IASME/WSEAS International
Conference in Fluid Mechanics (Fluid 2004)
Corfu Island, Greece Aug.17-19-2004
I
Computational Study of Three-Dimensional Non-Steady Steam Supersonic Pressure Exchange Ejectors
KHALED ALHUSSAN* and CHARLES GARRIS**
* Research Assistant Professor, Space Research Institute, KingAbdulazizCity for Science and Technology, P.O. Box 6086Riyadh11442, KSA
** Professor, Mechanical and Aerospace Engineering Department, GeorgeWashingtonUniversity, 801 22 Street N. W., Washington DC, USA
Abstract:-The work to be presented herein is a Computational Fluid Dynamics investigation of the complex fluid mechanisms that occur inside a non-steady, three-dimensional, supersonic pressure exchange ejector, specifically with regard to the pressure exchange mechanisms and the induction processes between a “driving” primary fluid and a “driven” secondary fluid using steam as working fluid. It is the purpose of this research to study from the computational perspective the complex non-steady flow processes and induction mechanisms within a supersonic pressure-exchange ejector, how they relate to overall ejector performance, and to obtain fundamental design information which would allow this technology to be utilized in many applications such as in ejector refrigeration systems. If this new concept in ejector technology based on non-steady flow processes can be shown to be viable, the impact on refrigeration and air conditioning in the commercial, automotive, and residential sectors would be enormous and would enable environmentally benign refrigerants such as water to replace the harmful CFC’s, and reduce the effluence of greenhouse gases by reducing fuel consumption through the use of waste heat and improved efficiency.
The investigation of a supersonic pressure exchange ejector using computational fluid dynamics has provided additional insight into the concept. This study has provided some insight into the complex flow phenomena that occur inside the supersonic pressure exchange ejector.
Results utilizing contour plots of total enthalpy, absolute Mach number, and static pressure showing the actual behavior of the steam supersonic pressure exchange ejector are presented. In this research, computational study is used to show how the aerodynamics flow is managed to provide the desirable flow induction characteristics of steam supersonic pressure exchange ejector.The adiabatic efficiency of the steam ejector is important, and this research shows that the adiabatic efficiency is as high as 23%.
Key- Words: Ejector, Pressure Exchange, Ejector Refrigeration, CFD.
1
Nomenclature
Symbol Meaning
Ps Static pressure
Pe Exit static pressure
Pts Total pressure of secondary fluid
Ptp Total pressure of primary fluid
Tts Total temperature of secondary fluid
Ttp Total temperature of primary fluid
T Temperature ratio of the primary fluid to
secondary fluid
Mass flow ratio of secondary fluid to
primary fluid
d Adiabatic Efficiency
1 Introduction
All the attempts to improve the ejector performance have involved variations on the conventional design of the steady-flow ejector. The physical principle upon which this ejector operates is that of entrainment of a secondary flow by an energetic primary flow by virtue of the work of turbulent shear stresses. Thus, the relatively low-energy secondary flow is dragged by the relatively high-energy primary flow through tangential shear stresses acting at the interface between the two contacting streams. These turbulent stresses are a result of mixing that occurs between primary and secondary streams and the consequent exchange of momentum.
While this mechanism is quite effective and has been widely adopted in many applications, an inherent characteristic of the mixing process is the dissipation of valuable mechanical energy. This results in a substantial entropy rise, which is intimately connected with ejector performance and consequently, refrigeration system performance[1-4].
On the other hand, the pressure-exchange ejector offers the possibility of attaining a breakthrough in the level of performance of ejectors by means of utilizing non-dissipative non-steady flow mechanisms [5-6].
Unlike the steady flow conventional ejector, the non-steady pressure exchange ejector is designed to utilize an entirely different physical principle, which is based on the pressure exchange phenomenon. Pressure exchange utilizes the reversible work of interface pressure forces, which exist only in non-steady flows. This mode of energy exchange is inherently non-dissipative. The utilization of this mode of energy-transfer is of interest, because of its potential to produce high efficiency [7-10]. The overarching goal is to create a flow induction machine which utilizes the work of interface pressure forces available in non-steady flows through direct contact of two fluids.
Pressure exchange is a designation applied to any process whereby contiguous fluid bodies or flows exchange mechanical energy through the work of mutually exerted pressure forces at their interfaces [11]. Pressure exchange cannot take place in steady flow, because no work is done by pressure forces acting on a stationary interface [12]. Therefore, pressure exchange is always a non-steady process.
An ejector is a direct contact flow induction device, which exchanges mechanical energy and momentum between a high-energy primary “driving” fluid and a relatively low-energy secondary “driven” fluid to produce a discharge of an intermediate specific energy level. The transfer of momentum gives rise to an increase in the stagnation enthalpy of the secondary fluid and enables the ejector to function as a compressor [13-15].
The work to be presented herein is a Computational Fluid Dynamics investigation of the complex fluid mechanisms that occur inside a non-steady, three-dimensional, supersonic pressure exchange ejector, specifically with regard to the pressure exchange mechanisms and the induction processes between a “driving” primary fluid and a “driven” secondary fluid [16].
This research is based upon utilizing a non-steady flow field resulting in the work of pressure forces acting at a fluid interface between primary fluid and secondary fluid. These interfaces are produced through the aerodynamic design of a flow field, non-steady in the laboratory frame of reference, consisting of rotating oblique shock waves and expansion fans. Minimizing the possible losses from the oblique shocks and boundary layers offer the potential of achieving adiabatic efficiencies approaching those of turbo-machines[5-6 & 17].
A number of important conclusions follow from the current research. Study of the actual flow configuration inside the complex three dimensional supersonic pressure exchange ejector offers some insight into the complex flow phenomena that occur inside the ejector. Designing the aerodynamic flow structure, that produces the right environment for pressure exchange to take place, for the supersonic pressure exchange ejector that generates a high adiabatic efficiency about 25% for steam as working fluid. Adiabatic efficiency is related to both the ratio of mass flow rate and the ratio of temperature of secondary fluid to primary fluid [2 & 18]. The efficiency of the energy exchange is increased if it is made to take place, at least in part, through the non-dissipative work of interface pressure forces.
2 Computational Fluid Dynamics Analysis
The flow induction in the supersonic pressure exchange ejector is so complex that there exist direct fluid-fluid interactions, oblique shock waves, expansion fans, slip surfaces, and shock wave interactions and reflections. The flow is non-steady, viscous, compressible, and high-speed supersonic.
The governing equations are a set of coupled nonlinear, partial differential equations. In order to formulate or approximate a valid solution for these equations they must be solved using computational fluid dynamics techniques. To solve the equations numerically they must be discretized. That is, the continuous control volume equations must be applied to each discrete control volume that is formed by the computational grid. The integral equations are replaced with a set of linear algebraic equations solved at a discrete set of points.
CFX-TASCflow is used in the current research to model the flow in the supersonic pressure exchange ejector. The CFD code is an integrated software system capable of solving diverse and complex multidimensional fluid flow problems. The fluid flow solver provides solutions for incompressible or compressible, steady-state or transient, laminar or turbulent single-phase fluid flow in complex geometries. The code uses block-structured, non-orthogonal grids with grid embedding and grid attaching to discretize the domain. The code system has additional capabilities that can predict subsonic, transonic and supersonic compressible flows, including temperature solutions in solid regions of the domain for laminar or turbulent flow.
CFX-TASCflow is a finite volume method, but is based on a finite element approach of representing the geometry. Thus, the method used here possesses much of the geometric flexibility of finite element methods as well as the important conservation properties of the finite volume method.
It should be possible to model the interaction of the shock waves and expansion fans around the rotating vanes and describe how the secondary flow is drawn into the interstices. It should be possible to study the mutual deflection and pressure exchange processes between primary and secondary flows using the CFD analysis.
A numerical analysis must start with breaking the computational domain into discrete sub-domains, which is the grid generation process. A grid must be provided in terms of the spatial coordinates of grid nodes distributed throughout the computational domain. At each node in the domain, the numerical analysis will determine values for all dependent variables such as pressure and velocity components.
Creating the grid is the first step in calculating a flow. A 180-deg sector was chosen to model the flow. The grid is refined near the surface of the vanes in order to model the large gradient in that region. For computation, a Mach Number of 3.0 is used as the Nozzle Exit Mach Number. Solution parameters and fluid properties are defined in the parameter file. For the steady-state solution, the time step is selected equal to 0.00001. The advection discretization scheme selected is the Modified Linear Profile Skew scheme with the Physical Correction. The convergence criterion is 10E+04 and the maximum number if iteration is 300. The maximum number of iteration is increased form 300 to 1000 to allow the solver to run until a converged solution is found.
A computational model that illustrates the physics of flow induction through non-steady shock waves and expansion fans was developed. This provides strong insight into the mechanisms through which the supersonic pressure exchange ejector operates.
Through this computational analysis, a better interpretation of the physical phenomenon of the non-steady pressure exchange ejector can be achieved. The results from the numerical analysis are used to study the flow structure inside the complex geometry of the pressure exchange ejector and to develop a design methodology so as to predict optimal ejector performance.
3 Scope of the Analysis
It is computationally possible to study the real behavior of the supersonic pressure exchange ejector. A complete investigation of the actual behavior of the flow inside the supersonic pressure exchange ejector is analyzed. The assumptions in this analysis are listed below:
A)Free spinning rotor.
B)Steam as working fluid.
C)Isentropic expansion of primary flow inside the primary nozzle.
D)Matching the static pressure at the discharge nozzle.
E)Steady flow in the rotor frame of reference.
F)Laminar flow.
G)Compressible and viscous flow.
H)Initial guess:
1-using a coarse grid for the first run then improving the solution with a finer grid.
2-starting with subsonic flow, increasing to low-speed supersonic flow and finally to the high speed supersonic flow (Mach number=3.0).
I)Real flow boundary conditions that specify total pressure and total temperature for the inlet conditions and static pressure for the outlet condition.
4 Discussions
Water is an excellent refrigerant, which has a high latent heat of vaporization, a high specific heat, good heat transfer characteristics, non-corrosive, and is totally in harmony with the environment. However, for normal air conditioning applications, the specific volume of water vapor under operating conditions must be hundreds of times larger than that of a system using CFC’s under comparable environmental conditions and design requirements. Water as a refrigerant, when used with a positive displacement type compressor, requires a much larger compressor displacement volume. The need for a much larger compressor, and the associated increased cost, has rendered water less desirable as a refrigerant for conventional air conditioning. However, this problem can be resolved by the use of an ejector, which is capable of transporting large volumes of vapor within a relatively small space and at a low cost [6].
It is an objective of this research to provide an ejector refrigeration system with a Coefficient of Performance considerably higher than that of the conventional steady flow ejector and approaching that of the ideal turbo-machinery standard. The pressure-exchange ejector utilizes a non-steady flow principle to obtain higher adiabatic efficiencies than conventional ejector while retaining much of the simplicity of construction and the low manufacturing cost of a conventional ejector [5-6 & 17].
Advantages of the Pressure-Exchange Ejector in Refrigeration Systems:
1-The pressure-exchange ejector could benefit the environment by reducing pollutants at their source.
2-The pressure-exchange ejector retains much of the mechanical simplicity of conventional steady flow ejector.
3-The pressure-exchange ejector could be amenable to the utilization of environmentally benign refrigerants such as water instead of chlorofluorocarbons.
4-This ejector is capable of compressing high specific volume vaporized refrigerants with an ejector of reasonable size and cost.
5-Since this ejector refrigeration system uses a boiler, which could be energized by waste heat instead of a compressor, the emissions of undesirable greenhouse gases, i.e., carbon dioxide (CO2), nitrous oxide (N2O), methane (CH4), etc., could be reduced considerably.
Fig.1: Basic Ejector Refrigeration System
A basic ejector refrigeration system is shown in figure 1.A pump discharges condensate to a boiler/superheater that releases energetic primary vapor to the ejector. The ejector draws secondary vapor from the evaporator and discharges it to the condenser. The condensate from the condenser is divided between the pump inlet and the expansion means that supplies cool vapor/liquid to the evaporator.A high-energy primary fluid compresses a lower energy secondary fluid through direct fluid-fluid momentum exchange.
It can be shown [1-2], that the COP for a basic ejector refrigeration system is given by:
Equation1
where COP is the Coefficient of Performance, the ratio of energy extracted from the evaporator to the energy provided in the boiler/superheater and the pump; is the ratio of secondary mass flow rate to primary mass flow rate; ha, hb, hd, hf are the specific enthalpies at points a, b, d, and f in the system as indicated in figure 1.
Equation 1 shows that with the system operating at prescribed evaporator, condenser, and superheater conditions the COP is directly proportional to the ratio of the ejector secondary mass flow rate to the ejector primary mass flow rate. This ratio is commonly known as a fundamental figure of merit for the flow induction efficiency of an ejector. Hence, the higher the ratio of secondary to primary mass flow rates, the higher the COP [19].
The performance of the ejector is a controlling factor in determining the performance of the refrigeration system. This has been recognized in the literature with many attempts at improving the ejector performance [6].
The efficiency of an ejector is closely connected with the entropy generation processes occurring within it. The operating principles of a conventional steady-flow ejector result in two major sources of entropy generation: turbulent mixing and strong normal shock waves.By means of the pressure-exchange ejector that utilizes physical mechanisms which produces modest entropy rises, a substantial improvement over conventional technology is possible.
The advantage of the pressure exchange process is that, even accounting for shock losses, the entropy rise can be small. Post-pressure-exchange mixing will incur a much smaller entropy rise than would have occurred with primary-secondary mixing in a conventional ejector, since the energy levels in the former are nearly equalized by pressure exchange [6].
It can be shown [2 &18] that the ejector efficiency is defined as:
Equation2
From this equation, one can see that increasing the mass flow ratio, , of the ejector will result in increasing the overall adiabatic efficiency d. Remember that increasing the ratio of the mass flow rate of the ejector also will result in increasing the COP of the refrigeration cycle. Thus one can conclude that the higher the adiabatic efficiency, the higher the COP.
5Results
The domain of interest is a complex, three-dimensional, bounded conical shape. The flow is non-steady and compressible. In this situation, one should expect oblique shock waves, expansion fans, shock wave interactions, and slip surface generation.
The previous discussion demonstrated that steam makes an excellent working fluid for the pressure exchange ejector. In this paper a numerical analysis was conducted to study the actual behavior of the steam supersonic pressure exchange ejector. The effect of temperature ratio was also investigated.
Figure 2 shows the absolute Mach number for steam as working fluid. This figure shows the contour plot of absolute Mach number for planes passing over the vanes. The oblique shock wave was designed to be a weak one and extend to touch the top surface of the leading edge of the vane, as shown in figure 2.
Fig. 2: Contour Plot of Absolute Mach Number for Steam Ejector, Planes Passing Over the vanes