This paper presents a new analytical model of surge dynamics in turbo heat pumps. Turbo heat pumps use refrigerants as the working fluid and consist of a centrifugal compressor, condenser, expansion valve, and evaporator. Compared with a gas turbine engine, the turbo heat pump system introduces additional complexities. First, the turbo heat pump forms a closed-loop system. Second, the system has two plenums, condenser and evaporator, which are coupled to each other. Third, the heat pump runs on a refrigeration cycle with two phases: vapor and liquid. Fourth, heat transfer effects of evaporation and condensation have to be considered. Fifth, unlike air, a refrigerant has strong real gas effects and thus cannot be modeled as an ideal gas. The new model addresses such additional complexities on the basis of the first principles of conservation of mass, momentum, and energy. When applied to a gas turbine system, the new model’s predictions become identical to those from the Greitzer’s model. Furthermore, comparison with the available experimental data shows that the model can also accurately predict surge behavior in actual turbo heat pumps. Finally, the effects of Greitzer’s $B$ parameter and the ratio of evaporator and condenser volume have been examined. Parameter $B$ influences both surge shape and frequency. Finally, surge frequency is extremely sensitive to the ratio of the two plenum volumes.

1.
Greitzer
,
E. M.
, 1976, “
Surge and Rotating Stall in Axial Flow Compressors—1. Theoretical Compression System Model
,”
ASME J. Eng. Power
0022-0825,
98
(
2
), pp.
190
198
.
2.
Greitzer
,
E. M.
, 1976, “
Surge and Rotating Stall in Axial Flow Compressors—2. Experimental Results and Comparison With Theory
,”
ASME J. Eng. Power
0022-0825,
98
(
2
), pp.
199
217
.
3.
Hansen
,
K. E.
,
Jorgensen
,
P.
, and
Larsen
,
P. S.
, 1981, “
Experimental and Theoretical Study of Surge in a Small Centrifugal Compressor
,”
ASME J. Fluids Eng.
0098-2202,
103
(
3
), pp.
391
395
.
4.
Gysling
,
D. L.
,
Dugundji
,
J.
,
Greitzer
,
E. M.
, and
Epstein
,
A. H.
, 1991, “
Dynamic Control of Centrifugal Compressors Surge Using Tailored Structures
,”
ASME J. Turbomach.
0889-504X,
113
(
4
), pp.
710
722
.
5.
Botha
,
B. W.
,
du Toit
,
B.
, and
Rousseau
,
P. G.
, 2003, “
Development of a Mathematical Compressor Model to Predict Surge in a Closed Loop Brayton Cycle
,”
ASME
Paper No. GT2003-38795.
6.
Rothe
,
P. H.
, and
,
P. W.
, Jr.
, 1978, “
First-Order Pump Surge Behavior
,”
ASME Trans. J. Fluids Eng.
0098-2202,
100
(
4
), pp.
459
466
.
7.
Tsujimoto
,
Y.
,
Kamijo
,
K.
, and
Yoshida
,
Y.
, 1993, “
A Theoretical Analysis of Rotating Cavitation in Inducers
,”
ASME J. Fluids Eng.
0098-2202,
115
(
1
), pp.
135
141
.
8.
Kakaç
,
S.
, and
Bon
,
B.
, 2008, “
A Review of Two-Phase Flow Dynamic Instabilities in Tube Boiling Systems
,”
Int. J. Heat Mass Transfer
0017-9310,
51
(
3–4
), pp.
399
433
.
9.
Chi
,
J.
, and
Didion
,
D.
, 1982, “
A Simulation Model of the Transient Performance of a Heat Pump
,”
Int. J. Refrig.
0140-7007,
5
(
3
), pp.
176
184
.
10.
Bendapudi
,
S.
,
Braun
,
J. E.
, and
Groll
,
E. A.
, 2008, “
A Comparison of Moving-Boundary and Finite-Volume Formulations for Transients in Centrifugal Chillers
,”
Int. J. Refrig.
0140-7007,
31
(
8
), pp.
1437
1452
.
11.
Ng
,
E. Y. K.
, and
Liu
,
N. Y.
, 2007,
Compressor Instability With Integral Methods
,
Springer
,
New York
, Chap. 5, pp.
107
123
.
12.
Private communication, LS Mtron, Co., Ltd.
13.
Lemmon
,
E. W.
,
Huber
,
M. L.
, and
McLinden
,
M. O.
, REFPROP, NIST Standard Reference Database 23, Version 8.0, Copyright 2007 by the U.S. Secretary of Commerce on behalf of the United States of America.
14.
Fink
,
D. A.
,
Cumpsty
,
N. A.
, and
Greitzer
,
E. M.
, 1992, “
Surge Dynamics in a Free-Spool Centrifugal Compressor System
,”
ASME J. Turbomach.
0889-504X,
114
(
2
), pp.
321
332
.
15.
,
I. S.
, 1973, “
Speed of Sound in Two-Phase Vapor-Liquid Systems
,”
J. Appl. Mech. Tech. Phys.
0021-8944,
11
(
5
), pp.
778
784
.