14.2. Coefficient of flow deceleration.
Generally
wing, horizontal and vertical tail installed onto fuselage will be
flown with speed differs from speed of incoming flow
.
It occurs due to influence of viscosity and to appearance of head
shock waves at
.
Coefficient of flow deceleration
is used for the account of this effect, which is a ratio of mean
dynamic pressure before a considered aircraft element to dynamic
pressure of undisturbed flow
:
;
;
,
(14.1)
where
- dynamic pressure of undisturbed flow;
,
,
- dynamic pressure before a wing, horizontal and vertical tail-plane.
If assumes,
that density
and pressure
,
we shall record:
,
,
.
At known
coefficient of flow deceleration the mach number
before an aircraft element is determined by the following formulas:
,
,
.
These numbers are necessary for taking into account at calculation of the aerodynamic characteristics of the isolated parts.
For
example, lift of a wing and its drag depend on
,
.
Let's
consider the process of flow deceleration. An the beginning we shall
study flow about a wing (horizontal tail), located on a fuselage. In
a subsonic flow (
)
speed deceleration before a wing for the normal configuration and
before horizontal tail for the canard configuration occurs only in a
boundary layer on a part of a fuselage located ahead of a wing or
horizontal tail. Taking into account, that the thickness of a
boundary layer
is much less than wing span or tail span, it is possible to assume
,
,
.
Fig.
14.1.
(Fig. 14.1). Flow rate decreases behind the shock wave. The
amount of flow deceleration coefficient depends on intensity of the
shock wave. In turn, intensity of the shock wave depends on wave drag
of the fuselage nose and number
.
Approximately it is possible to adopt that:
.
Fig. 14.2.
Let's consider the case, when the wing and horizontal tail are located on the fuselage. For such configuration the leading lifting surface can effect onto flow deceleration before the trailing lifting surface.
Deceleration is occurred due to of viscosity (trailing lifting surface getting into an aerodynamic trail) at and, in addition, behind the shock wave from the trailing lifting surface at (Fig. 14.3). Here it is necessary to distinguish the aircraft normal configuration and canard configuration.
Fig. 14.3. Influence of trailing lifting surface: a) - normal configuration; b) - canard configuration; c) - field of speeds behind the wing.
Let's determine thickness of a boundary layer in an aerodynamic trail behind the wing for the normal configuration
,
where
and
- geometrical parameters of the semispan of horizontal tail
(Fig. 14.3).
If
,
then tail-plane (wing) does not fall into an aerodynamic trail caused
by wing (horizontal tail). In this case, for the normal configuration
we receive
at
,
at
,
where
- coefficient of flow deceleration behind a system of shock waves
from the fuselage nose and wing,
.
At
horizontal tail falling into an aerodynamic trail from a wing (
)
we shall have
at
,
at
.
where
- factor, which characterizes flow deceleration in an aerodynamic
trail behind the wing.
In the canard configuration the coefficient of flow deceleration before a wing is determined under the formula
,
where
factor
.
Multiplier
at
and
at
.