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Introduction
Regenerator is a regenerator gas chiller core component of their work
For performance will directly affect the overall performance. Regenerator is equipped with a high mesh
The number of large heat capacity of metal mesh, in the refrigerator during the hot and cold working
Alternating air flow in order to fill mesh as an intermediary to achieve flow of hot and cold
Between the heat exchange, so that played a regenerator cold storage and recovery of the
Role, and establish a refrigerator cold-side (cavity) and the hot-side (cavity) of the
Very large temperature gradient. Usually require regenerator heat transfer efficiency
More than 99%, otherwise the work of a direct impact on chiller performance.
Stirling Cryocooler regenerator packing in the gas flow is three-dimensional
Unsteady flow process. As the Stirling refrigerator inside the gas delivery
Variable flow process to bring the issue of Thermodynamics and Kinetics of coupling, while
Because rapid reciprocating ejector movements and tightly filled regenerator filler,
Regenerator caused by lack of access to the performance and structure of size, condition and other related
Impact of information on the relationship, these are right back to bring Experimental Study of Heat
Difficulty I3. Refrigerator at low temperature, the regenerator of the basic packing
Requirements are: to ensure there is sufficient heat recovery capacity, access to small temperature difference heat transfer
Requirements; to provide adequate air gap channels to accommodate the gas flow or
Pressure wave propagation needs. Regenerator heat transfer element is also a resistance
Components, heat and momentum transfer and conversion process is interactive,
To obtain accurate and irreversibility inside the regenerator the size of the rational design of low -
Refrigerator temperature have a major impact '.
In this paper, the small Stirling refrigerator regenerator to establish the theory
Model, by controlling non-dimensional equation processing and reasonable Jane
Of deduced characterization of small Stirling refrigerator recuperator irreversible
Nature of entropy flow equation. This can be quantitatively to obtain a small Stirling refrigeration
Machine regenerator irreversibility on optimal design and performance improvement machine
Of great significance.
A theoretical model and governing equations
Heat a small Stirling refrigerator back to the physical model shown in Figure 1
Knife.
,, L ^
■ - ◆
Hot chamber
■ - ◆
Cold chamber
Figure 1 Physical model of a small Stirling refrigerator schematic
(Gas flow of traffic along the arrow direction is positive, otherwise negative)
Can be simplified further in order to build meaningful mathematical model
Type, do the following assumptions:
(1) The working fluid is ideal gas, and the specific heat capacity as a fixed value;
(2) regenerator isotropic, and the regenerator packing grid are
Uniform distribution;
(3) Fill a rigid incompressible, packing coefficient of thermal diffusion
Flow is much larger than the thermal diffusion coefficient;
(4) The flow Mach number M 10, far less than the length of the regenerator gas
Flow acoustic wavelength;
(5) the quality of regenerator packing flow is much greater than one cycle of the
Air quality.
In all state and motion parameters indicated both volume and volatility is too
The amount of the sum of conditions, return to heat flow and the filling inside the control equation
As follows:
+ (Lu mu) = 0 (1)
p Sin + lD (mu) = 1 V P +) (2)
(+ Lost p (mu house)) +
(p clouds [c + 1 (cloud)】 1 I) I 1) = 0 (3)
Pmc Police = (4)
In fluid contact interface with the filler, =, =
.
Two equations dimensionless and Simplification
Mechanical engineering research in the power field, a problem, affect the
Tend to have a number of elements, which are composed of a certain form based on the amount of some
Dimensionless quantity criteria can be used to simplify the problem of similarity theory study
It also made findings also have greater versatility, which leads to
Dimensionless research methods, theory of the method according to dimension.
To take along the regenerator length of the integral average time-average pressure p,
Integral average temperature of the state when both the corresponding volume as a reference state,
On the density, pressure, temperature and material parameters etc. dimensionless Office
Reasonable time period t to compress the piston movement as a reference r, the speed of "
L / r as a reference to non-dimensionless. It should be clear is that, Ray
Novo qualitative measure of the number of filler wire thickness d, set X, sub -
Do not relative L, d non-dimensional coordinates of the space. Considering the whole regenerator
A length of the pressure gradient with 0 (1) of the order of magnitude, from the momentum equation
Viscous forces can be drawn items also have 0 (1) magnitude, combined with the previous
Assume that conditions may include:
Lu testosterone =-o (1) (5-A)
Chu =: 0 (1) (5.B)
Then the right equation (1) 1 (4) for non-dimensional, then it can get
(For the convenience of writing, there is no longer right after the dimensionless parameters
A few other mark):
M (Ot +) + (= 0 (6)
eP u = 1 E (P +) +
(U) + o (M) (7)
(P: () +. (1) (8)
Police = (poison) +. ((9)
The use of perturbation method to simplify the above equations were solved, all the amount of
Exhibition for the M's series, namely,
u = u '. + M u '+ M u' +? (10 1 A)
lD = lD '. + M lD '+ M lD' +? (10 1 B)
P: P '. + M P '+ M P' +? (10 1 C)
= '. + M T '+ M T' +? (10 1 D)
The above equation generation equation (6) (9), and take the zero-order
Items available.
(| D '.'.) = 0 (11)
P '∞ = 0 (12)
R (1D (0) T) = (such as T '.) (13)
= ((· 4)
So, are:
P '∞: P'. (X, t) (15 1 A)
'∞
: T '. (X) (15 1 B)
lD '∞ = lD'. (X, t) (15 1 C)
'∞
= 0 (15 1 D)
The equation (10) and (15) on behalf of the people equation (6) (9),
And to take a first-order items available:
o
a
p (o)
at +. The case of a X +. '∞ +.
R '. 』D '" = 0 (16)
. '
= 1 special (+ p (n) +
.
u
'
= 0 (17)
To the average x coordinate scales, which is defined type as follows:
AU = I dA (18)
'
Of equation (16) for integration, combined with the boundaries u = 0
Constraints, may have
Ku +: 0 '
Following the introduction of only depends on the time scale instantaneous R and screen
d of the space vector and non-dimensional pressure P, has the following definition of formula:
= 0 '(20 1 A)
= U (20 1 B)
R = a p + V 2 v (20.C)
Taking into account flow in the filler wall of the no-slip boundary condition and flow
The amount of normalization conditions may include:
』GTdA = A (21)
Joint equation (20 1 A), (20 1 B), (20 1 C), (21)
And (17) can be:
p (1) + swine chip =
Of equation (22) along the regenerator length two locations
n, b be points may include:
(6-n) = (1)) I (23)
Noting friction factor = 1 R 1
1 ∞
p
b South "I = 0, so:
1 fu (24)
The P change is limited, the amount of packing space coordinates for the X-scale integration
Total sense, even under the conditions, the friction factor can be a number of steady-state
Experience laminar flow formula, then the zero-order one-dimensional equations (for
The convenience of eliminating the need for angle S) is:
+ = 0 (25)
OP
= 1 fu (26)
T = T () = P / p (27) '
So that the cold chamber and hot chamber for a given regenerator pressure, temperature side
Bounded case is a very easy to solve the equations.
3 regenerator entropy calculation
Stirling refrigerator for liquid nitrogen temperature range, using the working fluid is helium
Gas. Can be used as an ideal gas processing. Than the entropy formula as follows: