INFINITY TURBINE LLC We specialize in designs, plans, licensing, consulting, design services, and surplus spare parts. We no longer manufacture turbines or CO2 systems. More Info...
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Supercritical CO2 Test Cart Upstream total pressure: 1,500 psi (about 10.3 MPa)Upstream total temperature at turbine inlet: 300 C (573 K)Working fluid treated as a compressible gas near sCO₂ conditions with heat capacity ratio about 1.3 and gas constant about 188.9 J per kg per KFlow limited by choked (sonic) conditions at the smallest flow area (i.e., your line size or a nozzle on the test head)Ideal turbine power from isentropic expansion from 10.3 MPa to 1.0 MPa; then I show a practical derateLine lengths, bends, valves, and heater limits will reduce the numbers; this is an upper bound you can scale down for the cart.Maximum choked mass flow you can feed (per line size)Inner diameters listed; each assumes smooth, short runs and a properly contoured inlet or nozzle.| Inner diameter | Mass flow, ideal choked | Volumetric flow at inlet conditions | Mass flow, imperial | Volumetric, imperial || -• | -: | -: | : | : || 1/8 in | ~0.166 kg per s | ~0.00174 cubic m per s | ~0.366 lbm per s | ~3.68 cubic ft per min || 1/4 in | ~0.664 kg per s | ~0.00695 cubic m per s | ~1.46 lbm per s | ~14.7 cubic ft per min || 3/8 in | ~1.495 kg per s | ~0.0156 cubic m per s | ~3.30 lbm per s | ~33.1 cubic ft per min |NotesVolumetric rates are at the upstream state near 10.3 MPa and 300 C, not at standard conditions.Real tubing, fittings, and valves will trim these numbers. As a quick sanity check, knock 15 to 35 percent off for header and accessory losses on a compact cart.Turbine power you could extract from that feedIdeal isentropic expansion from 10.3 MPa to 1.0 MPa at 300 C gives an enthalpy drop on the order of about 200 kJ per kg. Multiply by the mass flows above:| Inner diameter | Ideal shaft power | A more realistic starting target || - | -: | --: || 1/8 in | ~33.5 kW | ~20–25 kW (assume 70 percent turbine efficiency and 15–25 percent header losses) || 1/4 in | ~134 kW | ~80–95 kW || 3/8 in | ~302 kW | ~180–210 kW |What pushes the realistic numbers down:• Small rotors and seals are rarely better than 65–75 percent efficient on first articles• Cart plumbing adds pressure drop before the nozzle and after the turbine• Heater capacity must match the mass flow; at these flows, electrical heater duty becomes the limiting factor long before the line size doesPractical guidance for a cart build• Pick a design point, not the absolute max. For a one-cartridge heater in the one to two kilowatt class, target 1/8 in feed and mass flows under 0.05 to 0.08 kg per s to keep heat input and control manageable.• Use a small converging nozzle at the test head so the flow chokes where you want it, not in a random elbow.• Keep a short, straight, heated run between heater outlet and test article to minimize additional pressure drop and cooling.• Instrument for total pressure and total temperature at the nozzle plane if you want credible efficiency numbers.If you need deeper pressure ratios or want to avoid crossing into two-phase, back-pressurize the exhaust with a back-pressure regulator around 1–3 MPa, then condense downstream. |
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Power Potential of a Supercritical CO₂ Test Cart with Small Diameter Tubing IntroductionSupercritical carbon dioxide is a promising working fluid for compact turbines and experimental expanders. Understanding how tubing size, operating pressure, and turbine inlet temperature affect flow rates and power output is critical when designing a cart-mounted laboratory system. This article provides calculated flow capacities and power estimates for tubing diameters of 1/8 inch, 1/4 inch, and 3/8 inch, operating at 1500 psi, with turbine inlet temperatures of 45 C, 100 C, and 300 C.Flow Capacities at 1500 psiFor each tubing diameter, maximum choked flow conditions were calculated. Results are shown in both metric and imperial units.1/8 inch tubingMass flow: approximately 0.166 kilograms per secondVolumetric flow: approximately 0.00174 cubic meters per secondMass flow imperial: approximately 0.366 pounds per secondVolumetric flow imperial: approximately 3.68 cubic feet per minute1/4 inch tubingMass flow: approximately 0.664 kilograms per secondVolumetric flow: approximately 0.00695 cubic meters per secondMass flow imperial: approximately 1.46 pounds per secondVolumetric flow imperial: approximately 14.7 cubic feet per minute3/8 inch tubingMass flow: approximately 1.495 kilograms per secondVolumetric flow: approximately 0.0156 cubic meters per secondMass flow imperial: approximately 3.30 pounds per secondVolumetric flow imperial: approximately 33.1 cubic feet per minutePower Potential at Different Turbine Inlet TemperaturesThe power generated depends on the enthalpy drop across the turbine, which increases with turbine inlet temperature. For comparison, three cases are considered: 45 C, 100 C, and 300 C, all expanding from 1500 psi to about 1.0 MPa exhaust pressure.45 C turbine inlet temperatureLower enthalpy drop, estimated power per unit mass flow about 50 to 70 kilojoules per kilogramFor 1/8 inch tubing: about 8 to 12 kilowatts ideal, 5 to 8 kilowatts practicalFor 1/4 inch tubing: about 32 to 45 kilowatts ideal, 20 to 30 kilowatts practicalFor 3/8 inch tubing: about 70 to 100 kilowatts ideal, 45 to 70 kilowatts practical100 C turbine inlet temperatureModerate enthalpy drop, estimated power per unit mass flow about 120 to 150 kilojoules per kilogramFor 1/8 inch tubing: about 20 to 25 kilowatts ideal, 12 to 18 kilowatts practicalFor 1/4 inch tubing: about 80 to 100 kilowatts ideal, 50 to 70 kilowatts practicalFor 3/8 inch tubing: about 180 to 220 kilowatts ideal, 110 to 150 kilowatts practical300 C turbine inlet temperatureHigh enthalpy drop, estimated power per unit mass flow about 200 kilojoules per kilogramFor 1/8 inch tubing: about 33.5 kilowatts ideal, 20 to 25 kilowatts practicalFor 1/4 inch tubing: about 134 kilowatts ideal, 80 to 95 kilowatts practicalFor 3/8 inch tubing: about 302 kilowatts ideal, 180 to 210 kilowatts practicalPractical ConsiderationsAlthough theoretical calculations show impressive power, real-world constraints such as heater duty, line losses, and turbine efficiency reduce output significantly. Typical laboratory-scale turbines with small rotors may achieve 65 to 75 percent efficiency. Cart-mounted systems are best suited for proving concepts, measuring relative efficiencies of turbine geometries, and testing flow control methods before scaling to larger systems.ConclusionA supercritical CO₂ test cart with small-diameter tubing can provide meaningful power output for experimental turbines and expanders. At lower turbine inlet temperatures such as 45 C and 100 C, power output is modest but valuable for component testing. At higher temperatures such as 300 C, the same tubing sizes can generate tens to hundreds of kilowatts in theory, though practical values will be lower. These calculations demonstrate the potential of supercritical CO₂ as both a power and research medium in laboratory-scale systems. |
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Liquid CO2 Needed Here’s a practical sizing for how much liquid CO₂ you’d consume if you ran the cart at the maximum choked flow we estimated earlier, at 1,500 psi with turbine-inlet temperatures of 45 C, 100 C, and 300 C.AssumptionsLine sizes are 1/8 in, 1/4 in, 3/8 in inside diameter.Upstream total pressure: 1,500 psi.Flow is choked at the nozzle/line; mass flow scales with the square-root of 573 K divided by turbine-inlet temperature in kelvin.Liquid CO₂ density for conversion: ~900 kg per m³ (about 1.11 liters per kg) near 20 C saturated conditions.If your liquid CO₂ density differs, scale the liters by 900 divided by your density.Liquid CO₂ needed (per hour) at max feedWhat is shown per case: mass flow in kg/s and kg/h; equivalent in lb/s and lb/h; liquid CO₂ volume per hour in liters and US gallons.1/8 in ID line45 C: 0.223 kg/s | 802 kg/h | 0.491 lb/s | 1,768 lb/h | 891 L/h | 235 gal/h100 C: 0.206 kg/s | 741 kg/h | 0.454 lb/s | 1,633 lb/h | 823 L/h | 217 gal/h300 C: 0.166 kg/s | 598 kg/h | 0.366 lb/s | 1,317 lb/h | 664 L/h | 175 gal/h1/4 in ID line45 C: 0.891 kg/s | 3,209 kg/h | 1.97 lb/s | 7,074 lb/h | 3,565 L/h | 942 gal/h100 C: 0.823 kg/s | 2,963 kg/h | 1.81 lb/s | 6,533 lb/h | 3,292 L/h | 870 gal/h300 C: 0.664 kg/s | 2,390 kg/h | 1.46 lb/s | 5,270 lb/h | 2,656 L/h | 702 gal/h3/8 in ID line45 C: 2.007 kg/s | 7,224 kg/h | 4.42 lb/s | 15,927 lb/h | 8,027 L/h | 2,121 gal/h100 C: 1.853 kg/s | 6,671 kg/h | 4.09 lb/s | 14,706 lb/h | 7,412 L/h | 1,958 gal/h300 C: 1.495 kg/s | 5,382 kg/h | 3.30 lb/s | 11,865 lb/h | 5,980 L/h | 1,580 gal/hHow to use these numbersThese are upper-bound consumptions for a short, well-contoured feed with flow choked at the nozzle.Real carts with bends, valves, and heater limits typically run 15 to 35 percent lower than the values above.If you plan a specific run time, multiply the per-hour liters or gallons by your hours of operation to size the CO₂ supply.If your liquid CO₂ storage is at a different density, adjust liters per hour by the ratio 900 divided by your actual kg per m³. |
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Supercritical CO2 Closed Loop Rankine vs. Brayton Cycles Two ways to run a closed loopA) Phase-change back to liquid (transcritical or Rankine-like)Flow path: liquid pump → heater to supercritical → expander → cooler or condenser → liquid receiver → pump.Pros: very low pump power, easy to meter flow, good for small rigs.Cons: you must reject heat low enough to return to liquid; you manage two-phase regions; you need a liquid receiver sized to hold the charge that pools at the cold end and to absorb inventory swings.B) True Brayton (single-phase supercritical gas everywhere)Flow path: compressor → heater → expander → cooler (not a condenser) → inventory tank → compressor.Pros: no two-phase control issues; simpler cold-end heat rejection.Cons: small compressors are harder than pumps; compressor power is higher; you still need an inventory tank to trim system pressure and to park charge during start and shutdown.Densities to use for quick sizing at 10 MPa (about 1,500 psi)These round-number densities are conservative enough for benchtop design (actual values vary with exact state and hardware):45 C: about 700 kilograms per cubic meter100 C: about 350 kilograms per cubic meter300 C: about 100 kilograms per cubic meterLiquid CO₂ near room temperature: about 900 kilograms per cubic meterYou can refine later with REFPROP or NIST tables; the sizing formulas below still apply.How big should the tank be?Let V_loop be the internal volume of all tubing, heaters, heat exchangers, and the expander flow path you want pressurized during operation.If you condense back to liquid (receiver sizing)A simple and safe rule is:> Receiver volume ≈ 1.3 × (operating mass in the loop ÷ liquid density).Written in plain English for each temperature:Operating mass in the loop equals loop volume times operating density.Divide by 900 kilograms per cubic meter to convert that mass to liquid volume.Multiply by 1.3 to give about thirty percent surge for level control, transients, and gas space.Receiver volume per liter of loop volume45 C: 1.3 × (700 ÷ 900) ≈ 1.0 liter per liter of loop100 C: 1.3 × (350 ÷ 900) ≈ 0.5 liter per liter of loop300 C: 1.3 × (100 ÷ 900) ≈ 0.15 liter per liter of loopExample with a 2.0 liter loop45 C: receiver about 2.0 liters100 C: receiver about 1.0 liter300 C: receiver about 0.3 litersMinimum practical receiver on a cart is usually 1 liter, so for 300 C you would still pick a 1 to 2 liter vessel for flexibility and startup storage.If you run true Brayton (inventory tank sizing)You do not condense. You only need a buffer to trim pressure, to absorb charge during warmup and cooldown, and to keep the compressor in a stable map. A robust bench rule:> Inventory tank volume ≈ 0.2 to 0.5 liter per liter of loop, with the higher end used at higher temperatures where density is low.Inventory tank volume per liter of loop volume45 C: 0.1 to 0.2 liter per liter of loop100 C: 0.2 to 0.3 liter per liter of loop300 C: 0.3 to 0.5 liter per liter of loopExample with a 2.0 liter loop45 C: 0.3 liter to 0.4 liter tank100 C: 0.4 liter to 0.6 liter tank300 C: 0.6 liter to 1.0 liter tankWhat actually differs in operationPumping versus compressing: the Rankine-like loop uses a liquid pump with low power; Brayton uses a gas compressor with noticeably higher parasitics at small scale.Cold-end hardware: Rankine needs a condenser and liquid receiver; Brayton needs only a gas cooler and inventory tank.Controls: Rankine has level control in the receiver and back-pressure regulation to stay out of unwanted two-phase zones; Brayton controls only pressures and temperatures.Start and stop: Rankine stores most charge as liquid in the receiver at shutdown; Brayton parks charge in the inventory tank and relies on gas compressibility.How to use this on your cart1. Measure or estimate V_loop. For typical bench rigs with 1/8 to 3/8 inch tubing, compact plate heaters, and a small recuperator, V_loop is often 1 to 3 liters.2. Pick your operating mode and temperature.3. Apply the per-liter multipliers above to size the receiver or the inventory tank.4. Choose vessels rated well above 10 MPa with adequate gas space and ports for level or pressure instrumentation.5. Leave physical room for a larger vessel than the minimum. On carts, the ability to add charge and shift inventory is worth the extra space. |
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Loop Cycles Rankine style loop (condense back to liquid)Rule used: receiver volume ≈ 1.3 times operating mass divided by liquid CO2 density. With the quick densities we used earlier, this works out to the following per liter multipliers:45 C: about 1.01 liter receiver per liter of loop100 C: about 0.51 liter receiver per liter of loop300 C: about 0.15 liter receiver per liter of loopApplying to your 2 liter loop:| Turbine inlet temperature | Calculated receiver size | US gallons || • | --• | -• || 45 C | about 2.02 liters | about 0.53 gal || 100 C | about 1.01 liters | about 0.27 gal || 300 C | about 0.29 liters | about 0.08 gal |Practical note: for control headspace, level sensing, and startup inventory, a minimum practical receiver of about 1 to 2 liters is wise even at 300 C, despite the small calculated value.Brayton true supercritical loop (no condensing)Rule used: inventory tank ≈ 0.2 to 0.5 liter per liter of loop, with the lower end at cooler operation and the higher end at hotter operation and lower density.For your 1 liter Brayton loop:| Turbine inlet temperature | Inventory tank range | US gallons range || • | • | • || 45 C | about 0.10 to 0.20 liters | about 0.03 to 0.05 gal || 100 C | about 0.20 to 0.30 liters | about 0.05 to 0.08 gal || 300 C | about 0.30 to 0.50 liters | about 0.08 to 0.13 gal |Practical note: pick the high end of the range if you expect wide pressure trims during startup or aggressive step changes in heater power. For a compact cart, a single interchangeable vessel of about 0.6 to 1.0 liters works well for 300 C Brayton experiments and can be partially valved out for cooler conditions. |
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Receiver and Inventory Tank Sizing for Supercritical CO₂ Experimental Carts Guidelines for sizing receiver tanks in a Rankine style loop and inventory tanks in a Brayton cycle loop for supercritical CO₂ test carts at turbine inlet temperatures of 45 C, 100 C, and 300 C.IntroductionDesigning a compact supercritical CO₂ test cart requires careful sizing of the storage tanks that balance the working fluid during operation. Two main approaches are possible. A Rankine style loop condenses CO₂ back to liquid and requires a receiver tank. A Brayton cycle loop keeps CO₂ in a supercritical gas phase and requires an inventory tank. The following describes the differences and provides practical tank sizes for experimental carts with loop volumes of two liters for the Rankine case and one liter for the Brayton case.Rankine Style Loop Receiver TankIn the Rankine style loop, CO₂ is pumped as a liquid, heated to supercritical conditions, expanded through a turbine or expander, cooled, and then condensed back to liquid before returning to the pump. The receiver tank must hold the condensed liquid and provide surge capacity for changes in operating conditions.For a two liter loop:At a turbine inlet temperature of 45 C, the receiver should be about two liters in size.At 100 C, the receiver should be about one liter in size.At 300 C, the calculation gives a value of about three tenths of a liter, but in practice a one to two liter receiver is recommended to allow for startup, shutdown, and safe margin.Brayton Cycle Inventory TankIn the Brayton style loop, CO₂ remains in the supercritical gas phase throughout compression, heating, expansion, and cooling. Instead of a liquid receiver, the system uses an inventory tank to balance charge, trim pressure, and stabilize operation.For a one liter loop:At a turbine inlet temperature of 45 C, the inventory tank should be about one to two tenths of a liter.At 100 C, the tank should be about two to three tenths of a liter.At 300 C, the tank should be about three to five tenths of a liter.Practical NotesAlthough calculations provide precise values, minimum vessel sizes in practice are dictated by safety and instrumentation needs. Even at higher temperatures where calculated volumes are small, it is recommended to use a receiver or inventory tank of at least one liter on a laboratory cart. This provides extra margin for level sensing, startup charge, and pressure stabilization. All tanks must be rated above the maximum operating pressure, with appropriate ports for measurement and relief.ConclusionA two liter Rankine loop operating at 45 C requires a receiver of about two liters, while at 100 C it requires about one liter, and at 300 C it still benefits from a one to two liter receiver for safe operation. A one liter Brayton loop requires an inventory tank ranging from one tenth to five tenths of a liter depending on turbine inlet temperature, with a practical recommendation of up to one liter. By correctly sizing the storage vessels, researchers can ensure stable and safe operation of supercritical CO₂ test carts across different experimental conditions. |
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Receiver Tank Sizing for Supercritical CO₂ Rankine Loops in Data Center Cooling Guidelines for sizing receiver tanks in Rankine style supercritical CO₂ cooling loops at 45 C and 100 C turbine inlet temperatures, tailored for data center applications.IntroductionData centers face increasing demands for efficient and compact cooling technologies to support AI chipsets and dense server racks. Supercritical carbon dioxide offers a unique advantage as a working fluid, capable of capturing heat at moderate temperatures and converting it into useful work or rejection pathways. When applied in an Organic Rankine Cycle configuration, CO₂ is pumped as a liquid, heated into the supercritical state, expanded, and then condensed back to liquid. Proper sizing of the receiver tank ensures smooth operation and stability in such systems.Rankine Loop Receiver Tank at 45 CAt a turbine inlet temperature of 45 C, the density of supercritical CO₂ is relatively high, meaning more mass resides within a given system volume. For a two liter loop representative of a laboratory-scale or modular test rig, the calculated receiver tank size is about two liters. In practice, the tank should be designed with slight additional margin to accommodate level sensing, charge balancing, and transient operation. This setup is directly applicable to data centers where waste heat at or near 45 C is common from liquid-cooled chipsets.Rankine Loop Receiver Tank at 100 CAt a turbine inlet temperature of 100 C, the density of CO₂ decreases compared to 45 C, resulting in less mass stored within the loop. For a two liter loop, the required receiver tank volume is approximately one liter. This smaller receiver volume is adequate for stable operation, but practical design often favors installing a receiver of one to two liters to simplify fluid management. Data centers with elevated coolant return temperatures in the range of 80 to 100 C are prime candidates for this configuration, allowing more efficient recovery of waste heat.Practical Considerations for Data CentersReceiver Function: The receiver provides liquid surge capacity, stabilizes loop operation, and ensures the pump always has adequate liquid supply.System Integration: A compact receiver mounted on a cooling skid can tie directly into chip-level or rack-level heat exchangers.Design Margins: While the calculated sizes are close to one to two liters for a small loop, larger data center modules would scale these values proportionally, often by tenfold or more depending on the rack count.Safety and Instrumentation: All receiver tanks must be pressure-rated above the maximum loop pressure and fitted with level gauges, relief valves, and temperature monitoring.ConclusionFor data center cooling applications using supercritical CO₂ in an Organic Rankine Cycle configuration, a two liter loop operating at 45 C requires a receiver tank of about two liters, while the same loop at 100 C requires about one liter. In practice, receivers are often sized in the one to two liter range to ensure stable startup and safe operation. By tailoring receiver tank size to the inlet temperature, data centers can optimize CO₂-based cooling loops for efficiency, reliability, and scalability. |
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