EFFECT OF BLOWING CONDITIONS ON HEAT TRANSFER BETWEEN A GRANULAR BED AND A HEATING SURFACE

A. D. Alekseev, V. I. Osin

(Presented by the scientific seminar of the Department of Processes, Machines, and Apparatuses of Chemical Production)

The aim of the study was to determine the influence of the regime and character of motion of the fluidizing medium on the heat-transfer coefficient \(\alpha\) from the heated surface to the bed. The investigations were carried out in two stages. First, the hydrodynamic characteristics of the bed were obtained for stationary and sinusoidally pulsating types of motion of the fluidizing agent, and the regularities governing the change in the resistance and volume of the bed as functions of the filtration velocity and pulsation frequency were determined.

River sand with a density \(\rho = 2659\ \text{kg}/\text{m}^3\) (fraction \(0.5 \div 1\ \text{mm}\)) was used as the dispersed material. The bulk density of the bed was \(\rho_{\text{sl.}} = 1430\ \text{kg}/\text{m}^3\). The material was loaded into a transparent cylindrical chamber with a diameter of 200 mm and a height of 470 mm. The sinusoidally pulsating character of the air motion through the system was provided by a rotary converter, whose drive made it possible to vary the pulsation frequency from 0 to 25 Hz.

The hydrodynamic characteristics of the bed were determined at air-flow pulsation frequencies \(f = 3.35;\ 6.7;\ 10;\ 16.7\ \text{Hz}\) and time-averaged filtration velocities from 0 to 68 m/s. The corresponding characteristics were obtained when the bed was blown with an undisturbed (stationary) flow.

Figure 1a presents data on the change in volume obtained at an initial bed height \(H_0 = 82\ \text{mm}\) and a total weight of loaded material \(G = 3780\ \text{g}\).

Visual observations established a qualitative difference in the behavior of the bed when it was blown with a sinusoidally pulsating flow. This difference consists in the fact that the stage of expansion (pseudofluidization) of the bed is preceded by its compaction, the magnitude of which depends on the pulsation frequency and filtration velocity. The figure also shows a quantitative difference, manifested in the fact that expansion of the bed occurs at velocities much lower than in the case of motion through it of an undisturbed flow.

Heat-transfer studies were carried out at time-averaged filtration velocities close to \(0.063;\ 0.073;\ 0.1;\ 0.175;\ 0.225;\ 0.38;\ 0.51\) and \(0.58\ \text{m/s}\). The velocity values were chosen on the basis of the results of the study of the hydrodynamics of the bed, taking into account that, at all frequencies, similar states were observed, namely:

a) filtration velocities less than \(0.075\ \text{m/s}\) correspond to the descending curves of bed compaction;

b) velocities close to \(0.1\ \text{m/s}\) correspond to maximally compacted states;

Fig. 1. Effect of the filtration velocity and blowing conditions on the change in bed volume (a) and heat-transfer coefficient (b).
\(H_p\) is the bed height under operating conditions. \(f=0\) — steady flow; \(f=3.35\ldots16.7\) — pulsation frequency, Hz.

c) in the velocity range from 0.1 to 0.175 m/s the bed is expanded, but its porosity is less than the porosity of freely poured sand;

d) velocities greater than 0.175 m/s correspond to various intermediate states of the bed.

The heating element was placed along the axis of the apparatus at a distance of 28 mm from the distribution grid. Thermocouples were arranged in a line at various distances from the heater. Unprotected junctions were located at a height of 41 mm from the grid. During the experiment, the current \(I\) and the temperature in three regions of the bed were measured.

The average values of the heat-transfer coefficient \(\alpha_T\) were determined by calculation using the formula [1]

\[ \alpha_T=\frac{4926\cdot I^2}{85-t_{\text{sl}}}\quad \text{W}/\text{m}^2\cdot\text{deg}. \]

Figure 1b shows the nature of the change in \(\alpha_T\) as a function of the filtration velocity.

From the data presented it is seen that, when a fixed bed is blown with a steady flow (filtration regime), a slow increase in \(\alpha_T\) is observed, caused mainly by an increase in the velocity of the gas washing the heating surface. With the transition of the bed into a fluidized state, the intensity of pulsational mixing of the particles increases and, as a result, \(\alpha_T\) rises more rapidly. The maximum value of the heat-transfer coefficient occurred at a filtration velocity close to 0.68 m/s and at a “fluidization number” of 1.8.

According to [2, 3], the maximum value of the heat-transfer coefficient for a sand bed is about 238 kcal/m\(^2\)·h·deg (205 W/m\(^2\)·deg) and is observed at a “fluidization number” of 1.7–1.9. In our experiments \(\alpha_{T\max}=198.5\) W/m\(^2\)·deg, which practically coincides with the data of other investigators.

It is seen from Fig. 1b that, in the case of blowing sand with an unsteady flow, the dependence \(\alpha_T=\varphi(w)\) has a different character. The heat-transfer coefficient increases sharply even at filtration velocities below 0.1 m/s, which is probably due to a denser arrangement of particles in the bed. In the compacted state, a greater influence should be expected—

…on heat transfer of the thermal conductivity of the material, since the distance between particles decreases, their contact surface increases, and the relative mobility of the particles is small. With an increase in velocity, the rate of growth of \(\alpha_{\mathrm{t}}\) slows down, and after reaching a maximum value its decrease is observed. The maximum value of \(\alpha_{\mathrm{t}}\) under pulsating flow occurs at lower filtration velocities. Thus, at frequencies of 3.35; 6.7; 10 Hz, \(\alpha_{\mathrm{t,max}}\) is observed at filtration velocities of about \(0.5\ \mathrm{m/sec}\), which is 32% less than the corresponding values of the velocity for the steady fluidization regime. At an unsteady filtration velocity close to \(0.25\ \mathrm{m/sec}\) and pulsation frequencies of 3.35 and 6.7 Hz, the heat-transfer coefficient differs little from the maximum for these frequencies. Thus, at \(f=3.35\) Hz and \(w=0.25\ \mathrm{m/sec}\), \(\alpha_{\mathrm{t}}=173\ \mathrm{W}/\mathrm{m}^{2}\cdot\mathrm{deg}\), while \(\alpha_{\mathrm{t,max}}=185\ \mathrm{W}/\mathrm{m}^{2}\cdot\mathrm{deg}\), which occurs at \(w=0.51\ \mathrm{m/sec}\). In this case \(\alpha_{\mathrm{t}}\) decreased by only 6.5%, while the velocity decreased by a factor of two.

At pulsation frequencies of 10; 16.7 Hz and low filtration velocities, the rate of increase of \(\alpha_{\mathrm{t}}\) is more gradual. With increasing filtration velocity the opposite picture is observed. The curves of the dependence of \(\alpha_{\mathrm{t}}\) on \(w\) at higher frequencies occupy an intermediate position between the curve for blowing with an undisturbed flow and fluidization with a pulsating flow at low frequencies. The higher the pulsation frequency, the closer the \(\alpha_{\mathrm{t}}\) curve approaches the heat-transfer curve of the steady regime, which indicates that increasing the pulsation frequency of the gas flow brings the heat-transfer regime closer to steady conditions.

The influence of the pulsation frequency on heat transfer is shown in Fig. 2a, from which it is seen that at filtration velocities below \(0.3\ \mathrm{m/sec}\), the largest values of \(\alpha_{\mathrm{t}}\) occur at a pulsation frequency \(f=3.35\) Hz. With a further increase in velocity, the maximum values of the heat-transfer coefficient shift toward higher frequencies.

Figure 2b shows the effect of pulsating supply on heat-transfer efficiency.

From the data presented it is seen that the maximum value of the coeffi-

Fig. 2. Effect of the filtration velocity and blowing conditions on the heat-transfer coefficient (a) and heat-transfer efficiency (b)

\(\alpha_{0}, \alpha_{\mathrm{n}}\)—heat-transfer coefficients for steady and unsteady conditions; \(f=3.35\ldots16.7\)—pulsation frequency, Hz.

of the efficiency coefficient is observed at filtration velocities below \(0.175\ \mathrm{m/sec}\) and at low pulsation frequencies of the gas flow. This is yet another confirmation of the advantages of pseudo-fluidizing granular materials with a pulsating flow.

Although, as the filtration velocity increases, the values of the heat-transfer coefficient also increase, the relative effectiveness of pulsating action decreases, approaching unity.

Conclusions

1. The chosen research method makes it possible to assess qualitatively and quantitatively the influence of the regime and character of motion of the fluidizing medium on the heat exchange of the bed with the heating surface.

2. The maximum heat-transfer coefficient under pulsating blowing of the bed is achieved at velocities 30% lower, while its numerical values differ little from the corresponding values for a bed blown through by an undisturbed flow.

3. The greatest effect from the use of a pulsating gas flow is observed at frequencies of \(3.35\), \(6.7\ \mathrm{Hz}\) and in the “loosened” state of the bed.

4. The numerical values of the heat-transfer coefficient at low pulsation frequencies change little over a wide range of filtration velocities.

5. As the pulsation frequency increases, the character of the change in the heat-transfer coefficient approaches that under conditions of blowing the bed with an undisturbed gas flow.

References

1. A. D. Alekseev, V. I. Osin. An installation for investigating heat exchange of a dispersed bed with a surface. In the present collection.

2. S. S. Zabrodskii. Hydrodynamics and Heat Transfer in a Fluidized (Boiling) Bed. Gosenergoizdat, Moscow, 1963.

3. N. I. Gelperin, V. G. Ainshtein, V. B. Kvasha. Fundamentals of Fluidization Engineering. Khimiya, Moscow, 1967.