Enhancement of Heat Transfer by Flow Pulsation Randall H. Keill and Malcolm H. 1. Baird2 Chemical Engineering Department, Illc;llaster University, Hamilton, Ontario, Canada
The effect of pulsations in water flow on the overall heat transfer coefficient of a shell-and-tube heat exchanger with steam in the shell has been investigated. The pulsation frequency was 0.4 to 1.1 Hz, and the amplitude could be made large enough to cause periodic reversal of the flow. The heat transfer coefficient enhancement was related to a quasisteady-state model and to the compressed air requirements. The economic feasibility of air pulsation in enhancing heat transfer was discussed.
T h e enhancement of heat transfer by mechanical vibration or fluid-borne oscillation is one of the oldest topics of chemical engineering research. Martinelli and Boelter (1938) reported that heat transfer b y free convection from a cylinder was increased as much as fivefold b y vibration. Since then, substantial research effort has been expended in this area; reviews have been carried out b y Lemlich (1961) and Bergles and Morton (1965). However, as far as is known no major industrial use of vibration or pulsation to enhance heat transfer has been reported. There are two possible reasons for the lack of industrial interest. One is the fear of uncontrollable and damaging oscillations such as sometimes have occurred spontaneously in heat transfer equipment (Cohan and Deane, 1965). The other reason is that, while previous workers have usually found t h a t vibration or pulsation enhances heat transfer, the experiments have been done on a laboratory scale and the results have not provided a basis for economic justification of a plant scale installation. Pulsed heat transfer, as distinct from vibration-assisted heat transfer, has been investigated previously b y a number of different workers. West and Taylor (1952) obtained u p to 70% enhancement of the heat transfer coefficient by pulsing the water feed to a single-tube heat exchanger. A pistondriven pulsator was used, at a frequency of 1.67 Hz. Linke and Hufschmidt (1958) also used a piston unit, and concluded that although heat transfer was enhanced, the additional percentage power input needed was always greater than the percentage enhancement in heat transfer. Darling (1959) and Lemlich and Armour (1965) employed solenoid valve interrupters to generate water flow pulsations. I n this case, the enhancement in heat transfer was partly due to water-hammer effects. Jackson and Purdy (1965) reported interesting local variations of heat transfer in gas streams pulsed a t high frequency, owing to the formation of standing waves. An air-pulsing technique employing no moving parts was proposed by Baird (1967) and has since been tested on a turbulent water flow in a 2-inch pipeline (Milburn, 1969; Milburn and Baird, 1970). The smoothness of the wave-form and the low operating frequency were such that no mechanical vibration or damage to equipment were seen to occur. I n the present investigation, the technique is used to pulse the water flow through the tubes of :t commercial shell-and-tube heat exchanger with steam on the shell side. The observed enhancePresent address, Aluminum Co. of Canada Ltd., Arvida, Que., Canada. To whom correspondence should be addressed.
meiit in heat transfer is compared with theoretical prediction and with the compressed air requirements for the pulsing unit. Theoretical Approach
Previous workers (Lemlich, 1961, and Linke and HufSchmidt, 1958) have used the “quasisteady-state” model, according to which the time-average heat transfer coefficient in pulsating flow is obtained from the instantaneous coefficient calculated from steady-flow relationships. For steady turbulent flow in a tube, the film heat transfer coefficient is of the form:
h
= kU0.8
(1)
where the constant k may be obtained from the Dittus Boelter equation. Let us assume a sinusoidal variation of velocity:
u
=
a(l
+ V sin ut)
(2)
Then according to the quasisteady-state model, the timeaverage heat transfer coefficient is:
Xote that it is necessary to include a modulus sign in the integral t o allow it to have a real value when V exceeds unityLe., when the flow reverses for part of the cycle. The term in square brackets is the enhancement E in the heat transfer coefficient relative to that for unpulsed flow a t the same timeaveraged velocity. Equation 3 can readily be solved numerically, but it has some limitations which should be noted. First, it assumes that Equation 1 is satisfied a t all times; but if the flow reverses (V > 1) , there must be a n interval in which the velocity is so low that the Reynolds number is below 2000. I t is open to speculation whether laminar flow conditions are ever established, or whether the turbulent “history” of the flow persists during the reversal of direction. According to the above model, the exit fluid temperature will vary with time. Stermole and Larson (1963) and Yang (1964) have analyzed the response of a heat exchanger to small sinusoidal flow disturbances (V
