Purdue University
Purdue e-Pubs International Compressor Engineering Conference
School of Mechanical Engineering
1996
CFD Studies of Flow in Screw and Scroll Compressors N. Stosic City University
I. K. Smith City University
S. Zagorac DRUM International
Follow this and additional works at: http://docs.lib.purdue.edu/icec Stosic, N.; Smith, I. K.; and Zagorac, S., "CFD Studies of Flow in Screw and Scroll Compressors" (1996). International Compressor Engineering Conference. Paper 1103. http://docs.lib.purdue.edu/icec/1103
This document has been made available through Purdue e-Pubs, a service of the Purdue University Libraries. Please contact
[email protected] for additional information. Complete proceedings may be acquired in print and on CD-ROM directly from the Ray W. Herrick Laboratories at https://engineering.purdue.edu/ Herrick/Events/orderlit.html
CFD STU DIE S OF FLO W IN SCR EW AND SCR OLL COM PRE SSO RS N. Stosic and I. K. Smith, Professors1 Depa rtmen t of Mechanical Engin eerin g and Aeron autics! City University! Londo n ECl V OHB1 U.K.
S. Zagorac, DRU M Intern ation al1 Edwa rd St Work s Tong St 1 Bradf ord BD4 9SH1 U.K.
ABS TRA CT An analysis of flow in rotary positive displacement machines has been carrie d out using a stand ard CFD package by separ ating out the motio ns of the fluid and the instan taneo us volume in which it is contained. Examples are given of both twin screw and scroll compressors. Pressure-volume diagrams obtained from such analyses are comp ared with exper imental result s and good agreement shown. Longer term aims of such studies are to obtai n a bette r under stand ing of the intern al flow processes, especially where two component flow, such as oil/ai r mixtures are involved.
INTR ODU CTIO N This paper describes the first stages of a longer term proje ct to obtai n great er under stand ing of the natur e of fluid flow withi n rotary positi ve displaceme nt machines such as those of the screw and scroll type. The great est need for such impro ved under stand ing is where there is more than one flow component as in oil inject ed compressors. In such cases, the assum ption s normally made on oil and gas separ ation withi n the machines may thus be checked. Flow of fluid in a rotary positive displa ceme nt compressor is unsteady, three-dimensional, turbulen t and compressible. Its analysis may be simplified if a grid is defined to describe the instan taneous volume of fluid trapp ed in the mach ine and the motio n is described first in terms of the fluid relati ve to the grid and then of the grid itself. By this mean s fluid motio n throu gh all compressors of this type may be analysed with stand ard nume rical proce dures. The flow of the fluid relati ve to the grid may be calcu lated using
a nume rical proce dure, but with the grid motion replaced by exter nal body forces on the fluid. Altho ugh the grid is continuously in motio n and changing in shape , its geom etry may be defined at all times and its motio n described 181
by simultaneous translation and rotation. Thus the grid acceleration is calculated for each time step and included in the momentum equation terms while all other terms in the equation would be unchanged. The result is the same as would be obtained if a general moving grid was built into the numerical procedure, but such a procedure would be more complex, and would require the use of more advanced CFD solvers than those currently in use. Available CFD packages usually contain a preprocessor, which prepares a grid for the solver to integrate equations and a postprocessor which conveniently present results calculated. Despite their sofistication, commercial preprocessors can barely cope with any unusual shapes and, despite its simplicity, this appears to include screw and scroll compressor geometry. Our attempts to use commercial preprocessors to generate proper grids for screw and scroll compressor working chambers flow calculations failed. Finally we reprogrammed part of a general grid generator and applied it succesfully to produce grids to perform the calculations presented in this paper.
BASIC EQUATIONS By use of mass averaged Navier-Stokes equations, the continuity equation may be written as:
where p and U; are density and velocity, while the momentum equation may be expressed as:
_ a ap au; au; p-a + pUj-a =--a +-a [p.S;j- puiuj + pa;] t
Xj
X;
Xj
s-- _au;+ auj tJ -
axj
ax;
_ ~auk 5 __ 3 OXk
tJ
where S;j denotes for the strain, p the pressure, pu;uj the Reynolds stress, k turbulent kinetic energy and f.L is a fluid dynamic viscosity.
1
-. lS ?,PUiUi
the
The total velocity is the sum of the transfer (grid point) velocity Bxd 8t and the velocity relative 2 2 to the grid Ui. Transfer acceleration is given as a; = xd8t . Forces caused by the grid motion are implemented into the source terms in the same maner as other external body forces, as for
a
example, gravity force. In the absence of heat sources the transport equation for internal energy E is given as:
aE Pat
8E
8Ui
aU; -] 8 [ p. 8E . . - peuj - p.S;j-a -Pr -a X X,
· +-a + pUj-a x 3. X, x · = p-a 1
182
3
where Pr is Prandtl number. The turbule nce model implem ented is a plane k- c: model with no addition al terms.
o(pc:) at
+ o(pUjc:) axj
= CdPk: _- pCe:z c:z
k
k
+ _!_ axj
[(f.t + ()""f.lt)
oc: axj
l
where c is the turbule nt energy dissipation, Pk = 2f.l,tSijSij for turbule nce energy product ion, f.lt = pCI-Lk 2 jE: is a turbule nt viscosity and O" is a turbule nt Prandtl number . Reynolds stress and turbule nt heat flux are given as: _
f.tt
aE
peu·= - 2 Pr OXi Constan ts of k- c: turbule nce model are: Cjl.
= 0.09, o-k =
1, O"e:
= 1.3, Ce1 = 1.44, C,z = 1.92
Standar d wall functions are implem ented on all walls, and a standar d constan t pressure ary condition was used at all flow faces.
bound~
NUME RICAL SOLUT ION PROC EDUR E The standar d 3d finite volume colocated grid numeric al procedu re "Fastes t" [1], [3] was employed to obtain numeric al solutions. The force terms arising from the grid motion were added to the momen tum equatio n source terms. This part of the numeric al procedu re was most conveniently introdu ced through user defined functions. The SIMPL E pressur e procedu re was adapted to ac~ count for fluid compre ssibility by means of an equaton of state with a pressure correcti on correction transpo rt equatio n of a mixed convection~diffusion type [2].
CALC ULAT ION OF SCREW COMP RESSO R FLOW Fig 1 present s a screw rotor mesh generat ed by the adopted grid preprocessor. Fig 2 shows how the male and female rotor passages were created by the same preprocessor. One block, contain ing 2420 control volumes, was constru cted for each passage and the multigr id procedu re was used to obtain a final solution. Initially, two grids of control volumes were tried and the second grid used contained 38720 control volumes. The full multigr id procedu re required less than one minute per unit time step, using a P166MHz worksta tion, and a full cycle calculation was perform ed in less than six hours. The results obtaine d were ploted by the "Fastes t" postprocessor in the form corresponding to experim ental 183
and velocity results which were used to validate numeric al calculations. Absolute velocity vectors vectors relative to the grid are present ed Fig 3. and The screw compressor flow thus calculat ed has been partiall y validate d experim entally comparative results in the form of a pressure-volume plot are shown in Fig 4.
CALC ULAT ION OF SCROL L COMP RESSO R FLOW used to An outline of a scroll compressor configuration is shown in Fig 5 togethe r with the grid 384 control describe it. The grid is comprised of two blocks, namely: the discharge passage with rale block is volumes and the interspi ral chmabe r with 600 control volumes. In Fig 6 the interspi were very presented in the third grid comprising 38400 control volumes. Compu ter perform ances similar to those obtaine d for the screw compressor. grid in Velocity vectors in the grid coordin ate system and the absolut e velocity values for the in Fig 8. motion are given in Fig 7. Finaly, a pressur e history for the scroll compressor is given
CONC LUSIO NS history in As may be seen, the agreem ent between the only quantit y measured, the pressur e It is hoped the screw compressor chambe r and its estimat ed counter part was reasona bly good. any type of that further development of this techniq ue will enable the flow charact eristics within new insights rotary positive displace ment machin e to be modelle d accurat ely and thereby lead to ly, lead to into :flow within them. This should be a useful tool in compressor design and, hopeful would be designs with improved performance. Also a more detailed measur ments of velocity field appreciated for a thoroug h comparison with calcula ted data.
REFER ENCE S
geome[1] Schafer M, Stosic N, 1994: Parallel multigr id calculations of turbule nt flows in complex tries Proc. World CFD User Conference Basle 1 Switzerl and Thesis 1 Uni[2] Stosic N, 1982: Numeri cal modelling of internal flows of compressible fluid, PhD versity of Sarajevo
[3] -
1995: Fastest: Parallel Multigr id Solver for Flows in Complex Geometries: User Manual
Lehrstuhl fiir Stromun gsmech anik 1 Universitiit Erlangen-Niirnberg1 German y
184
Fig 1 Screw roto r mesh
'!
-
;::_ I
-
'!.; __ _
1;/j /___ _
It/- ----
'~ ;1: ~-- ,__
----
~~ ,___ --- \ 0 Y/ ;;::/ ~...-_~----~ ''-...
Qj
/_ '1'\
'~ ~'!;;I1/;,, ~I/ ' ? ;1/\JII -'/ / j//i Jl' 'lf//jl' ~---//I I! I
0
1--'
:-,'
"-'
\ \ l ! r , ___ ,_,
I "'',\\11 ... _, \' . . . . . . . ,, "'·-\'-·I .._ ' ' ' " ' I'.·
\ '''--;I \.'-! '' '
-
--._ -
r
15.0
"'-
I
12.0
-
=-:'': - . : . --
'
'L' 0
e ~
..
6.0
il ~
"4.0
~
~
ll.O -400
-200
()
v 200
IJ
!
4ll0
500
Rotor ongle (deg)
Fig 7 Calculated velocity vectors in relative (grid) coordinate system and for the stationary (absolute) coordinate system
Fig 8 Calculated pressure changes in a scroll compressor
