Thermal Analysis Pressure Drop Calculations in a Chassis Before performing thermal analysis on a chassis, it is necessary to calculate total pressure drop within the system. This 1 Formula consists of the pressure drops of1all- system subcomponents. Formula Formula 1 The total pressure drop (system curve), which also depends on the volumetric flow rate in the system, can be shown as: Formula 1 - Formula 2 - mula 1 - mula 2 - mula 3 - Formula 2, -where Formula 3 - and are the system component resistances, volumetric flow rate. mula 6 - mula 7 - The following shows the calculation of several of the above Formula 2 The units are square meter for the area, cubic Formula 1resistances. meter per second for volumetric flow rate and Pascal for Formula 2 - 1pressure. Formula Formula 3 Formula 2A.- Perforated plate: Formula 3- 2Formula is the - can be used to deliver air Generally, oneFormula or two fan 3trays Formula 4 through a chassis. TheFormula operating4point - of a fan tray is whereFormula 3 the system curve intersects the fan tray curve. Formula 1 -4 Formula Formula 5 Operating Points Formula 6 Formula 6 Formula 7 Formula 7 Formula 8 Formula 8 - Where A is the area of open holes exposed to air flow Formula 3 - B. Filter: Figure 1 shows the operating point. It is recommended to Formula 5operate the fans belowFormula the stall range. Formula 4 5- Formula 4 - mula 4 - mula 5 - , 4. Flow bending from inlet to plenum 5. Contraction to the inlet plenum 6. Expansion from inlet to plenum 7. Circuit cards component blockade 8. Circuit card friction (generally small) 9. Flow bending to exit plenum 10. Contraction to exit of plenum 11. Expansion from exit of the plenum Formula 2 -5 - 4 Formula Formula Where A is the filter exposed area and L is the filter loss coefficient provided by manufacturer. Formula 6 Formula 5 Formula 3 -6 - 5C.- Boards: Formula Formula Formula 7 Formula 6 Formula 4 -7 - 6 Formula Formula Formula 8 Formula 7 Formula 5 -8 - 7 Formula Formula Where L is the board length and A is the effective free area of the channel. If there are N similar boards mounted in a chassis in parallel, their equivilent resistence is calculated as: Formula 9 Formula 8D.- Fan trays contraction and expansion: Formula 9 Figure 1. Graph showing the intersection of system and fan curve. Formula 6 -9 - 8 Formula Formula mula 8 The flow going into and out of the fan trays exhibits contraction Formula 9 Formula This intersection equals the system pressure, and thus pro- 10 and expansion with their associated losses. 9vides the flow rate through the system. is Formula 10 - Total pressure drop Formula 7 -10 - 9 Formula generally affected by the following subcomponents Formula if they areFormula mula 9 - part of that specific chassis: Formula 10 Sudden Expansion: Formula 11 1. Air filter Formula 10 Formula 11 2. Honeycomb Formula 8 -11 - 10 Formula Where A1 is the small area Formula mula 10 - 3. Fan tray due to sudden expansion and contraction and A2 is the larger. Formula 11 of flow through blades Formula 12 Formula 11 Formula 12 PAGE 7 Formula 9 Formula 12 Formula 11 mula 11 Formula 12 - 02062 P. 781.769.2800 WWW. QATS . A DVANCED TThermal HERMAL SSolutions, OLUTIONS, Inc., I NC.89-27 89-27Access A CCESS ., NFormula ORWOOD , 13 MA Advanced Rd.,RDNorwood, MA 02062 Formula 12Ph. - 781-769-2800 WWW.QATS.COM Formula 13 - Formula 7 -5 Formula Formula 1 Formula 5ormula 4- Formula 11 - Formula 8 -6 Formula Contraction: Formula 2Formula 6ormula 5 - Formula 9 -7 Formula Where A is the small area. Formula 3 Formula 7 - tray ormula 6 - E. Fan Formula 10 - Formula When8 fans are mounted in a fan tray, the combined fan curve is calculated Formula 4 - based on the fan laws. For M fans in parallel Formula 8ormula 7 - assembled in one fan tray, the fan volumetric flow rate increases11 by -a factor of M for the same pressure drop. For two fan Formula Formula trays9in-series such as a push-pull system, pressure doubles for the same Formula 5 - volumetric flow rate. So if the characteristic curve Formula 9 - fan is: ormula 8 - of one Formula 1210 - Formula Formula 6 Formula 10 ormula 9The curve of the combined fans can be Formula 13characteristic - Formula 11 represented as: Formula 7 Formula ormula 10 - 11 Formula 1412 - Formula The factor 2 is for two fan trays and M is the number of Formula 8 - tray. fans in one Formula ormula 11 - 12 - The Formula 15total - -head generated by a push-pull system is: Formula 13 Formula 9 Formula ormula 12 - 13 - Where is the fan duct size. Formula 14 - The above relations can be used for a quick analysis of a system12 to -find the volumetric flow rate, which can then yield Formula the system temperature rise if the total heat dissipation is known. As a simple example, consider a system that has two fan trays. Each fan tray has two fans. This system has five perforated Formula 13 - plates with a 56% opening. Let’s assume the area open to air flow is about 0.03 m2 and that the system also has a filter at the inlet with a loss coefficient of 0.008. The fan curve indicates that maximum pressure is 225 Pa at zero flow and 0.13 Formula 14 m- 3/sec at zero pressure. Assuming a linear relationship between the pressure and the volumetric flow rate would give the single fan curve as: Formula 15 Assuming negligible resistance from boards and fan hubs, Table 1 shows the resistances due to all the parameters and their calculated values. Solve the following equation: Which yields a value for G equal to 0.12 m3/sec for the system volumetric flow rate. References: 1. Ellison G., Thermal Computations for Electronic Equipment, Krieger Publishing Company, 1984. Formula 10 Formula ormula 13 - 14 Inlet Cross section (m ) ...............................................................................................................................................0.03 2 Single perforated plate resistance ................................................................................................................................ 2933 FormulaCombined 15 - perforated plate resistance ......................................................................................................................... 14668 Filter resistance ......................................................................................................................................................4540 Formula 11 Formula 15 ormula 14 - Total- system resistance ..........................................................................................................................................1 9208 Fan curve ..................................................................................................................................................... 225-1665XG Push pull Fan tray curve ............................................................................................................................... 2(225-1665/2*G) Formula 12 ormula 15 -Table 1. Flow resistances for different system components. The second term is the velocity pressure head associated with Formula 13 - fan that contributes to the total pressure. Solving the entrance the following equation, it would yield the system pressure drop and volumetric flow rate: Formula 14 PAGE 8 Formula 15 A DVANCED TThermal HERMAL SSolutions, OLUTIONS, Inc., I NC.89-27 89-27Access A CCESS ., N ORWOOD , MA 02062 P. 781.769.2800 WWW. QATS . Advanced Rd.,RDNorwood, MA 02062 Ph. 781-769-2800 WWW.QATS.COM