Applied Mathematics and Mechanics

, Volume 2, Issue 2, pp 237–254

# An analysis and calculation on unsteady flow in exhaust system of diesel engine

• Liu Zhao-rong
• Chen Jin-e
Article

## Abstract

In this paper, the unsteady and non-homoentropic flow in exhaust system of diesel engine is analysed and calculated by means of characteristic method. This paper makes proper treatment in calculation, particularly in calculation of boundary conditions, then the calculation program obtained is rather common and the convergence of calculation is faster too. Finally, in this paper, we take exhaust system of 6135 turbocharged diesel engine for an example and make numerical calculation for it, The results obtained are quite satisfactory.

## Keywords

Boundary Condition Mathematical Modeling Diesel Numerical Calculation Industrial Mathematic
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

## Nomenclature

K

ratio of specific heats

pa

reference pressure

p

pressure

u

velocity of liquid

ϱ

density

@

reference sound speed

T

temperature

S

entropy

F

area of cross-section of pipe

C

circumferential length of cross-section

d

hydraulic diameter of cross-section$$\left( { = \frac{{4F}}{C}} \right)$$.

τ0

friction per unit area of wall

q

absorption heat per unit mass and per unit time

λ, β

Riemann variables

aa

sound speed of gas which changes by homoentropy to reference pressurep c

mcr

mass of gas in cylinder when it is released.

M

dimensionless mass$$\left( { = \frac{m}{{m_{cr} }}} \right)$$.

r

dimensionless pressure$$\left( { = \frac{p}{{p_a }}} \right)$$

l

length of piston

α

angle of crank

n

speed of engine

Vc

volume of cylinder

ϕ

effective area of equivalent nozzle; ratio of area of cross-section.

ψ

effective area of air valves; ratio of area of cross-section

## Subscript

c

cylinder

N

turbine

t

throat (air valves or equivalent nozzle)

ex

exhaust pipe

s

air pipe

o

stagnation state

cr

release state

in

input

out

output

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## References

1. 1.
Benson, R. S., et al, A numerical solution of unsteady flow problems,Intern. J. of Mech. Sci., 6, 1, (1964), 117–144.Google Scholar
2. 2.
Benson, R. S., et al, Unsteady flow in simple branch systems,Thermodynamics and Fluid Mechanics Convention, Paper 17, IME, Cambridge. 9–10, April, (1964).Google Scholar
3. 3.
Benson, R. S., et al, Unsteady flow in pipe with gradual or sudden area changes,Thermodynamics and Fluid Mechanics Convention, Paper 16, IME, Cambridge, 9–10, April, (1964).Google Scholar
4. 4.
Wards, W. A., et al, On the selection of a root of a quadratic equation applied to a problem in gas dynamics.J. of Royal Acron. Soc., 69, 655, July (1965).Google Scholar