Cyclic variations of the swirling flow in a Diesel transparent engine

Abstract

PIV data obtained in a transparent motored Diesel engine are presented and discussed in this paper. These data are obtained in severe thermodynamical conditions in the cylinder during the cycle and in the bowl at top dead center (TDC). Moreover, they are obtained at consecutive cycles. We first consider the flow in the middle of the compression phase. In particular, instantaneous velocity fields are analyzed and classified by computing circulation statistics. We show that the structure of the swirling motion is varying very significantly from “vortex type” to “annular type” from one cycle to another. In-cycle and inter-cycle statistics of these structure fluctuations are discussed. For example, we do not find any cycle-to-cycle correlation. The circulation data are then decomposed by using a proper orthogonal decomposition of the statistical set. The possibility of low order description of this kind of flow is considered. Finally, we study the in-bowl flow at the very end of the compression phase. The quantitative analysis based on circulation statistics show that we still detect strong structure fluctuations of the swirling flow at TDC and that the intensity of these fluctuations have not decreased after the squish phase.

Appendix: list of symbols

1.1 Experimental set-up

θ:

crank angle position

x :

axis between the two intake ports

z :

ascendant axis

S :

stroke

$\bar{V}_{\rm p}$ :

mean piston velocity

V _p :

instantaneous piston velocity

ω:

rotation rate of the engine

b :

cylinder bore

p :

depth of the bowl

d _b :

diameter of the bowl

z _p :

position of the piston crown

ρ:

air density inside the chamber

1.2 Measurements

Δ:

size of the PIV interrogation window

〈 〉:

phase-averaging operator

M :

number of velocity fields per phase

ν_t :

turbulent diffusivity

l :

integral length scale

δ:

characteristic length affected by the turbulent diffusion of momentum

t :

time taken by the piston to move half way

u′:

rms velocity

ρ_p :

particles density

d _p :

particles median diameter

μ_a :

air viscosity inside the chamber

ω _S :

equivalent air rotation rate

N _S :

swirl number

L :

size of the energy containing eddies

τ_e :

engine time scale

τ_p :

particles time response

τ_S :

swirl time scale

τ_t :

turbulent turn-over time scale

τ_Δ :

turn-over time scale of eddies of the size Δ

S _t :

Stokes number

1.3 Physical analysis

U :

instantaneous velocity component along x axis

V :

instantaneous velocity component along y axis

W :

instantaneous velocity component along z axis

U _m :

highest velocity magnitude

W ₀ :

solenoidal velocity component

W ₁ :

velocity component induced by dilatation rate

$\tilde{W}_{0}$ :

spatial average of W ₀

α:

angle between W and U components

Γ:

circulation

Γ′:

centered circulation

A :

centered and reduced circulation

σ _Γ :

standard deviation of the circulation

γ:

contour used in the computation of the circulation

R :

radius of the circle γ

β:

length of the radius of γ

I _Γ :

fluctuation intensity of the circulation

$\mathfrak{I}$ :

normalized correlation coefficient

i :

cycle number

$\delta \mathfrak{I}$ :

statistical uncertainty of $\mathfrak{I}$

I _N :

intercorrelation between cycles

N :

cycle shift

U _n :

realization of the flow number (n) of the velocity vector field

u _n :

fluctuating part number (n) of U _n

${\varvec{\Phi}}^{(k)}$ :

POD mode number (k)

λ^(k) :

POD eigenvalue number (k)

a ^(k) _n :

POD coefficient for the realization number (n) and the mode number (k)

(·, ·):

inner product associated with the square-norm

E :

total kinetic energy of the flow

m :

truncation order of the POD decomposition

σ₁ :

standard deviation of the first POD coefficient

I ₁ :

fluctuation intensity of the first POD coefficient

Γ _n :

circulation of the realization of the flow number (n)

Γ _n ′:

centered circulation number (n)

b ^(k) _n :

normalized POD coefficients

P ^(k) :

correlation coefficient between normalized circulations and POD coefficients

R*:

normalized radius