Calculating the requirements of a tube bundle section evolves around two basic equations of heat transfer. They are:
where Q is the required heat load in BTU/hr, m is the mass flow rate in lb/hr, Cp is the specific heat, T2 is temperature in, T1 is temperature out, U is the overall rate, A is the area of bare tube surface, and LMTD is the average temperature minus the ambient temperature multiplied by the MTD Correction Factor. The program sets the Q's equal to each other and solves for the desired variable. If it's sizing, it solves for "A". If it is check rating, it determines the ratio between Q(actual) and Q(required). If that ratio is greater than one, everything is o.k.
So the big secret about how to rate coolers revolves around five basic sets of data. They are:
Specific Heat Water and air are easy and well documented. The Specific Heat of oil surprisingly changes very little from brand to brand and from viscosity to viscosity. We account for it, but it's not much. Natural Gas, however, has big deviations as a function of specific gravity, pressure, and temperature. This empirical data has always been closely held within the industry. We have taken that data and curve fitted into equations for the use on the internet. Ethylene Glycol/Water mixtures for engine jacket water have a specific heat which is a function of the percent mixture. Most programs from cooler companies only account for either pure water, or 50/50 ethylene glycol. Neither is real world. We have added the ability to vary the percentage and come up with the correct specific heat. The relationship between mixture percentage and the specific heat is logarithmic. Most of the cooler companies just use a multiplier for 50/50. This creates an error of plus or minus 10% depending on the flow. We use a logarithmic relationship which is far more accurate. Inside Film Coefficients Again, water and air are easy and well documented. Natural gas really isn't that hard to find if you look for it. The important thing to remember is the inside film coefficient is a function of the velocity going through the tube. The faster the velocity, the better the film coefficient and the smaller the cooler. That is why understanding how much pressure drop you can really tolerate is critical. The more pressure drop, the better the cooling (generally, oil can be an exception). Since velocity is the critical component for heat transfer inside the tube, the viscosity of the fluid plays an important role with fluids. So the film coefficient has a viscosity component. For instance, increasing the amount of Ethylene Glycol in an engine jacket water section will decrease the film coefficient by increasing the viscosity. Lube Oil is an interesting media. When I was studying oil, I went to HTRI, in Bryan Texas and learned no one had ever actually tested oil. They simply use the vendor's data and put it in their program. Since one turbulator company out of the U.K. claimed to increase inside film coefficients by 600%, I got a little suspicious. We've tested well over a hundred turbulator configurations and the vast majority of them increase pressure drop, but do absolutely nothing for the inside film coefficient. There are, however, a few that do work. To discover this, we have set up a double pipe heat exchanger and have pumped about twenty different types of oil through, measuring film coefficients as a function of temperature, flow, and viscosity. If you ever try this, oil is incredibly messy. Have lots of absorbent around. Outside Film Coefficients The industry has long adapted a set of curves for the outside film coefficient that are a function of the "velocity factor" of the air traveling across the tube bundle. The relationship between the outside film coefficient and the air flow is, again, logarithmic. We have taken that empirical data and and curve fitted it for this program. We have tested the "SMOOTH" function used by the program in wind tunnels and feel very confident to it's accuracy. The "WHEEL" function is a set of curves used in the industry that shows the slots in the "high efficiency" wheel feel can practically double the outside film coefficient, thus creating smaller water sections. We've tested the wheel fin in a wind tunnel and I'm not comfortable giving it more than a 5% increase, which is negligible. I added the function as I didn't want to argue with the cooler guys and I wanted their specification sheets to come out exactly as my program. The reality is, if I was check rating a unit, I would only use the SMOOTH function. It is closer to reality for either design of fin. MTD Correction Factor The industry has long adapted a set of data for MTD correction factor which is a three dimensional curve that is different for counter flow and cross flow. We have curve fitted that data within .05% Viscosity for Pressure Drop calculations Again, air and natural gas are fairly easy to calculate. Where I see the most deviation from vendor to vendor, and from what I can tell, errors, evolves around oil and ethylene glycol/water mixtures. One vendor uses a standard specific gravity to calculate all oil viscosities and pressure drops. Another vendor I studied, doesn't take into account ethylene glycol mixture at all in calculating pressure drop in an engine jacket water. This can be a disaster. Always ask for the calculated viscosity of the fluid from your vendor. If they cannot come up with it, you might want to double check their results.
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