Method and Apparatus for Determining the Heat Transfer Characteristics of a Tube

The present invention is related to a measuring and testing apparatus, and more particularly to a measuring and testing apparatus which will measure the heat transfer and frictional resistance characteristics of a tube such as used in a water-tube heat exchanger.

Apparatus has been provided to determine heat conductance of tubes. A review of the prior art apparatus and methods is provided in an article in "Condenser Biofouling," 1980, by J. G. Knudsen, Prof. of Chemical Eng., Oregon State University, Corvallis, Ore.

The present invention is directed to an apparatus for measuring the heat transfer characteristics of a tube through which a liquid such as water is passed. There is associated with the tube a heater which includes a block of heat conducting material, as aluminum, which is clamped to the exterior of the tube being tested along a portion of its length, which is the test section. This block has associated with it an electric heater. To measure the heat flux, there are embedded in the block, at different radii from its internal face, a pair of temperature probes, such as a pair of thermistors. Water is forced through the tube, passing through an entrance section in advance of the test section, from a pump which has its discharge connected to one end of the tube and its inlet connected to the other end of the tube, there being a bypass circuit with a motorized control valve in it around the pump, so as to by-pass a variable amount of water from the pump. The tube is insulated, and a small electric heater is placed on the tube, beneath the insulation, between the end of it and the heating block. Ports are provided in the tube on either side of the heating block, and a pressure drop sensor is connected to the ports. A flow meter is provided to measure the rate of water flowing through the tube.

Preferrably, the measuring devices provide output signals, which are converted, where necessary, to digital signals, which are fed to a computer. The computer calculates the total heat transfer resistance, the convective heat transfer resistance and the conductive heat transfer resistance, thereby providing an indication of the reduction in thermal efficiency of the tube due to build-up of contaminants on the interior wall of the tube, this being accomplished together with a calculation of the friction factor of the tube.

FIG. 1 is a schematic view, partly diagrammatic, of an apparatus in accordance with the present invention.

FIG. 2 is a schematic diagram of the interface circuitry which couples the measuring apparatus to the computer.

FIG. 3 is a diagram of the thermistor amplifier.

FIG. 4 is a diagram of the circuit for controlling the motorized by-pass valve.

Referring now to the drawings, wherein like or corresponding parts are designated by like or corresponding reference numerals throughout the several views, there is shown in FIG. 1 an apparatus 10 in accordance with the present invention, the apparatus 10 including a tube 12 which is of heat conducting material, and of conventional construction as used in tubular heat exchangers. The tube 12 may, for example, be a sample tube of the same alloy as in a particular tubular heat exchanger, for use as a specimen for various test purposes, or may be a new alloy, being tested.

A pump 14 is provided, having its outlet connected by a conduit 16 to the inlet end of the entrance section of the tube 12, the outlet end of the tube 12 being connected by a conduit 18 to the inlet of the pump. A bypass conduit 20 bypasses the pump 14, and has therein a valve 22 controlled by a motor 24. Alternatively the valve can be in series with the pump and test section. In the conduit 18 there is a flow meter 26 of known construction which produces pulses in proportion to the velocity, and therefore the rate, of water flow through the closed circuit, including particularly the tube 12.

The pump 14 may be a separate pump forming a part of the test equipment, or may be the pump of a power plant or the like; in that case, the tube 12 is mounted in the power plant, in series with the tube of the heat exchanger, and thereby receives water from the same pump which forces water through the tubes of the heat exchanger.

The tube 12 is provided with one or more thermometers 28a, 28b, herein illustrated as being of the electrical type and called thermistors. Thus, the output of the thermometers 28a, 28b is in the form of an electrical analog signal.

The tube 12 is covered over the entry section, in advance of the test section, with insulating material 30, beneath which is an electrical heater 32 which is connected to a suitable source of electricity by the contacts 34. The heater 32 serves to create a fully developed thermal gradient in the water flowing through the pipe 12 to the test section as described below.

In order to make it possible to measure the thermal resistance to the introduction of a large quantity of heat into the water in the tube 12 in a short period of time, there is provided a high thermal conductivity radial heat flow concentrator; i.e. a heating block 40 which is of a suitable heat conducting material, such as aluminum. The block 40 is preferrably annular, having an inner cylindrical face which is in engagement with the exterior surface of the test section of tube 12. The block 40 is preferrably made in two or more parts, so that it may be releasibly clamped onto the tube 12. To measure heat flux into the tube 12, embedded in the heating block 40 are a pair of thermistors 42 and 44, which are located at different radii from the axis of the heating block 40, and are therefore at different distances from an electric heater 46 which is placed in surrounding relationship to block 40 and is connected to a suitable source of electric energy through the contacts 48.

To determine the pressure drop of the water flowing in the test section of tube 12 there are provided ports 52 and 54 on either side of the block 40 and adjacent thereto, conduits 56 and 58 connecting the ports to a differential pressure transducer 60 of known construction, having an analog output proportional to the noted pressure drop.

Where the word "water" has been used herein, it will be understood that this is the liquid that is most commonly dealt with, it being recognized that other liquids also may be caused to flow in heat exchanger tubes, and cause contamination or fouling of them. The most commonly used medium is water, however, and water is known to have various impurities in it, both of mineral materials, and biological materials. Mineral materials may include various salts, carbonates, sulfates, sulfites, etc., as is well known. Either type material may be found in the water of a particular installation, or it may be possible that both types of fouling materials may be found in a particular installation. A layer of fouling material which has as its source biological materials is known as biofilm, and a layer or coating which is of mineral or innert matter is known as scale.

Both biological fouling and scaling result in reduced heat exchanger efficiency, and it is known that the resistance of a tube to conductive heat transfer is different, to a marked degree, when biofilm is present, compared to scaling.

By utilizing the value of the pressure drop and the flow rate, it is possible to determine the friction factor by the following well known formula: ##EQU1## where f is the friction factor,

d is the inside diameter of the tube 12,

p is the differential pressure between ports 52 and 54,

L is the length of the tube 12 across where the pressure drop is measured,

.rho. is the density of the fluid directed through the tube 12, and

v is the average fluid flow velocity through tube 12.

The value of Reynold's number, N.sub.Re, is determined by the following known formula: ##EQU2## where N.sub.Re is the Reynold's number,

.mu. is the dynamic viscosity of the fluid

d is the inner diameter of the tube through which the fluid flows,

.rho. is the density of the fluid, and

v is the average fluid velocity through the tube.

Utilizing the values of temperature from the thermistors 42 and 44, and the value of the bulk water temperature from 28a and 28b, the total heat transfer resistance can be calculated using the following known formula: ##EQU3## r.sub.i is the radius at 42 and r.sub.ii is the radious at 44, T.sub.b is the bulk water temperature,

T.sub.i is the temperature at 42 and T.sub.ii is the temperature at 44,

k is the thermal conductivity of the block 40,

q is the heat flux radially inward in the block,

l is the length of the block, and

ln is the natural logarithm function

Where the liquid is not water, the temperature viscosity relationship is determined from standard reference sources.

The convective heat transfer resistance, is calculated from the values of the friction factor f using the following known formula: ##EQU4## where U.sub.cv is the convective heat transfer resistance,

f is the friction factor,

C.sub.p is the specific heat of the fluid directed through the tube 12,

R is the thermal conductivity of the fluid directed through the tube 12,

.rho. is the density of the fluid,

v is the average fluid flow velocity, and

.mu. is the dynamic viscosity of the fluid directed through the tube 12.

Since the total heat transfer resistance is the sum of the conductive heat transfer resistance and the convective heat transfer resistance, by subtracting the value of the convective heat transfer resistance from the total heat transfer resistance, the conductive heat transfer resistance is obtained.

Preferrably, the values of pressure drop, water flow rate, heat flux input to tube 12 and the water temperature, are realized as electrical signals, proportional to the physical characteristic being determined. In the case of the flow meter, the output will be in pulses, and in the case of the other measurements, the output is an electrical signal which is an analogue of the value measured, and in that case, the electrical output analog signals are converted to digital signals, and then all signals are fed to a suitable computer, the output of which may be by a video readout, printout, etc., and the computer may be used to perform functions, such as regulating the by-pass valve.

Referring again to FIG. 1, the differential pressure transducer 60 is connected by conductor 102 to a modulator-demodulator 104, which is connected by a conductor 106 to an analog multiplexer 110. Thermistor 28a is connected by conductor 112a to a thermistor amplifier 120, and thermistor 28b is connected by conductor 112b to the amplifier 120. Conductors 114 and 116 connect the thermistors 42 and 44, respectively, to the transistor amplifier 120, and the latter is connected by conductors 118a, 118b, 118c and 118d to the analogue multiplexer 110. The output from analog multiplexer 110 is connected by conductor 122 to an analog-digital converter 124, the output of which is connected to the computer 130 by a conductor 126.

The flow meter 26 has a pulse output, as is well known, and this output is provided by a conductor 128 to a pulse counter 132, the output of which is connected to the computer by conductor 134. Alternatively a magnetic flow sensor can be used which has an analog signal output. A real time clock 136 is connected to computer 130 by conductor 138. A data storage output 140 is connected to computer 130 by conductor 142 and there may be provided a keyboard input 144 connected to computer 130 by a conductor 146 and a video output 150 connected to the computer 130 by a conductor 148. The output of the computer may, through conductor 152, be directed to control switching 154 which is connected by conductor 156 to the motor 24 of bypass valve 22.

Computer 130 may be an Apple II, and may be programmed in accordance with the below described program, although it will be understood that any equivalent computer may be used.

Referring now to FIG. 2, there is shown an interface circuit whereby the various sensors including the thermistors 42 and 44, the differential pressure transducer 60, the thermometers 28a and 28b, the counted pulses derived from the flow meter 26 are input to the computer 130. Generally, the computer 130 is interconnected to a parallel peripheral interface 166 whereby inputs and outputs are made to and from the computer 130. The A0-A9 and C output terminals of the computer 130 are coupled by an address bus 164 to the parallel pheripheral interface 166, whereby corresponding address signals are applied by bus 190 to the analog multiplexer 110, whereby one of the inputs as obtained from one of the formentioned thermistors 42 and 44 and thermometers 28a and 28b is applied selectively to the computer 130. In particular, the bus 190 includes a timing or setting signal applied by line 190a through an inverter to a set input of a flip flop 168. Further, digital signals are applied via lines 190b to instruct the analog multiplexer 110 to select the output of but a single temperature sensor in accordance with the signal input applied thereto. Further, the address lines 190c apply a digital signal to instruct the bypass valve 22 whether to open or to close, thereby increasing or decreasing the flow through the tube 12. As illustrated in FIG. 2, the selected or multiplexed analog output is applied to the A/D converter 124 to be converted to corresponding digital signals which are applied by a parallel bus 191 to port A of the parallel pheripheral interface 166 and therefrom by a data bus 160 to the computer 130. In similar fashion, the series of pulses outputted by the flow meter 26 is applied to the digital flow meter pulse counter 132, which counts the inputted pulses to provide a digital output indicative thereof; the counter output is applied via parallel bus 193 to the parallel pheripheral interface 166 and therefrom via the data bus 160 to the computer 130. The counting of the output pulses from the flow meter 26 is under the control of a computer clock as taken from its output and applied to series connected dividers 172 and 174 to apply a timing signal of a defined period to one input of a NAND gate 176, whereby the output pulses of the flow meter 26 are applied to be counted by the counter 132 for that period, e.g., approximately 7.5 second, corresponding to when the output of the divider 174 goes high. Thus, the counter 132 provides a digital output indicative of the counted pulses during the defined period via a bus 193, the parallel pheripheral interface 166 and the data bus 160 to the computer 130, the number of pulses for a defined period of time being indicative of the flow rate through the tube 12. The flip flop 170 is also connected to the output of the divider 174 to provide a reset signal to the counter 132 and to provide an advance or timing signal to the interrupt input INT of the computer 130. The flip flop 168 provides a necessary interface between the analog to digital conversion as effected by the A/D converter 134 and the program to ensure that outputs are applied in discrete timing periods to the computer 130. The A/D converter 124 provides at the end of its conversion operation an output appearing on its EOC terminal indicating that an analog to digital conversion has been completed; the EOC output is applied to the clock CLK input of the flip flop 168. Upon the addressing of the analog multiplexer 110, an output is also applied via line 190a to set the flip flop 168. Upon the addressing of the analog multiplexer 110, an output is also applied via line 190a to set the flip flop 168. Thus if the A/D converter 124 completes its processing, its EOC signal will clock the flip flop 168 causing its Q output to go high telling port B that a digital input is also available at port A of the parallel peripheral interface 166. A voltage reference source 178 is connected to an available 12 volt terminal, to provide a stable reference voltage to the A/D converter 124. In an illustrative embodiment of this invention, the parallel pheripheral interface 166 is a circuit as manufactured by Intel Corporation under their designation number 8255, the counter 132 is manufactured by the Motorola Corporation under their designation number 14553, the A/D converter 124 is manufactured by the Motorola Corporation under their designation number 14433, the analog multiplexer 110 is manufactured by the Motorola Corporation under their designation number 14051, the dividers 172 and 174 are manufactured by the Motorola Corporation under their designation numbers 14020 and 14040, the flips flops 168 and 170 are manufactured by the Motorals Corporation under their designation number SN74LS74, and the voltage reference source 178 is manufactured by National Semiconductor under their designation number LM399.

Referring now to FIG. 3, there is shown a circuit for linearizing the output of each of the temperature sensors including the thermometers 28a and 28b, and the thermistors 42 and 44. It is understood that the circuit of FIG. 3 is interconnected between a temperature sensor and its input to the analog multiplexes 110. In particular, each of the aforementioned temperature sensors is comprised of thermistors 182 and 184, that are coupled by a shielded cable 185 to an operational amplifier 180, as manufactured by National Semiconductor Corporation under their designation number LM324. The plus input of the operational amplifier 180 receives a reference voltage as established by a resistance bridge comprised of potentiometer R1, resister R2 and resister R3. The negative input of the operational amplifier 180 is coupled to a potentiometer R5 and resister R4, as well as to the shielded cable 185. In a manner well known in the art, the potentiometer R5 establishes the zero potential, whereas, potentiometer R1 establishes the range of temperature input signals. Resisters R6 and R7 are connected in circuit with the shielded cable 185 and the operational amplifier 180 as shown in FIG. 4, to thereby compensate for the inherent nonlinearity of the thermistors 184 and 182.

The address and control signals of lines 190c are applied to the motor valve control circuit 24' as shown in FIG. 4 and in particular to the inputs of NAND gates 193 and 194. A logic circuit is formed by the NAND gates 193, 194 and 192 as shown in FIG. 4 to provide outputs to optical couplers 196 and 198, illustratively taking the form of couplers manufactured by Motorola under their designation numbers MOC3010. Firing outputs are developed by the optical couplers 196 and 198 and are applied respectively to the firing terminals of each TRIAC 1 and 2, whereby the TRIAC are rendered conductive to apply an alternating voltage, e.g. 110 volts AC, to the selected motor winding 24a or 24b of the reversible, induction motor driving the bypass valve 24 as shown in FIG. 1. Illustratively, the bypass valve motor may take the form of that induction motor as manufactured by W. W. Graingers as under their number P/N 2Z813. For example, upon the firing of the TRIAC 1, the coil 24a is energized to close the bypass valve 24, thus increasing the fluid flow through tube 12. Conversely, when the TRIAC 2 is fired, its winding 24b is energized, whereby the bypass valve is opened, thus reducing the fluid flow through tube 12. If a binary signal 1,1 is applied by line 190c to the valve control circuit 24', a low going signal will be applied to the optical coupler 196, whereby TRIAC 1 is fired and its winding 24a is energized. On the other hand, if a digital signal 1,0 is applied to the valve control circuit 24', the optical coupler 198 fires TRIAC 2 and energizes the winding 24b.

The computer 130, as shown in FIG. 1, has a programmable storage area in the form of a random access memory (RAM) that is programmed to access the various variables as discussed above, including the fluid flow as obtained from the flow meter 26, and the values of temperature as obtained from the thermometers 28a and 28b, and from the thermistors 42 and 44, and to effect a series of calculations in accordance with the formulas, as given above. To this end, the RAM of the computer 130 is programmed with a program, a listing of which is provided as follows: ##SPC1##

Particular attention is drawn to lines 300 to 595 of the above given program listing wherein the primary data gathering and calculating steps of the program are set out. In particular, on program line 350, an instruction is provided to be executed by the computer 130 to sample the temperature sensors including the thermometers 28a and 28b, and the thermistors 42 and 44, each of the sensors providing outputs identified by a letter T(0) to T(3) in the listing. As explained above, the computer 130 provides a digital signal via the address bus 164, the interface 166 and the bus 190 to direct the analog multiplexer 110 to access serially the forementioned sensors, their temperature values T(0) to T(3) being stored in known RAM locations. Next, as indicated beginning at program line 395, the output of the differential pressure transducer 160 is accessed and a digital indication of the pressure difference is stored in RAM. Similarly at line 430, the output of the counter 132 is accessed and a computation at line 440 is effected, whereby the flow rate in meters per second is calculated and stored in a known RAM location. Next, beginning at computer line 450, the heat transfer coefficient, i.e., the reciprocal of the total heat transfer resistance 1/U.sub.tot as defined above, is calculated at program line 455, where T(0) indicates the stored value of the bulk water temperature as measured by the thermometer 28a, T(1) indicates the water temperature measured by the thermometer 28b, T(2) and T(3) indicate the values of temperature as measured respectively by the thermistors 42 and 44, and "RFLOW" is the measured value of flow rate as obtained from the counter 132. Thus, program line 455 indicates that the heat transfer coefficient is calculated from the aforementioned values and thereafter restored in a known RAM location. Next, at computer line 460, the friction factor "f", as set out above, is calculated. Program line 465 indicates that the friction factor "f" is computed as a function of the pressure drop as measured by the transducer 60, and the square of the fluid flow as derived from the flow meter 26. At program line 467, the Reynold's number N.sub.Re, as given above, is calculated by multiplying the value of fluid flow times an exponential taken to the value T(1) of the bulk water temperature as measured by the thermometer 28a. At line 505, a data array is formed within the RAM to provide various value of temperature and flow rate.

The above provided listing does not set out a set of steps for calculating the values of the convective heat transfer resistance 1/U.sub.conv as provided by formula 4 is calculated at computer line 465, and the Reynold's number N.sub.Re is calculated at line 467. Thereafter the calculation would be executed to take the difference between the convective heat transfer resistance 1/U.sub.conv and the reciprocal of the heat transfer coefficient, i.e., the total heat transfer resistance 1/U.sub.tot, calculated at computer line 450. As indicated above, the value of 1/U.sub.cond of the conductive heat transfer resistance is indicative of the degree of fouling within the tube 12 and would be either automatically or at the command of an operator entered by the keyboard 144, would be displayed upon the video output 160.