Performance prediction method for compact steam piston engine
By constructing zero-dimensional thermodynamic and three-dimensional CFD models and combining experimental data to optimize performance prediction, the contradiction between accuracy and efficiency in the design of compact steam piston engines was resolved, and high-precision performance prediction and optimization were achieved.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- NORTHWESTERN POLYTECHNICAL UNIV
- Filing Date
- 2026-01-29
- Publication Date
- 2026-05-12
AI Technical Summary
In the design of compact steam piston engines, existing technologies cannot simultaneously guarantee prediction accuracy and design efficiency with single-dimensional models, and lack a collaborative framework for multi-dimensional models, resulting in high computational costs and insufficient verification.
We construct a zero-dimensional thermodynamic analytical model and a three-dimensional fluid dynamics CFD model, compare and adjust them with experimental data, and achieve multi-scale model synergy. We use the zero-dimensional model for rapid screening and the three-dimensional model for key point verification to optimize performance prediction.
It achieves high-precision prediction of key performance parameters such as engine output power, with the total error controlled within 8%, shortening the design and analysis cycle by more than 70%, and providing a basis for optimizing in-cylinder flow loss and heat transfer.
Smart Images
Figure CN122021431A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of thermal engine design and performance simulation technology, specifically relating to a performance prediction method for compact steam piston engines. Background Technology
[0002] In the field of small-scale distributed energy and industrial waste heat recovery, steam Rankine cycle (SRC) is a promising technological approach. However, the design and performance prediction of compact, high-power-density piston expanders suitable for this scenario face challenges. Traditional methods typically employ a single zero-dimensional thermodynamic model or a three-dimensional computational fluid dynamics (CFD) simulation model for performance prediction, but these methods suffer from the following problems:
[0003] Accuracy and efficiency are difficult to balance: zero-dimensional models are fast but cannot reveal the complex non-uniform flow and heat transfer details inside the cylinder, resulting in limited prediction accuracy; while three-dimensional CFD models can reflect details, their computational cost is extremely high, making them unsuitable for rapid analysis and optimization design under multiple operating conditions.
[0004] Insufficient model validation: Existing studies often lack systematic comparison and validation with real prototype experimental data, raising questions about the reliability of the models.
[0005] Lack of a collaborative framework: It fails to effectively integrate the advantages of different dimensional models to form an efficient, closed-loop design verification tool that ranges from rapid system-level evaluation to detailed component-level analysis. Summary of the Invention
[0006] The purpose of this invention is to provide a performance prediction method for compact steam piston engines, which solves the problem that the single-dimensional model in the prior art cannot meet the design efficiency requirements while ensuring prediction accuracy.
[0007] The technical solution adopted in this invention is a performance prediction method for a compact steam piston engine, comprising the following steps: Step 1: Construct a zero-dimensional thermodynamic analytical model of the engine and calculate the engine's indicated performance parameters using the model; Step 2: Establish a three-dimensional fluid dynamics CFD model of the engine and calculate the detailed parameters of the in-cylinder flow field based on the model; Step 3: Construct a compact steam piston engine, test the engine, and obtain the actual engine indicated performance parameters; Step 4: Compare the actual engine indicated performance parameters with the engine indicated performance parameters, adjust the zero-dimensional thermodynamic analytical model, and calculate the optimized indicated performance parameters; Step 5: Predict the performance of a compact steam piston engine based on optimized indicated performance parameters and detailed parameters of the in-cylinder flow field.
[0008] The invention is further characterized by: Step 1 is as follows: Step 1.1: Divide the actual working cycle of a single cylinder of the engine into the intake process, expansion process, early exhaust process, exhaust process, compression process, and early intake process; Step 1.2: Based on engine operating parameters, thermodynamic laws, engine valve timing, and piston kinematics, the working cycle is discretized. Within each discrete time step, the piston equations are solved simultaneously, and the key parameters in the cylinder at the times of the intake process, expansion process, early exhaust process, exhaust process, compression process, and early intake process are calculated iteratively. Engine operating parameters include clearance volume ratio Intake ratio Expansion ratio Pre-exhaust ratio Exhaust ratio Pressure ratio Pre-intake ratio Combustion chamber temperature Combustion chamber pressure and back pressure ; Step 1.3: Based on the key point parameters calculated in Step 1.2, integrate them on the pressure-volume indicator diagram to calculate the single-cylinder indicated work. Step 1.4: Calculate the theoretical indicated power of the engine based on the single-cylinder indicated power, engine speed, and number of cylinders.
[0009] Step 1.2 specifically involves: Step 1.2.1: Calculate the pressure at key points during the intake process according to equation (1); (1); in, P c This refers to the combustion chamber pressure. Calculate the valve timing angle during the intake process according to equation (2); (2); in, For intake ratio, This represents the number of peaks and troughs in the piston system. Calculate the pressure at the key points of the expansion process according to equation (3); (3); in, The pressure drop coefficient; Calculate the gas distribution angle during the expansion process according to equation (4); (4); Calculate the pressure at the key point of the pre-venting process according to equation (5); (5); in, The clearance volume ratio, For pre-exhaust ratio, The adiabatic index of the working fluid. Calculate the valve timing angle for the pre-exhaust process according to equation (6); (6); Calculate the pressure at key points during the exhaust process according to equation (7); (7); in, For back pressure, Calculate the valve timing angle during the exhaust process according to equation (8); (8); Calculate the pressure at the critical point during the compression process according to equation (9); (9); Calculate the valve timing angle during the compression process according to equation (10); (10); Calculate the pressure at the key point of the pre-intake process according to equation (11); (11); Calculate the valve timing angle for the advance intake process according to equation (12); (12); Step 1.2.2: Calculate the piston position according to equation (13); (13); Where S is the piston stroke. Piston peak number For rotational speed, For time; Step 1.2.3: Calculate the volume according to formula (14); (14).
[0010] The single-cylinder indicated work calculation in step 1.3 is as follows: Calculate the indicated work of a single cylinder according to equations (15), (16) and (17); (15); (16); (17); in, As an efficiency factor, it is generally taken as 0.9; f The fullness factor is generally taken as 0.98; This refers to the effective volume of the piston. The theoretical indicated power calculation in step 1.4 is as follows: Calculate the theoretical indicated power according to equation (18); (18); In the formula, For the number of pistons, The value is the rotational speed.
[0011] Step 2 is as follows: Step 2.1: Based on the engine size parameters, establish a fluid computational domain model that includes the valve train, cylinder, and piston motion domain. Engine size parameters include the number of pistons. z e Cam peak number i e Piston stroke S Piston diameter d Inlet diameter d jq Exhaust port diameter d pq Intake process θ 1. Expansion process θ 2. Pre-venting process θ 3. Exhaust process θ 4. Compression process θ 5 and pre-intake process θ 6; Step 2.2: Mesh the fluid computational domain model, set boundary parameters, and establish a simulation model; Boundary parameters include rotational speed, inlet temperature, inlet pressure, and outlet pressure; Step 2.3: Set up the multiphase flow model and turbulence model, set the wall as a non-slip adiabatic wall, and define the rotational motion of the gas distribution valve and the reciprocating motion of the piston. Use dynamic mesh technology for the piston motion area. Step 2.4: Select the solver and perform transient calculations to obtain the spatiotemporal distribution data of the pressure field, temperature field, and velocity field of the working fluid in the cylinder, i.e., the detailed parameters of the in-cylinder flow field of the engine.
[0012] In step 2.3, the VOF model is selected as the multiphase flow model; the basic governing equations of the VOF model include the continuity equation, the momentum equation, and the energy conservation equation. The continuity equation is shown in equation (19); (19); In the formula, The rate of change of fluid mass per unit volume over time; The net outflow mass flow rate per unit volume; The momentum equation is shown in equation (20); (20); In the formula, The rate of change of fluid momentum per unit volume over time; The convective term for momentum represents the momentum transport caused by fluid flow. For pressure gradient force; It is a viscous force; It is a volume force; The energy conservation equation is shown in equation (21); (twenty one); In the formula, It is the volume derivative of the total energy; It is energy transport caused by heat conduction; It is energy transport caused by component diffusion; It is viscous dissipation work; It is an external heat source; In step 2.3, the SST k-ω model is selected as the turbulence model; the SST k-ω model includes the turbulent kinetic energy k equation and the specific dissipation rate ω equation; The turbulent kinetic energy k equation is shown in equation (22); (twenty two); In the formula, This is an unsteady-state term; For convection terms; For turbulent kinetic energy generation; This is the turbulent kinetic energy dissipation term; For turbulent kinetic energy diffusion term; The specific dissipation rate ω is expressed as equation (23); (twenty three); In the formula, For transient terms; For convection terms; For generating items; It is a dissipation term; For molecular and turbulent diffusion terms; This is a cross-diffusion term; The specific laws governing the rotational motion of the valve and the reciprocating motion of the piston are as follows: Calculate the angular velocity of the valve according to equation (24); (twenty four); In the formula, Rotational speed; Calculate the piston reciprocating motion according to equation (25); (25); In step 2.3, the dynamic meshing technique for the piston movement area is specifically applied as follows: based on the cam profile of the engine, the motion law and velocity of the piston top surface changing with time are defined; the motion law is loaded into the simulation software through a user-defined function to drive the piston wall boundary movement; dynamic mesh parameters are set so that when the piston movement causes the height change of the adjacent mesh layer to exceed a preset ratio, a new mesh layer is automatically generated or the original mesh layer is merged to maintain mesh quality.
[0013] Step 2.4 specifically involves: Step 2.4.1 Solver and Algorithm Settings: Select a pressure-based coupled solver and enable transient calculation mode; select the SIMPLEC algorithm for the pressure-velocity coupled algorithm; use the least squares element method for gradient discretization, use a second-order scheme for pressure term discretization, and use a second-order upwind discretization scheme for the convection terms of the momentum equation, energy equation, and turbulence equation. Step 2.4.2, Time Step and Iteration Settings: Based on engine speed The time for a single work cycle is determined according to formula (26); (26); in For the number of cam peaks; Will Discretized a fixed time step Calculate according to formula (27) ; (27); To ensure that the increment of each crankshaft angle or cam angle is no greater than 0.05 degrees; At each physical time step Within the framework, 20 internal iterations are set, and the critical residuals are monitored to decrease to below 10^{-4} to ensure single-step convergence; Step 2.4.3, Flow field initialization and monitoring: Initialize the entire computational domain to static outlet pressure and ambient temperature; set pressure, temperature and velocity monitoring points in the cylinder, intake and exhaust ports and key areas of the valve; Step 2.4.4, Transient Calculation Execution: Start the solver and iteratively calculate each time step in sequence; Within each time step, the solver sequentially solves the continuity equation, momentum equation, energy equation, and turbulence model equation, and updates the dynamic mesh. When at least three complete working cycles have been completed, and the overlap of the cylinder pressure indicator diagrams for the last two cycles is higher than 99%, the transient calculation is considered to have reached periodic stability. Step 2.4.5: Data Extraction: Extract flow field data for all time steps from the last complete working cycle that has reached periodic stability; Detailed parameters of the in-cylinder flow field include: in-cylinder velocity distribution cloud map, in-cylinder pressure distribution cloud map, and in-cylinder temperature distribution cloud map.
[0014] The specific test in step 3 is as follows: Under the given steam inlet temperature, inlet pressure and back pressure conditions, run the physical prototype and simultaneously measure the speed and torque of the engine output shaft; The actual engine indicated performance parameters are calculated from the measured speed and torque according to formula (28); (28); in, For rotational speed, For torque.
[0015] In step 4, the actual engine indicated performance parameters are compared with the engine indicated performance parameters. The adjustment of the zero-dimensional thermodynamic analytical model is specifically as follows: the indicated power calculated by the zero-dimensional model is compared with the actual output power measured in the experiment. By adjusting the efficiency factor, flow loss coefficient or heat loss coefficient in the zero-dimensional model, the error between the calculation results of the zero-dimensional model and the experimental data is made less than the preset threshold.
[0016] Step 5 specifically involves: Using the calibrated zero-dimensional model, the output power and efficiency of the engine under different steam parameters and speeds can be quickly calculated. Using a 3D model, we perform detailed simulations of key or abnormal operating conditions selected from the 0D model, analyze the uniformity of in-cylinder flow, vortex structure and local heat transfer, evaluate their impact on performance and provide a basis for structural optimization.
[0017] The beneficial effects of this invention are: The performance prediction method for compact steam piston engines provided by this invention achieves high-precision prediction of key performance parameters such as engine output power through multi-scale model collaboration and experimental calibration, with the total error controlled within 8%, far superior to a single model. The three-dimensional CFD model effectively reveals the spatiotemporal non-uniform distribution characteristics of the in-cylinder working fluid temperature, pressure, and velocity fields, providing a direct basis for optimizing valve timing and reducing flow losses. The zero-dimensional model is responsible for rapid screening, while the three-dimensional model is responsible for key point verification, avoiding the huge computational overhead of full three-dimensional simulation and shortening the design and analysis cycle by more than 70%. The entire method is based on a combination of commercial software and proprietary code, with a clear process, and has been verified by prototype experiments with a power output of 16.28kW, and can be directly used for the research and development and performance improvement of similar engines. Attached Figure Description
[0018] Figure 1 This is a schematic diagram of a pressure-volume graph in Embodiment 6 of the performance prediction method for a compact steam piston engine according to the present invention; Figure 2 This is a schematic diagram of the fluid computational domain model in Embodiment 6 of the present invention; Figure 3 This is a schematic diagram of the mesh generation of the fluid computational domain model in Embodiment 6 of the present invention; Figure 4 This is a schematic diagram of the relationship between the speed of the valve and the reciprocating motion of the piston in Embodiment 6 of the present invention; Figure 5 This is the temperature cloud map at the intake moment in Embodiment 6 of the present invention; Figure 6 This is the pressure cloud diagram at the intake moment in Embodiment 6 of the present invention; Figure 7 This is the intake velocity cloud map in Embodiment 6 of the present invention; Figure 8 This is the temperature cloud map at the expansion moment in Embodiment 6 of the present invention; Figure 9 This is the pressure cloud diagram at the expansion moment in Embodiment 6 of the present invention; Figure 10 This is the velocity cloud map at the expansion moment in Embodiment 6 of the present invention; Figure 11 This is the temperature cloud map of the early exhaust time in Embodiment 6 of the present invention; Figure 12 This is the pressure cloud diagram at the early exhaust time in Embodiment 6 of the present invention; Figure 13 This is the velocity cloud map of the early exhaust timing in Embodiment 6 of the present invention; Figure 14 This is the temperature cloud map at the exhaust moment in Embodiment 6 of the present invention; Figure 15This is the pressure cloud diagram at the exhaust moment in Embodiment 6 of the present invention; Figure 16 This is the exhaust velocity cloud map in Embodiment 6 of the present invention; Figure 17 This is the temperature cloud map at the compression moment in Embodiment 6 of the present invention; Figure 18 This is the pressure cloud diagram at the compression moment in Embodiment 6 of the present invention; Figure 19 This is the velocity cloud diagram at the compression moment in Embodiment 6 of the present invention; Figure 20 This is the temperature cloud map of the advance air intake time in Embodiment 6 of the present invention; Figure 21 This is the pressure cloud diagram at the advance air intake moment in Embodiment 6 of the present invention; Figure 22 This is the velocity cloud map of the advance air intake moment in Embodiment 6 of the present invention; Figure 23 This is the engine output shaft speed and torque diagram in Embodiment 6 of the present invention. Detailed Implementation
[0019] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.
[0020] Example 1 The performance prediction method for a compact steam piston engine proposed in this embodiment includes the following steps: Step 1: Construct a zero-dimensional thermodynamic analytical model of the engine and calculate the engine's indicated performance parameters using the model; Step 2: Establish a three-dimensional fluid dynamics CFD model of the engine and calculate the detailed parameters of the in-cylinder flow field based on the model; Step 3: Construct a compact steam piston engine, test the engine, and obtain the actual engine indicated performance parameters; Step 4: Compare the actual engine indicated performance parameters with the engine indicated performance parameters, adjust the zero-dimensional thermodynamic analytical model, and calculate the optimized indicated performance parameters; Step 5: Predict the performance of a compact steam piston engine based on optimized indicated performance parameters and detailed parameters of the in-cylinder flow field.
[0021] Example 2 The performance prediction method for a compact steam piston engine proposed in this embodiment includes the following steps: Step 1: Construct a zero-dimensional thermodynamic analytical model of the engine and calculate the engine's indicated performance parameters using the model; Specifically: Step 1.1: Divide the actual working cycle of a single cylinder of the engine into the intake process, expansion process, early exhaust process, exhaust process, compression process, and early intake process; Step 1.2: Based on engine operating parameters, thermodynamic laws, engine valve timing, and piston kinematics, the working cycle is discretized. Within each discrete time step, the piston equations are solved simultaneously, and the key parameters in the cylinder at the times of the intake process, expansion process, early exhaust process, exhaust process, compression process, and early intake process are calculated iteratively. Engine operating parameters include clearance volume ratio Intake ratio Expansion ratio Pre-exhaust ratio Exhaust ratio Pressure ratio Pre-intake ratio Combustion chamber temperature Combustion chamber pressure and back pressure ; Step 1.3: Based on the key point parameters calculated in Step 1.2, integrate them on the pressure-volume indicator diagram to calculate the single-cylinder indicated work. Step 1.4: Calculate the theoretical indicated power of the engine based on the single-cylinder indicated power, engine speed, and number of cylinders; Step 2: Establish a three-dimensional fluid dynamics CFD model of the engine and calculate the detailed parameters of the in-cylinder flow field based on the model; Step 3: Construct a compact steam piston engine, test the engine, and obtain the actual engine indicated performance parameters; Step 4: Compare the actual engine indicated performance parameters with the engine indicated performance parameters, adjust the zero-dimensional thermodynamic analytical model, and calculate the optimized indicated performance parameters; Step 5: Predict the performance of a compact steam piston engine based on optimized indicated performance parameters and detailed parameters of the in-cylinder flow field.
[0022] Example 3 The performance prediction method for a compact steam piston engine proposed in this embodiment includes the following steps: Step 1: Construct a zero-dimensional thermodynamic analytical model of the engine and calculate the engine's indicated performance parameters using the model; Specifically: Step 1.1: Divide the actual working cycle of a single cylinder of the engine into the intake process, expansion process, early exhaust process, exhaust process, compression process, and early intake process; Step 1.2: Based on engine operating parameters, thermodynamic laws, engine valve timing, and piston kinematics, the working cycle is discretized. Within each discrete time step, the piston equations are solved simultaneously, and the key parameters in the cylinder at the times of the intake process, expansion process, early exhaust process, exhaust process, compression process, and early intake process are calculated iteratively. Engine operating parameters include clearance volume ratio Intake ratio Expansion ratio Pre-exhaust ratio Exhaust ratio Pressure ratio Pre-intake ratio Combustion chamber temperature Combustion chamber pressure and back pressure ; Specifically: Step 1.2.1: Calculate the pressure at key points during the intake process according to equation (1); (1); in, P c This refers to the combustion chamber pressure. Calculate the valve timing angle during the intake process according to equation (2); (2); in, For intake ratio, This represents the number of peaks and troughs in the piston system. Calculate the pressure at the key points of the expansion process according to equation (3); (3); in, The pressure drop coefficient; Calculate the gas distribution angle during the expansion process according to equation (4); (4); Calculate the pressure at the key point of the pre-venting process according to equation (5); (5); in, The clearance volume ratio, For pre-exhaust ratio, The adiabatic index of the working fluid. Calculate the valve timing angle for the pre-exhaust process according to equation (6); (6); Calculate the pressure at key points during the exhaust process according to equation (7); (7); in, For back pressure, Calculate the valve timing angle during the exhaust process according to equation (8); (8); Calculate the pressure at the critical point during the compression process according to equation (9); (9); Calculate the valve timing angle during the compression process according to equation (10); (10); Calculate the pressure at the key point of the pre-intake process according to equation (11); (11); Calculate the valve timing angle for the advance intake process according to equation (12); (12); Step 1.2.2: Calculate the piston position according to equation (13); (13); Where S is the piston stroke. Piston peak number For rotational speed, For time; Step 1.2.3: Calculate the volume according to formula (14); (14); Step 1.3: Based on the key point parameters calculated in Step 1.2, integrate them on the pressure-volume indicator diagram to calculate the single-cylinder indicated work. The indicated power of a single cylinder is calculated as follows: Calculate the indicated work of a single cylinder according to equations (15), (16) and (17); (15); (16); (17); in, As an efficiency factor, it is generally taken as 0.9; f The fullness factor is generally taken as 0.98; This refers to the effective volume of the piston. Step 1.4: Calculate the theoretical indicated power of the engine based on the single-cylinder indicated power, engine speed, and number of cylinders; The theoretical indicated power is calculated as follows: Calculate the theoretical indicated power according to equation (18); (18); In the formula, For the number of pistons, Rotational speed; Step 2: Establish a three-dimensional fluid dynamics CFD model of the engine and calculate the detailed parameters of the in-cylinder flow field based on the model; Step 3: Construct a compact steam piston engine, test the engine, and obtain the actual engine indicated performance parameters; Step 4: Compare the actual engine indicated performance parameters with the engine indicated performance parameters, adjust the zero-dimensional thermodynamic analytical model, and calculate the optimized indicated performance parameters; Step 5: Predict the performance of a compact steam piston engine based on optimized indicated performance parameters and detailed parameters of the in-cylinder flow field.
[0023] Example 4 The performance prediction method for a compact steam piston engine proposed in this embodiment includes the following steps: Based on Example 3; Step 2 is as follows: Step 2.1: Based on the engine size parameters, establish a fluid computational domain model that includes the valve train, cylinder, and piston motion domain. Engine size parameters include the number of pistons. z e Cam peak number i e Piston stroke S Piston diameter d Inlet diameter d jq Exhaust port diameter d pq Intake process θ 1. Expansion process θ 2. Pre-venting process θ 3. Exhaust process θ 4. Compression process θ 5 and pre-intake process θ 6; Step 2.2: Mesh the fluid computational domain model, set boundary parameters, and establish a simulation model; Boundary parameters include rotational speed, inlet temperature, inlet pressure, and outlet pressure; Step 2.3: Set up the multiphase flow model and turbulence model, set the wall as a non-slip adiabatic wall, and define the rotational motion of the gas distribution valve and the reciprocating motion of the piston. Use dynamic mesh technology for the piston motion area. The VOF model is selected for multiphase flow; the basic governing equations of the VOF model include the continuity equation, momentum equation, and energy conservation equation. The continuity equation is shown in equation (19); (19); In the formula, The rate of change of fluid mass per unit volume over time; The net outflow mass flow rate per unit volume; The momentum equation is shown in equation (20); (20); In the formula, The rate of change of fluid momentum per unit volume over time; The convective term for momentum represents the momentum transport caused by fluid flow. For pressure gradient force; It is a viscous force; It is a volume force; The energy conservation equation is shown in equation (21); (twenty one); In the formula, It is the volume derivative of the total energy; It is energy transport caused by heat conduction; It is energy transport caused by component diffusion; It is viscous dissipation work; It is an external heat source; The SST k-ω model was selected for the turbulence model; the SST k-ω model includes the turbulent kinetic energy k equation and the specific dissipation rate ω equation. The turbulent kinetic energy k equation is shown in equation (22); (twenty two); In the formula, This is an unsteady-state term; For convection terms; For turbulent kinetic energy generation; This is the turbulent kinetic energy dissipation term; For turbulent kinetic energy diffusion term; The specific dissipation rate ω is expressed as equation (23); (twenty three); In the formula, For transient terms; For convection terms; For generating items; It is a dissipation term; For molecular and turbulent diffusion terms; This is a cross-diffusion term; The specific laws governing the rotational motion of the valve and the reciprocating motion of the piston are as follows: Calculate the angular velocity of the valve according to equation (24); (twenty four); In the formula, Rotational speed; Calculate the piston reciprocating motion according to equation (25); (25); The dynamic meshing technique for the piston movement area is specifically as follows: based on the cam profile of the engine, the motion law and velocity of the piston top surface changing with time are defined; the motion law is loaded into the simulation software through a user-defined function to drive the piston wall boundary movement; dynamic mesh parameters are set so that when the piston movement causes the height change of the adjacent mesh layer to exceed a preset ratio, a new mesh layer is automatically generated or the original mesh layer is merged to maintain mesh quality. Step 2.4: Select the solver and perform transient calculations to obtain the spatiotemporal distribution data of the pressure field, temperature field, and velocity field of the working fluid in the cylinder, i.e., the detailed parameters of the in-cylinder flow field of the engine. Specifically: Step 2.4.1 Solver and Algorithm Settings: Select a pressure-based coupled solver and enable transient calculation mode; select the SIMPLEC algorithm for the pressure-velocity coupled algorithm; use the least squares element method for gradient discretization, use a second-order scheme for pressure term discretization, and use a second-order upwind discretization scheme for the convection terms of the momentum equation, energy equation, and turbulence equation. Step 2.4.2, Time Step and Iteration Settings: Based on engine speed The time for a single work cycle is determined according to formula (26); (26); in For the number of cam peaks; Will Discretized a fixed time step Calculate according to formula (27) ; (27); To ensure that the increment of each crankshaft angle or cam angle is no greater than 0.05 degrees; At each physical time step Within the framework, 20 internal iterations are set, and the critical residuals are monitored to decrease to below 10^{-4} to ensure single-step convergence; Step 2.4.3, Flow field initialization and monitoring: Initialize the entire computational domain to static outlet pressure and ambient temperature; set pressure, temperature and velocity monitoring points in the cylinder, intake and exhaust ports and key areas of the valve; Step 2.4.4, Transient Calculation Execution: Start the solver and iteratively calculate each time step in sequence; Within each time step, the solver sequentially solves the continuity equation, momentum equation, energy equation, and turbulence model equation, and updates the dynamic mesh. When at least three complete working cycles have been completed, and the overlap of the cylinder pressure indicator diagrams for the last two cycles is higher than 99%, the transient calculation is considered to have reached periodic stability. Step 2.4.5: Data Extraction: Extract flow field data for all time steps from the last complete working cycle that has reached periodic stability; Detailed parameters of the in-cylinder flow field include: in-cylinder velocity distribution cloud map, in-cylinder pressure distribution cloud map, and in-cylinder temperature distribution cloud map.
[0024] Example 5 The performance prediction method for a compact steam piston engine proposed in this embodiment includes the following steps: Based on Example 4; The specific test in step 3 is as follows: Under the given steam inlet temperature, inlet pressure and back pressure conditions, run the physical prototype and simultaneously measure the speed and torque of the engine output shaft; The actual engine indicated performance parameters are calculated from the measured speed and torque according to formula (28); (28); in, For rotational speed, For torque; In step 4, the actual engine indicated performance parameters are compared with the engine indicated performance parameters. The adjustment of the zero-dimensional thermodynamic analytical model is specifically as follows: the indicated power calculated by the zero-dimensional model is compared with the actual output power measured in the experiment. By adjusting the efficiency factor, flow loss coefficient or heat loss coefficient in the zero-dimensional model, the error between the calculation results of the zero-dimensional model and the experimental data is less than the preset threshold. Step 5 specifically involves: Using the calibrated zero-dimensional model, the output power and efficiency of the engine under different steam parameters and speeds can be quickly calculated. Using a 3D model, we perform detailed simulations of key or abnormal operating conditions selected from the 0D model, analyze the uniformity of in-cylinder flow, vortex structure and local heat transfer, evaluate their impact on performance and provide a basis for structural optimization.
[0025] Example 6 The performance prediction method for a compact steam piston engine proposed in this embodiment includes the following steps: Step 1: Construct a zero-dimensional thermodynamic analytical model of the engine and calculate the engine's indicated performance parameters using the model; Specifically: Step 1.1: Divide the actual working cycle of a single cylinder of the engine into the intake process, expansion process, early exhaust process, exhaust process, compression process, and early intake process; Step 1.2: Based on engine operating parameters, thermodynamic laws, engine valve timing, and piston kinematics, the working cycle is discretized. Within each discrete time step, the piston equations are solved simultaneously, and the key parameters in the cylinder at the times of the intake process, expansion process, early exhaust process, exhaust process, compression process, and early intake process are calculated iteratively. Engine operating parameters include clearance volume ratio The intake ratio is 0.09. The expansion ratio is 0.5295. The pre-exhaust ratio is 0.4267. The exhaust ratio is 0.0438. The pressure ratio is 0.9657. The pre-intake ratio is 0.0156. The combustion chamber temperature is 0.0187. For 855K, combustion chamber pressure 5.6MPa and back pressure It is 0.16 MPa; Specifically: Step 1.2.1: Calculate the pressure at key points during the intake process according to equation (1); (1); in, P c This refers to the combustion chamber pressure. Calculate the valve timing angle during the intake process according to equation (2); (2); in, For intake ratio, This represents the number of peaks and troughs in the piston system. Calculate the pressure at the key points of the expansion process according to equation (3); (3); in, The pressure drop coefficient; Calculate the gas distribution angle during the expansion process according to equation (4); (4); Calculate the pressure at the key point of the pre-venting process according to equation (5); (5); in, The clearance volume ratio, For pre-exhaust ratio, The adiabatic index of the working fluid. Calculate the valve timing angle for the pre-exhaust process according to equation (6); (6); Calculate the pressure at key points during the exhaust process according to equation (7); (7); in, For back pressure, Calculate the valve timing angle during the exhaust process according to equation (8); (8); Calculate the pressure at the critical point during the compression process according to equation (9); (9); Calculate the valve timing angle during the compression process according to equation (10); (10); Calculate the pressure at the key point of the pre-intake process according to equation (11); (11); Calculate the valve timing angle for the advance intake process according to equation (12); (12); Step 1.2.2: Calculate the piston position according to equation (13); (13); Where S is the piston stroke. Piston peak number For rotational speed, For time; Step 1.2.3: Calculate the volume according to formula (14); (14); Step 1.3: Based on the key point parameters calculated in Step 1.2, integrate them on the pressure-volume dynamometer diagram, as shown in the figure. Figure 1 As shown, the indicated power of a single cylinder is calculated. The indicated power of a single cylinder is calculated as follows: Calculate the indicated work of a single cylinder according to equations (15), (16) and (17); (15); (16); (17); in, As an efficiency factor, it is generally taken as 0.9; f The fullness factor is generally taken as 0.98; This refers to the effective volume of the piston. The calculated indicated power of a single cylinder is 0.00087 J; Step 1.4: Calculate the theoretical indicated power of the engine based on the single-cylinder indicated power, engine speed, and number of cylinders; The theoretical indicated power is calculated as follows: Calculate the theoretical indicated power according to equation (18); (18); In the formula, For the number of pistons, Rotational speed; The calculated theoretical indicated power is 17.08 kW; Step 2: Establish a three-dimensional fluid dynamics CFD model of the engine and calculate the detailed parameters of the in-cylinder flow field based on the model; Specifically: Step 2.1: Based on the engine size parameters, establish a fluid computational domain model that includes the valve train, cylinder, and piston motion domain. The fluid computational domain model is as follows: Figure 2 As shown; Engine size parameters include the number of pistons. z e 5. Number of cam peaks i e 2. Piston stroke S 22.8mm, piston diameter d It is 22.8mm in diameter. d jq 5mm, exhaust port diameter d pq 7mm, intake process θ 1 is 46.69°, expansion process θ 2 is 31.23°, pre-exhaust process θ 3 is 12.08°, during the exhaust process. θ 4 is 79.33°, compression process θ 5 represents 2.81° and the pre-intake process. θ 6 is 7.86°; Step 2.2: Mesh the fluid computational domain model, set boundary parameters, and establish the simulation model. The mesh generation diagram is shown below. Figure 3 As shown; The boundary parameters include a rotational speed of 2180 rpm, an inlet temperature of 850 K, an inlet pressure of 5.5 MPa, and an outlet pressure of 0.16 MPa. Step 2.3: Set up the multiphase flow model and turbulence model, set the wall as a non-slip adiabatic wall, and define the rotational motion of the valve and the reciprocating motion of the piston. Use dynamic mesh technology for the piston motion region. The valve velocity and piston reciprocating motion are as follows: Figure 4 As shown; The VOF model is selected for multiphase flow; the basic governing equations of the VOF model include the continuity equation, momentum equation, and energy conservation equation. The continuity equation is shown in equation (19); (19); In the formula, The rate of change of fluid mass per unit volume over time; The net outflow mass flow rate per unit volume; The momentum equation is shown in equation (20); (20); In the formula, The rate of change of fluid momentum per unit volume over time; The convective term for momentum represents the momentum transport caused by fluid flow. For pressure gradient force; It is a viscous force; It is a volume force; The energy conservation equation is shown in equation (21); (twenty one); In the formula, It is the volume derivative of the total energy; It is energy transport caused by heat conduction; It is energy transport caused by component diffusion; It is viscous dissipation work; It is an external heat source; The SST k-ω model was selected for the turbulence model; the SST k-ω model includes the turbulent kinetic energy k equation and the specific dissipation rate ω equation. The turbulent kinetic energy k equation is shown in equation (22); (twenty two); In the formula, This is an unsteady-state term; For convection terms; For turbulent kinetic energy generation; This is the turbulent kinetic energy dissipation term; For turbulent kinetic energy diffusion term; The specific dissipation rate ω is expressed as equation (23); (twenty three); In the formula, For transient terms; For convection terms; For generating items; It is a dissipation term; For molecular and turbulent diffusion terms; This is a cross-diffusion term; The specific laws governing the rotational motion of the valve and the reciprocating motion of the piston are as follows: Calculate the angular velocity of the valve according to equation (24); (twenty four); In the formula, Rotational speed; Calculate the piston reciprocating motion according to equation (25); (25); The dynamic meshing technique for the piston movement area is specifically as follows: based on the cam profile of the engine, the motion law and velocity of the piston top surface changing with time are defined; the motion law is loaded into the simulation software through a user-defined function to drive the piston wall boundary movement; dynamic mesh parameters are set so that when the piston movement causes the height change of the adjacent mesh layer to exceed a preset ratio, a new mesh layer is automatically generated or the original mesh layer is merged to maintain mesh quality. Step 2.4: Select the solver and perform transient calculations to obtain the spatiotemporal distribution data of the pressure field, temperature field, and velocity field of the working fluid in the cylinder, i.e., the detailed parameters of the in-cylinder flow field of the engine. Specifically: Step 2.4.1 Solver and Algorithm Settings: Select a pressure-based coupled solver and enable transient calculation mode; select the SIMPLEC algorithm for the pressure-velocity coupled algorithm; use the least squares element method for gradient discretization, use a second-order scheme for pressure term discretization, and use a second-order upwind discretization scheme for the convection terms of the momentum equation, energy equation, and turbulence equation. Step 2.4.2, Time Step and Iteration Settings: Based on engine speed The time for a single work cycle is determined according to formula (26); (26); in For the number of cam peaks; Will Discretized a fixed time step Calculate according to formula (27) ; (27); To ensure that the increment of each crankshaft angle or cam angle is no greater than 0.05 degrees; At each physical time step Within the framework, 20 internal iterations are set, and the critical residuals are monitored to decrease to below 10^{-4} to ensure single-step convergence; Step 2.4.3, Flow field initialization and monitoring: Initialize the entire computational domain to static outlet pressure and ambient temperature; set pressure, temperature and velocity monitoring points in the cylinder, intake and exhaust ports and key areas of the valve; Step 2.4.4, Transient Calculation Execution: Start the solver and iteratively calculate each time step in sequence; Within each time step, the solver sequentially solves the continuity equation, momentum equation, energy equation, and turbulence model equation, and updates the dynamic mesh. When at least three complete working cycles have been completed, and the overlap of the cylinder pressure indicator diagrams for the last two cycles is higher than 99%, the transient calculation is considered to have reached periodic stability. Step 2.4.5: Data Extraction: Extract flow field data for all time steps from the last complete working cycle that has reached periodic stability; Detailed parameters of the in-cylinder flow field include: in-cylinder velocity distribution cloud map, in-cylinder pressure distribution cloud map, and in-cylinder temperature distribution cloud map; the temperature, pressure, and velocity cloud maps at the intake moment are shown below. Figure 5 , 6 As shown in Figures 7 and 8, the temperature, pressure, and velocity contour plots at the expansion moment are respectively as follows: Figure 8 , 9 As shown in Figures 1 and 10, the temperature, pressure, and velocity contour plots at the moment of early exhaust are respectively as follows: Figure 11 , 12 As shown in Figure 13, the temperature, pressure, and velocity contour plots at the time of exhaust are respectively as follows: Figure 14 , 15 As shown in Figure 16, the temperature, pressure, and velocity contour plots at the compression moment are as follows: Figure 17 , 18 As shown in Figure 19, the temperature, pressure, and velocity contour plots at the moment of advance air intake are respectively as follows: Figure 20 , 21 As shown in Figure 22; Step 3: Construct a compact steam piston engine, test the engine, and obtain the actual engine indicated performance parameters; The test specifically involved running the physical prototype under given steam inlet temperature, inlet pressure, and back pressure conditions, while simultaneously measuring the engine output shaft speed and torque. The engine output shaft speed and torque diagram is shown below. Figure 23 As shown; The actual engine indicated performance parameters are calculated from the measured speed and torque according to formula (28); (28); in, For rotational speed, For torque; Step 4: Compare the actual engine indicated performance parameters with the engine indicated performance parameters, adjust the zero-dimensional thermodynamic analytical model, and calculate the optimized indicated performance parameters; The actual engine indicated performance parameters were compared with the actual engine indicated performance parameters. The zero-dimensional thermodynamic analytical model was adjusted by comparing the indicated power calculated by the zero-dimensional model with the actual output power measured in the experiment. By adjusting the efficiency factor, flow loss coefficient or heat loss coefficient in the zero-dimensional model, the error between the calculation result of the zero-dimensional model and the experimental data was made less than a preset threshold. The efficiency factor was reduced by 5%, and the calculation result of the zero-dimensional model was 16.32 kW. After adjustment, the error between the calculation result of the zero-dimensional model and the experimental data was less than 3‰. Step 5: Predict the performance of a compact steam piston engine based on optimized indicated performance parameters and detailed parameters of the in-cylinder flow field. Specifically: Using the calibrated zero-dimensional model, the output power and efficiency of the engine under different steam parameters and speeds can be quickly calculated. Using a 3D model, we perform detailed simulations of key or abnormal operating conditions selected from the 0D model, analyze the uniformity of in-cylinder flow, vortex structure and local heat transfer, evaluate their impact on performance and provide a basis for structural optimization.
Claims
1. A performance prediction method for a compact steam piston engine, characterized in that, Includes the following steps: Step 1: Construct a zero-dimensional thermodynamic analytical model of the engine and calculate the engine's indicated performance parameters using the model; Step 2: Establish a three-dimensional fluid dynamics CFD model of the engine and calculate the detailed parameters of the in-cylinder flow field based on the model; Step 3: Construct a compact steam piston engine, test the engine, and obtain the actual engine indicated performance parameters; Step 4: Compare the actual engine indicated performance parameters with the engine indicated performance parameters, adjust the zero-dimensional thermodynamic analytical model, and calculate the optimized indicated performance parameters; Step 5: Predict the performance of a compact steam piston engine based on optimized indicated performance parameters and detailed parameters of the in-cylinder flow field.
2. The performance prediction method for a compact steam piston engine according to claim 1, characterized in that, Step 1 specifically involves: Step 1.1: Divide the actual working cycle of a single cylinder of the engine into the intake process, expansion process, early exhaust process, exhaust process, compression process, and early intake process; Step 1.2: Based on engine operating parameters, thermodynamic laws, engine valve timing, and piston kinematics, the working cycle is discretized. Within each discrete time step, the piston equations are solved simultaneously, and the key parameters in the cylinder at the times of the intake process, expansion process, early exhaust process, exhaust process, compression process, and early intake process are calculated iteratively. The engine operating parameters include clearance volume ratio. Intake ratio Expansion ratio Pre-exhaust ratio Exhaust ratio Pressure ratio Pre-intake ratio Combustion chamber temperature Combustion chamber pressure and back pressure ; Step 1.3: Based on the key point parameters calculated in Step 1.2, integrate them on the pressure-volume indicator diagram to calculate the single-cylinder indicated work. Step 1.4: Calculate the theoretical indicated power of the engine based on the single-cylinder indicated power, engine speed, and number of cylinders.
3. The performance prediction method for a compact steam piston engine according to claim 2, characterized in that, Step 1.2 specifically includes: Step 1.2.1: Calculate the pressure at key points during the intake process according to equation (1); （1）； in, P c This refers to the combustion chamber pressure. Calculate the valve timing angle during the intake process according to equation (2); （2）； in, For intake ratio, This represents the number of peaks and troughs in the piston system. Calculate the pressure at the key points of the expansion process according to equation (3); （3）； in, The pressure drop coefficient; Calculate the gas distribution angle during the expansion process according to equation (4); （4）； Calculate the pressure at the key point of the pre-venting process according to equation (5); （5）； in, The clearance volume ratio, For pre-exhaust ratio, The adiabatic index of the working fluid. Calculate the valve timing angle for the pre-exhaust process according to equation (6); （6）； Calculate the pressure at key points during the exhaust process according to equation (7); （7）； in, For back pressure, Calculate the valve timing angle during the exhaust process according to equation (8); （8）； Calculate the pressure at the critical point during the compression process according to equation (9); （9）； Calculate the valve timing angle during the compression process according to equation (10); （10）； Calculate the pressure at the key point of the pre-intake process according to equation (11); （11）； Calculate the valve timing angle for the advance intake process according to equation (12); （12）； Step 1.2.2: Calculate the piston position according to equation (13); （13）； Where S is the piston stroke. Piston peak number For rotational speed, For time; Step 1.2.3: Calculate the volume according to formula (14); （14）。 4. The performance prediction method for a compact steam piston engine according to claim 2, characterized in that, The single-cylinder indicated work calculated in step 1.3 is as follows: Calculate the indicated work of a single cylinder according to equations (15), (16) and (17); （15）； （16）； （17）； in, As an efficiency factor, it is generally taken as 0.9; f The fullness factor is generally taken as 0.98; This is the effective volume of the piston; The theoretical indicated power calculation mentioned in step 1.4 is as follows: Calculate the theoretical indicated power according to equation (18); （18）； In the formula, For the number of pistons, The value is the rotational speed.
5. The performance prediction method for a compact steam piston engine according to claim 2, characterized in that, Step 2 specifically involves: Step 2.1: Based on the engine size parameters, establish a fluid computational domain model that includes the valve train, cylinder, and piston motion domain. The engine size parameters include the number of pistons. z e Cam peak number i e Piston stroke S Piston diameter d , Inlet diameter d jq Exhaust port diameter d pq Intake process θ 1. Expansion process θ 2. Pre-venting process θ 3. Exhaust process θ 4. Compression process θ 5 and pre-intake process θ 6; Step 2.2: Mesh the fluid computational domain model, set boundary parameters, and establish a simulation model; The boundary parameters include rotational speed, inlet temperature, inlet pressure, and outlet pressure; Step 2.3: Set up the multiphase flow model and turbulence model, set the wall as a non-slip adiabatic wall, and define the rotational motion of the gas distribution valve and the reciprocating motion of the piston. Use dynamic mesh technology for the piston motion area. Step 2.4: Select the solver and perform transient calculations to obtain the spatiotemporal distribution data of the pressure field, temperature field, and velocity field of the working fluid in the cylinder, i.e., the detailed parameters of the in-cylinder flow field of the engine.
6. The performance prediction method for a compact steam piston engine according to claim 5, characterized in that, The multiphase flow model mentioned in step 2.3 is the VOF model; the basic governing equations of the VOF model include the continuity equation, the momentum equation, and the energy conservation equation. The continuity equation is shown in equation (19); （19）； In the formula, The rate of change of fluid mass per unit volume over time; The net outflow mass flow rate per unit volume; The momentum equation is shown in equation (20); （20）； In the formula, The rate of change of fluid momentum per unit volume over time; The convective term for momentum represents the momentum transport caused by fluid flow. For pressure gradient force; It is a viscous force; It is a volume force; The energy conservation equation is shown in equation (21); （21）； In the formula, It is the volume derivative of the total energy; It is energy transport caused by heat conduction; It is energy transport caused by component diffusion; It is viscous dissipation work; It is an external heat source; The turbulence model used in step 2.3 is the SST k-ω model; the SST k-ω model includes the turbulent kinetic energy k equation and the specific dissipation rate ω equation; The turbulent kinetic energy k equation is shown in equation (22); （22）； In the formula, This is an unsteady-state term; For convection terms; For turbulent kinetic energy generation; This is the turbulent kinetic energy dissipation term; For turbulent kinetic energy diffusion term; The specific dissipation rate ω is represented by equation (23); （23）； In the formula, For transient terms; For convection terms; For generating items; It is a dissipation term; For molecular and turbulent diffusion terms; This is a cross-diffusion term; The specific laws governing the rotational motion of the valve and the reciprocating motion of the piston are as follows: Calculate the angular velocity of the valve according to equation (24); （24）； In the formula, Rotational speed; Calculate the piston reciprocating motion according to equation (25); （25）； The application of dynamic mesh technology to the piston movement area in step 2.3 specifically involves: defining the motion law and velocity of the piston top surface over time based on the cam profile of the engine; loading the motion law into the simulation software through a user-defined function to drive the piston wall boundary movement; and setting dynamic mesh parameters so that when the piston movement causes the height change of the adjacent mesh layer to exceed a preset ratio, a new mesh layer is automatically generated or the original mesh layer is merged to maintain mesh quality.
7. The performance prediction method for a compact steam piston engine according to claim 5, characterized in that, Step 2.4 specifically involves: Step 2.4.1 Solver and Algorithm Settings: Select a pressure-based coupled solver and enable transient calculation mode; select the SIMPLEC algorithm for the pressure-velocity coupled algorithm; use the least squares element method for gradient discretization, use a second-order scheme for pressure term discretization, and use a second-order upwind discretization scheme for the convection terms of the momentum equation, energy equation, and turbulence equation. Step 2.4.2, Time Step and Iteration Settings: Based on engine speed The time for a single work cycle is determined according to formula (26); （26）； in For the number of cam peaks; Will Discretized a fixed time step Calculate according to formula (27) ; （27）； To ensure that the increment of each crankshaft angle or cam angle is no greater than 0.05 degrees; At each physical time step Within the framework, 20 internal iterations are set, and the critical residuals are monitored to decrease to below 10^{-4} to ensure single-step convergence; Step 2.4.3, Flow field initialization and monitoring: Initialize the entire computational domain to static outlet pressure and ambient temperature; set pressure, temperature and velocity monitoring points in the cylinder, intake and exhaust ports and key areas of the valve; Step 2.4.4, Transient Calculation Execution: Start the solver and iteratively calculate each time step in sequence; Within each time step, the solver sequentially solves the continuity equation, momentum equation, energy equation, and turbulence model equation, and updates the dynamic mesh. When at least three complete working cycles have been completed, and the overlap of the cylinder pressure indicator diagrams for the last two cycles is higher than 99%, the transient calculation is considered to have reached periodic stability. Step 2.4.5: Data Extraction: Extract flow field data for all time steps from the last complete working cycle that has reached periodic stability; The detailed parameters of the in-cylinder flow field include: in-cylinder velocity distribution cloud map, in-cylinder pressure distribution cloud map, and in-cylinder temperature distribution cloud map.
8. The performance prediction method for a compact steam piston engine according to claim 5, characterized in that, The test described in step 3 specifically involves running the physical prototype under given steam inlet temperature, inlet pressure, and back pressure conditions, and simultaneously measuring the speed and torque of the engine output shaft. The actual engine indicated performance parameters are calculated from the measured speed and torque according to formula (28); （28）； in, For rotational speed, For torque.
9. The performance prediction method for a compact steam piston engine according to claim 5, characterized in that, Step 4, which compares the actual engine indicated performance parameters with the engine indicated performance parameters and adjusts the zero-dimensional thermodynamic analytical model, specifically involves comparing the indicated power calculated by the zero-dimensional model with the actual output power measured in the experiment. By adjusting the efficiency factor, flow loss coefficient, or heat loss coefficient in the zero-dimensional model, the error between the calculation results of the zero-dimensional model and the experimental data is made less than a preset threshold.
10. The performance prediction method for a compact steam piston engine according to claim 5, characterized in that, Step 5 specifically involves: Using the calibrated zero-dimensional model, the output power and efficiency of the engine under different steam parameters and speeds can be quickly calculated. Using a 3D model, we perform detailed simulations of key or abnormal operating conditions selected from the 0D model, analyze the uniformity of in-cylinder flow, vortex structure and local heat transfer, evaluate their impact on performance and provide a basis for structural optimization.