Investigation of flow and heat transfer at the circular fins

For simultaneous investigation of heat transfer and hydraulic parameters of finned circular tube is proposed to connect PIV (Particle Image Velocimetry) method and thermal imaging with gradient heat flux measurement. In the first series of experiments, the hollow fin was investigated. The hollow fin was heated with saturated water steam and its isothermal surface simulated the ideal (isothermal) fin. The solid fin made of titanium alloy was investigated in similar regimes for comparison. In the second series, the influence of distance between fins on the heat transfer coefficients (HTC) at the circular fin, mounted on a circular cylinder was studied. The unique Gradient Heat Flux Sensors (GHFSs) were installed at different places of the fin surface. Comprehensive method including heat flux measurement, PIV and thermal imaging allows to study flow and heat transfer at the surface of the fin in real time. Possibility of complex study of flow and heat transfer for non-isothermal fins is shown.


Introduction
A number of recuperative heat exchangers use circular tubes whose finning increase their heat transfer surface. There are a lot of finning types and techniques. However, despite wide finning application there is no universal and accurate method for calculation of finned heat exchangers. Distribution of the heat transfer coefficient (HTC) at the surface of the fin is the main problem here [1,2]. It is necessary to ensuring the exact angle between the velocity vector and tube axis [3] and space between fines. Since heat transfer and hydrodynamics are closely interrelated, it is important to study them nonselective. All of the above served as a foundation for present study.
Traditionally heat transfer and hydrodynamics have been studied during separate measurements. There are a lot of techniques and equipment for experimental research of fluid mechanics. For example PIV (Particle Image Velocimetry), hot-wire anemometry are diverse and approved. However, the investigation of heat transfer at different surfaces was troubled by the missing of heat flux sensors with the required response time. Therefore, more often, temperature was measured and HTCs were calculated from similarity equations. For more accurate comparison of flow and heat transfer, a combination of approaches that includes simultaneous measurement of heat flux per unit area and HTC using unique gradient heat

Investigation method
Since the experience includes several complex technologies, it is necessary to explain the specifics of each of them separately.

Heat flux measurement
Heat flux per unit area was measured by the unique GHFSs with response time of 10 -8 … 10 -9 s. GHFSs have been developed, created and integrated into the laboratorial and industrial experience at "Thermophysics of Power Units" department of Peter the Great St. Petersburg Polytechnic University since 1996. Such a small response time of GHFS makes them practically inertialess instrument for study of most heat transfer types [4,5,6]. Figure  1 shows the scheme (a) and the general view (b) of the battery GHFS based on bismuth single crystals, which were used in our experiments. The choice of GHFS type was due to low surface temperatures and small temperature drop. Fig. 1, c shows three GHFSs mounted at the circular fin. The action of GHFS is based on Seebeck's transverse effect: when a heat flux passes through a plate with anisotropy of thermophysical and thermoelectric properties, thermopower arises proportionally to heat flux value. We used 5 sensors for our experiments; the dimensions of three GHFSs in plan were of 2 × 2 mm, the fourth sensor was of 4 × 7 mm, and the fifth one was of 5 × 5 mm. All sensors were of 0.2 mm thick; their volt-watt sensitivity was about 10 mV/W. GHFSs were mounted with a special compound with high thermal conductivity. Wires soldered to the GHFSs were led along the fin and the cylinder and attached to the cylinder surface at some points with a glue. Additionally, in selected range of regimes, the velocity did not exceed 15 m/s.

PIV method
PIV technology made it possible to visualize the flow near the surface of the fin by non-invasive method which allows to record instantaneous velocity fields in plane of the laser sheet. Principle of any PIV system operation is that tracers are fed into the air flow: fine particles (with a diameter of 2 … 3 μm) which are illuminated by laser beam reshaped by lens system into the laser sheet. In our case, the supply of tracers was provided by fog machine. A digital camera fixed the image of tracers at moments of double flashes. Our POLIS system [7,8] renders possible to adjust supply of tracers and the frequency of photographs under the flow regime. All photos were processed in ActualFlow program which gives the velocity field for each time step. Correlation methods of image processing to obtain particle shifts were used.

IR imaging
To measure temperature of the fin, we used thermographic camera FLIR P640. Software of it allows to produce powerful temperature analysis and automatic reporting. In addition, the camera has several aiming points, which allow us to measure temperature at the places where GHFSs were installed.

Experimental model
The first model of finned cylinder of 66 mm in diameter and of 600 mm in length was made of a steel sheet of 0.1 mm thick. Two circular fins with external diameter of D = 146 mm were mounted at the cylinder. The first fin was hollow, and it simulated "ideal" (isothermal) fin, and the second was made of titanium alloy with thermal conductivity about k = 9 W/(m×K). The second model of the finned cylinder was made similarly, but the outer diameter of the fins was of 186 mm. The GHFSs were mounted at the fins surface ( Figure 2). Both models were heated with saturated water steam under the atmospheric pressure; therefore cylinder temperature was close to 100°C. The cylinder was turned around it's axis which allowed us to move the sensors in circumferential direction.
For the "ideal" fin surface temperature TW = const for all 0 ≤ φ ≤ 180 o (Fig. 2, a), and for the fin made from a titanium alloy, TW depends on the fin height and the angular coordinate: The experiments were carried out in subsonic wind tunnel (Fig. 3) of "Thermophysics of Power Units" department of Peter the Great Saint Petersburg Polytechnic University. • The heat exchanger (cooler) connected to the cold water supply system ensures long operation of the tunnel in air, which practically does not change its temperature (the spread of the values is ± 0.1 °С).
• Eiffel camera allows to use PIV system without appreciable dispersion of tracers.

Results
Research was carried out for Reynolds number where Waverage air flow velocity, m/s; d -diameter of cylinder, m; ν -kinematic viscosity of air, m 2 /s. Dependence of average (over the fin's length) HTC on Reynolds number for isothermal (a, c) and non-isothermal (b, d) fins of different heights is shown at Fig. 4. Here it can be seen that HTC decreases in interval of φ = 120 ... 180 °. This can be explained by the fact that nature of flow is such that behind the midsection of the cylinder a vortex is formed, and there is a stagnant zone near the cylinder.
(qφ -local heat flux per unit area, W/m 2 ; Tf -air flow temperature, K; Tw -surface temperature, K) Flow temperature was measured by the multifunction tool testo-435-4 and fin surface temperature sensed by IR imaging.
Local heat flux per unit area was measured by GHFSs and equal to: (E -thermopower, mV; S0 -volt-watt sensitivity, mV/W; F -GHFS area, m 2 ) Signal E was measured with a digital voltmeter. The sensitivity was known according to predetermined calibration with measurement uncertainty of 1,3 % [11]. With a non-cross flow around a "small" edge, a vortex is formed and increases with increasing of yaw angle.
Also, proposed method allowed to obtain three-component fields of HTC. For example, Fig. 8 shows three-component distribution of HTC for non-cross flow. Since flow is not symmetrical, the figure shows the distributions of HTCs at the overtype (I) and undertype (II) surfaces of the fin. To verify the obtained data, the heat flux at various points was measured 2…3 times. Our work repeats the studies [9,10,18] in its methods, however, use of thermal imager makes it possible to solve the problem connected with the investigation of heat transfer at any nonisothermal surface [19,20].

Conclusions
The proposed technique, including superposition of gradient heat flux measurement, PIV diagnostics and thermal imaging, allowed to study flow and heat transfer at the surface of a