Ranque-Hilsch Tube Experiments and cfd




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ME 398-Btech-Seminar report:

Ranque-Hilsch Tube Experiments and CFD

By

Preyas Shah

Roll No: 06010017



Department of Mechanical Engineering

INDIAN INSTITUTE OF TECHNOLOGY, BOMBAY

April 2009

Guide: Prof A. W. Date

ABSTRACT

Ranque-Hilsch vortex tube (RHVT) is a long hollow cylinder with tangential nozzle (δ) placed near one end for air injection. It generates stratified streams of cold and hot gas. The flow inside an RHVT is highly turbulent and swirling. This makes measurements difficult and unreliable. Pitot tubes are one of the few reliable instruments used in RHVT experiments. In this report profiles of velocity components, pressure, temperature and more obtained through experiments and CFD are observed. Comparison of works of different authors has been made. The degrading effect of secondary circulation on performance and a possible energy separation mechanism based on it has been discussed. CFD has been used to discuss and verify tangential velocity shear work theory as another possible theory. The various geometric and thermophysical parameters have been optimized for better performance using both experimental studies and CFD. New designs developed by some authors also has been discussed.

Key words: adiabatic expansion, adiabatic compression, CFD, Energy separation, Forced vortex, high radial pressure gradient, maximum cold temperature difference, measurements, optimization, secondary circulation, shear work transfer and stagnation point.


DECLARATION


  1. This text is an original compilation of the literature and is in the student’s own language and not a mere verbatim reproduction of the sources.

  2. The references are listed as per format and are appropriately cited in text, and also in captions of figures and tables thereby acknowledging the source.



Signature and name of student. Roll No.


CONTENTS

Contents



  1. Introduction to RHVT. . . . . . . . . 01

    1. Ranque-Hilsch Vortex Tube (RHVT) . . . . . . 01

    2. Definitions. . . . . . . . . . 01

  2. Experimental work. . . . . . . . . 03

    1. Measurements . . . . . . . . . 03

      1. Setup. . . . . . . . . 03

      2. Pitot tubes. . . . . . . . 03

    2. Experiments. . . . . . . . . . 06

      1. General results and entrance round-off effect. . . . 06

      2. Energy separation: Secondary circulation theory. . . 09

  3. CFD in RHVT. . . . . . . . . . 12

    1. Governing Equations. . . . . . . . . 12

      1. Numerical modeling. . . . . . . 12

      2. Turbulence model. . . . . . . 12

    2. Modeling. . . . . . . . . . 13

      1. Working Conditions. . . . . . . 13

      2. Results of CFD modeling. . . . . . 13

      3. Energy separation: Tangential shear work theory. . . 15

  4. Optimization. . . . . . . . . . 18

    1. Optimization through experiments. . . . . . . 18

    2. Optimization through CFD. . . . . . . . 20

  5. Conclusion. . . . . . . . . . 21



Nomenclature. . . . . . . . . . . 22

References. . . . . . . . . . . . 23

Acknowledgements. . . . . . . . . . . 23


List of tables


  1. Working conditions and major dimensions used in experiments (length unit in mm) [6] 06

  2. General measurement results [6]. . . . . . . . 11

  3. Working conditions for CFD models for different authors [4] [5]. . . . 13

  4. Magnitude of energy transfer for L/D=10 and 30. [4]. . . . . 16

  5. Magnitudes of energy transfer L/D=10, D=12mm [4]. . . . . 17

  6. Results obtained by different authors for different conditions. [3] [8]. . . 18

  7. Working conditions and results of Behera et al (2005) in CFD [5]. . . . 20



List of Figures


  1. RHVT (a) Side view (b) Cross-section view. [6]. . . . . . 01

  2. The flow pattern in an RHVT. [3]. . . . . . . . 01

  3. A general schematic of the experimental setup for RHVT. [9]. . . . 03

  4. (a) Pressure profile and (b) Pressure curve seen by the pitot tube in the RHVT [1]. . 04

  5. Typical pressure distributions over the pitot tube [6]. . . . . 05

  6. Schematic of the pitot tube and its use [6]. . . . . . . 05

  7. entrance conditions [6]. . . . . . . . . 06

  8. Comparison of flow directions at (a) Z/D=1.47 (b) Z/D=2.97 [6]. . . . 06

  9. Mach number components (a) Z/D=1.47 (b) Z/D=2.97 [6]. . . . . 07

  10. Static and Stagnation temperatures in (a) Z/D=1.47 (b) Z/D=2.97b [6]. . . 07

  11. Comparison of dimensionless swirl velocities with varying cold fractions [6]. . 08

  12. Comparison of dimensionless axial velocities with varying cold fractions [6]. . 08

  13. Comparison of dimensionless (a) stagnation (b) static temperatures [6]. . . 08

  14. Variation of rc with yc [1]. . . . . . . . . 09

  15. (a) Mass flux rate as function of r/R at Z=L/2, yc=0.4 [1]

(b) The mass flux rate as a function of r/R at station 2 [6]. . . . . 10

  1. Schematic of primary and secondary circulation [1]. . . . . . 10

  2. Path ∆s and N as function of r/R [1]. . . . . . . . 11

  3. Velocity variation of the tracked particle with axial distance (a) exiting through

the hot end (b) exiting through the cold end after flow reversal [4]. . . . 13

  1. (a) Swirl velocity (b) Axial Velocity (c) Radial velocity profile [4]. . . 13

  2. Pressure of the tracked particle (a) exiting through the hot end (b) exiting

through cold end after flow reversal [4]. . . . . . . 14

  1. Static pressure profile [4]. . . . . . . . . 14

  2. Angular velocity profile [4]. . . . . . . . . 14

  3. Temperature profile of the tracked particle

(a) exiting through the hot end (b) through the cold end after flow reversal [4]. . 14

  1. (a) Static temperature profile (b) total temperature [4]. . . . . 15

  2. Streamlines predicted by the CFD model [2]. . . . . . 15

  3. Energy transfer rate for (a) yh=0.15 (b) yh=0.26 (c) yh=0.35 [4]. . . . 16

  4. Direction and magnitude of heat, axial shear work and tangential shear work transfer [2] 17

  5. Vortex angle generator [11]. . . . . . . . . 19

  6. Heating efficiency profile [11]. . . . . . . . 19

  7. Cooling efficiency profile [11]. . . . . . . . 19

  8. Comparison between concentional and developed vortex tube (VT) [10]. . . 19

  9. (a) Conventional nozzle (b) Developed nozzle [10]. . . . . . 19

  10. Flow pattern for 0.05m length sections at Z/L=0.0374, 0.46, 0.95. [2]. . . 20

  11. Flow pattern through the nozzle [5]. . . . . . . . 20

  12. Th variation with L/D [5]. . . . . . . . . 20



CHAPTER 1: INTRODUCTION TO RHVT

    1. RANQUE-HILSCH VORTEX TUBE (RHVT)



The Ranque-Hilsch vortex tube is a device that generates a hot and a cold flow streams from a common inlet flow stream (see Fig. 1,2). Gas enters the vortex chamber through a nozzle (δ) and moves across the length L of the tube, with high swirl velocity (u) and exits from the periphery of the other end through a diffuser. A control valve or a ‘plug’ is usually fitted to control the gas fractions. A part of the flow reverses at the stagnation point and moves towards the vortex chamber. An orifice plate is generally fitted to decide the cold flow exit diameter. The cold flow cools down by losing heat to the hot stream moving across in the opposite direction. There have been many theories proposed to describe this behavior, but none of them explains it completely. The difficulty associated with measurement within the turbulent swirling flow makes it difficult to verify a theory. From the thermodynamic point of view, the RHVT involves a process in which we have “adiabatic expansion of a part of a gas from higher to lower pressure. The expansion work is transferred to the other part of the gas, which is simultaneously adiabatically compressed, and then after throttling to the same low pressure leaves the system” (Aydin and Baki (2005) [3]). A large radial pressure gradient sets up heat transfer from cold to hot region. Different parameters can be optimized for maximum performance of the tube. Vortex tubes are now used commercially for low-temperature applications like cooling parts of machines, electric or electronic control cabinets, chill environmental chambers, cool food,, nuclear reactors, firemen suits and many more.

Figure 1. RHVT (a) Side view (b) Cross-section view. [6]



Figure 2. The flow pattern in an RHVT. [3]



    1. DEFINITIONS AND CONCEPTS



Coefficient of performance: the amount of heating or cooling effect obtained compared to the electric or other energy input (in this case, is called coefficient of performance. (COP)


Cold fraction: the ratio of cold stream mass flow rate to the inlet stream mass flow rate is the cold fraction. (yc). Similar definition can be made for hot fraction (1-yc).


Cold end exit diameter: the diameter of the flow at the exit of the cold stream is the cold end exit diameter (dc).


Diffuser: a section of flow with increasing area of cross-section.


Energy separation: the energy transfer from the cold to the hot stream is called energy separation


Fhj : the diffusion thermal energy in the xj direction is Fhj


Forced vortex: a vortex with same angular velocity throughout is a forced vortex. The swirl velocity varies linearly with radius.


Free vortex: a vortex with same circulation at every radius is a free vortex. The velocity varies inversely with radius.


Maximum performance: in this context, it means either maximum COP or maximum cold or maximum hot temperature difference or maximum temperature difference between hot and cold end-whichever is specified.


Mach number: the ratio of the speed of gas to the speed of sound in the gas at that point is the Mach number. (M)


Nozzle (δ): a short pipe with varying area of cross-section is a nozzle.


Pitot tube: a thin single or multiple holed capillary used to measure static and dynamic pressures and flow angles in a fluid flow field is a pitot tube.


Radial Stagnation point: the radius where the axial velocity becomes zero is called the radial stagnation point.


Stagnation condition: the condition obtained by isentropically and adiabatically bringing the fluid velocity to zero is called stagnation condition. This condition occurs naturally as seen in pitot tubes.


Swirl (or tangential), radial, axial velocity: the velocities of flow along the tangential direction, the radial direction and paralle to the axis of the tube are the swirl (or tangential), radial and axial velocity respectively. (u,v,w)


ui: the velocity component in the xi direction.


Z/D: the ratio of the distance along the axis of RHVT from its nozzle to its diameter D.


τij : it is the shear stress component in the ij plane.


CHAPTER 2: EXPERIMENTAL WORK

2.1 MEASUREMENTS


2.1.1 SETUP


Rotameters are connected at the inlet and outlet hot and cold ends to measure flow rates. Thermocouples are used for measuring temperatures at the ends. Sensors also may be used for temperature measurements. Pressure gauges are fitted to measure the inlet and exit pressures. Other instruments like pressure diaphragms also may be used. Different vortex generators and types of nozzle may be used in the vortex chamber to generate the swirling flow.




Figure 3. A general schematic of the experimental setup for RHVT. [9]


2.1.2 PITOT TUBES


As mentioned before, measurement is a problem with experiments regarding RHVT, partially being responsible for proposed theories being still in question. Because of strong re-circulating nature of the flow field, invasive measuring instruments affect the entire flow. Laser Doppler methods which involve seeding the flow offer non-invasive alternative for measurement. However this is not possible in this case since the centrifugal accelerations involved are of the order 106g so that all injected particle remain near the wall and do not scatter to the axial regions of the flow. Thus, many times the tried and proven pitot tube is used for measurements. Ahlborn (Ahlborn and Groves, 1997), [1] devised a pitot tube of diameter 1.6mm and a tiny hole of diameter 0.3 mm on the side for measurements in vortex tube of D=25.4mm. It can rotate about its axis and one end is closed. Length of pipe being H, the pipe is entered vertically and passing through the center of the cross-section. Fig. 4a. shows the pressure variation as measured by rotating the pitot tube about its axis. In the experiment, the pitot tube is completely rotated, then shifted back a small distance ∆h along the radius towards the center. The rotation and translation may be coupled together as well. Fig. 4b. shows the pressure trace as seen by the pitot tube.



Figure 4. (a) Pressure profile around the pitot tube

(b) Pressure curve seen by the pitot tube in the RHVT [1]


In Fig. 4a. φ=0 corresponds to the positive axial direction. ps is the stagnation pressure at angle φs, pb base pressure, and pf is the local free stream pressure at the angle φf. pw is wall pressure, used as reference here. Initially measuring hole is set at h=0 ( r ≈ R, at the bottom). Each full revolution shifted the hole by ∆h=1.1mm. 21 measuring points were used across the diameter of the tube. If φm is angle where a peak is detected then,

(1)

and the angle φs between the direction of maximum pressure and positive axial direction is

(2)

where n is the nearest number to full revolutions. If φv is the angle the velocity vector V makes with the z –axis in the plane of the cross-section of the pitot tube,

(3)

Thus, the velocity vector in z-φ plane can be found. Using Bernoulli’s equation,

(4)

The base pressure and free stream pressure are related by the backpressure coefficient .

(5)

Thus we get a measureable (6)

Cp is usually ≈ -1 for laminar flow. So 1- Cp = 2. Then from ideal gas law,

(7a)


by using ideal gas law. ∆p << pf so pf can be approximated as average of ps and pb . Usually radial velocity v << u and w, the tangential and axial velocities respectively. Also it v is parallel to the pitot axis, so it will not affect the stagnation pressure. So,


(7b) (7c)


where is the component of velocity in the plane perpendicular to the pitot axis, which is almost V. This probe yielded consistent direction fields and velocity magnitudes. It had errors of 16% in low velocity region and 21% in higher velocity region. Thus the pitot tube was a good addition to the arsenal of velocity probes for twisted flow fields.


Gao et al. (2004) [6] came up with a similar cylindrical pitot tube. The diameter of the capillary was 1mm and it had a single hole of diameter 0.1mm for vortex tube diameter D=16mm. A similar distribution of pressure is seen in Fig. 5 below as seen in Fig. 4a. Note that the angle is measured from a different reference here.




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