The compressed visibility graph construction algorithm is proposed first to determine rapidly the rough path and interference relationship of the pipes to be routed. Based on these rough paths, the information of pipe grouping and sequencing are obtained according to the difference degree and interference degree, respectively. Subsequently, a coevolutionary improved differential evolution algorithm, which adopts the coevolutionary strategy, is used to solve multiple pipe layout optimization problem. By using this algorithm, pipes in the same group share the layout space information with one another, and the optimal layout solution of pipes in this group can be obtained in the same evolutionary progress. Furthermore, to eliminate the minor angle deviation of parallel pipes that would cause assembly stress in actual assembly, an accurate parallelization processing method based on the simulated annealing algorithm is proposed. Finally, the simulation results on an aero-engine demonstrate the feasibility and effectiveness of the proposed method.

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Abbreviations

2D, 3D:

Two- and three-dimensional, respectively

CIDE:

Coevolutionary improved differential evolution algorithm

CVG:

Compressed visibility graph

DE:

Differential evolution

PSO:

Particle swarm optimization

Re :

Reynold number

SA:

Simulated annealing algorithm

SVGAS:

Surface visibility graph with adaptive strategy

VG:

Visibility graph

B i :

Length of the ith bending pipe segment

CR :

Crossover rate for DE

D :

Inner diameter of pipe

D i :

Distance between endpoint and its effective projection point

d 1, d 2, d 3, d 4 :

Minimum projection distance from one pipe segment endpoint to other segments

d int :

Interval distance set for discrete pipe path

d P :

Distance between two pipes

d s :

Extension distance of starting port

d t :

Extension distance of ending port

e j :

Energy value of the jth grid cell

F :

Scaling factor for DE

f c(x):

Generatrix function of engine casing

f d :

Distance between pipes and engine casing

f dif :

Difference degree value of two pipe routes

f i :

Fitness value of the ith individual

f L :

Length of the whole pipe

f P :

Parallelism degree value

F b :

Expected value for parallelization processing

F m :

Fitness value of multiple pipe

F Mi :

Fitness value of all pipes in the ith pipe group

f PS :

Pressure drop of fluid in straight segment

f PE :

Pressure drop of fluid in elbow pipe segment

F S :

Fitness value of single pipe

F Si :

Fitness value of the ith pipe

K :

A constant with large value

L coin1 :

Projection overlap length of S1 to S2

L coin2 :

Projection overlap length of S2 to S1

L coinj :

Projection overlap length of the jth segment to the segment with maximal parallelism degree

L E :

Visible edge set

L i :

Length of the ith straight pipe segment

L p :

Projection overlap length of one pipe to the other

L S :

Start point set of CVG

L S1 :

Length of pipe centerline Si

L S2 :

Length of pipe centerline S2

L V :

Exploration vector set

M :

Difference degree matrix

M i,j :

Difference degree of two pipes with index of i and j

N E :

Number of all effective projection points

N G :

Number of grid cells that one pipe passes through

N S :

Number of straight pipe segments in a pipe

NP :

Population capacity of DE

P :

Penalty term of single pipe evaluation function

P r :

Random number between 0 and 1

P c :

Reference value for random number Pr

P i :

The ith endpoint of the pipe segment

P′i :

The effective projection point corresponding to Pi

r 1, r 2 :

Radius of pipe1 and pipe2

R :

Representative individual pool

R B :

Bending radius of pipe

ST :

Exploration vector constructed by points S and T

SV i :

Exploration vector constructed by points S and Vi

S :

Starting point in visibility graph

T :

Ending point in visibility graph

ū :

Average velocity of fluid

U G :

Trail population under the Gth iteration

U i,G :

The ith individual of UG

u j i, G :

The jth variable in Ui,G

V G :

Mutant population under the Gth iteration

V i,G :

The ith individual of VG

v j i,G :

The jth variable in Vi,G

x′, y′:

Coordinate components of the projected vertex in 2D space

X G :

Population under the Gth iteration

X i,G :

The ith individual of XG

x j i, G :

The jth variable in Xi,G

X G,max :

Upper limit of individuals

X G,min :

Lower limit of individuals

X rand1,G, X rand2,G,X rand2,G :

Three nonrepetitive individuals randomly selected from XG

z i :

Coordinate component of the ith discrete point

α i :

The ith bending angle of one pipe

γ :

Volumetric weight of fluid

δ min :

Minimum clearance distance between two parallel pipes

δ max :

Maximum clearance distance between two parallel pipes

ρ i :

Distance between the ith discrete point and engine casing axis

θ P :

Included angle of two pipes

ρ, θ, z :

Cylindrical coordinate components of the spatial point

λ :

Friction factor of fluid

ω 1 :

Weight coefficient of fL

ω 2 :

Weight coefficient of fPS + Jpe

ω 3 :

Weight coefficient of fS

ω d :

Weight coefficient of dP

ω e :

Weight coefficient of ej

ω p :

Weight coefficient that reflect the contribution of the pipe clearance and the projection overlap length to difference degree

ω L :

Weight coefficient of Lcoinj

ω θ :

Weight coefficient of θP

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Acknowledgements

This work was supported by the Fundamental Research Funds for the Central Universities, China (Grant No. N2003025) and the Major Projects of Aero-engines and Gas Turbines, China (Grant No. J2019-I-0008-0008).

Author information

Authors and Affiliations

  1. School of Mechanical Engineering and Automation, Northeastern University, Shenyang, 110819, China

    Hexiang Yuan, Jiapeng Yu & Hui Ma

  2. Key Laboratory of Vibration and Control of Aero-Propulsion System (Ministry of Education), Northeastern University, Shenyang, 110819, China

    Jiapeng Yu & Hui Ma

  3. Shenyang Engine Research Institute of AECC, Shenyang, 110015, China

    Duo Jia

  4. School of Information and Control Engineering, Liaoning Petrochemical University, Fushun, 113001, China

    Qiang Liu

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  1. Hexiang Yuan
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  2. Jiapeng Yu
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  5. Hui Ma
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Correspondence to Jiapeng Yu.

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Yuan, H., Yu, J., Jia, D. et al. Group-based multiple pipe routing method for aero-engine focusing on parallel layout. Front. Mech. Eng. 16, 798–813 (2021). https://doi.org/10.1007/s11465-021-0645-3

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  • DOI: https://doi.org/10.1007/s11465-021-0645-3

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